Introduction

The photogrammetry has been derived from three Greek words: o Photos: means light o Gramma: means something drawn or written o Metron: means to measure

This definition, over the years, has been enhanced to include interpretation as well as measurement with photographs.

Definition The art, science, and technology of obtaining reliable information about physical objects and the environment through process of recording, measuring, and interpreting photographic images and patterns of recorded radiant electromagnetic energy and phenomenon (American Society of Photogrammetry, Slama).

Originally photogrammetry was considered as the science of analysing only photographs.

But now it also includes analysis of other records as well, such as radiated acoustical energy patterns and magnetic phenomenon.

Definition of photogrammetry includes two areas:

(1) Metric:

It involves making precise measurements from photos and other information source to determine, in general, relative location of points. Most common application: preparation of plannimetric and topographic maps.

(2) Interpretative:

It involves recognition and identification of objects and judging their significance through careful and systematic analysis. It includes photographic interpretation which is the study of photographic images. It also includes interpretation of images acquired in Remote Sensing using photographic images, MSS, Infrared, TIR, SLAR etc. Definitions

Aerial Photogrammetry Photographs of terrain in an area are taken by a precision photogrammetric camera mounted in an aircraft flying over an area. Terrestrial Photogrammetry Photographs of terrain in an area are taken from fixed and usually known position or near the ground and with the camera axis horizontal or nearly so. Photo-interpretation Aerial/terrestrial photographs are used to evaluate, analyse, and classify and interpret images of objects which can be seen on the photograph

Applications of photogrammetry

Photogrammetry has been used in several areas. The following description give an overview of various applications areas of photogrammetry (Rampal, 1982) (1) Geology:

Structural geology, investigation of water resources, analysis of thermal patterns on earth's surface, geomorphological studies including investigations of shore features.

engineering geology

stratigraphics studies

general geologic applications

study of luminescence phenomenon

recording and analysis of catastrophic events

earthquakes, floods, and eruption.

(2) Forestry:

Timber inventories, cover maps, acreage studies (3) Agriculture

Soil type, soil conservation, crop planting, crop disease, crop-acreage. (4) Design and construction

Data needed for site and route studies specifically for alternate schemes for photogrammetry. Used in design and construction of dams, bridges, transmission lines. (5) Planning of cities and highways

New highway locations, detailed design of construction contracts, planning of civic improvements. (6) Cadastre

Cadastral problems such as determination of land lines for assessment of taxes. Large scale cadastral maps are prepared for reapportionment of land. (7) Environmental Studies

Land-use studies. (8) Exploration

To identify and zero down to areas for various exploratory jobs such as oil or mineral exploration. (9) Military intelligence

Reconnaissance for deployment of forces, planning manoeuvres, assessing effects of operation, initiating problems related to topography, terrain conditions or works. (10) Medicine and surgery

Stereoscopic measurements on human body, X-ray photogrammetry in location of foreign material in body and location and examinations of fractures and grooves, biostereometrics. (11) Miscellaneous

Crime detection, traffic studies, oceanography, meteorological observation, Architectural and archaeological surveys, contouring beef cattle for animal husbandry etc.

Categories of photogrammetry

Photogrammetry is divided into different categories according to the types of photographs or sensing system used or the manner of their use as given below:

(1) On the basis of orientation of camera axis: (i) Terrestrial or ground photogrammetry When the photographs are obtained from the ground station with camera axis horizontal or nearly horizontal (ii) Aerial photogrammetry

If the photographs are obtained from an airborne vehicle. The photographs are called vertical if the camera axis is truly vertical or if the tilt of the camera axis is less than 3

o. If tilt is more than (often given intentionally), the photographs are

called oblique photographs. (2) On the basis of sensor system used: Following names are popularly used to indicate type of sensor system used in recording imagery.

Radargrammetry: Radar sensor

X-ray photogrammetry: X-ray sensor

Hologrammetry: Holographs

Cine photogrammetry: motion pictures

Infrared or colour photogrammetry: infrared or colour photographs

(3) On the basis of principle of recreating geometry When single photographs are used with the stereoscopic effect, if any, it is called monoscopicphotogrammetry. If two overlapping

photographs are used to generate three dimensional view to create relief model, it is called stereophotogrammetry. It is the most popular and widely used form of photogrammetry. (4) On the basis of procedure involved for reducing the data from photographs

Three types of photogrammetry are possible under this classification: (a) Instrumental or analogue photogrammetry It involves photogrammetric instruments to carry out tasks. (b) Semi-analytical or analytical Analytical photogrammetry solves problems by establishing mathematical relationship between coordinates on photographic image and real world objects. Semi-analytical approach is hybrid approach using instrumental as well analytical principles. (c) Digital Photogrammetry or softcopy photogrammetry It uses digital image processing principle and analytical photogrammetry tools to carry out photogrammetric operation on digital imagery. (5) On the basis of platforms on which the sensor is mounted: If the sensing system is spaceborne, it is called space photogrammetry, satellite photogrammetry or extra-terrestrial photogrammetry. Out of various types of the photogrammetry, the most commonly used forms are stereophotogrammetry utilizing a pair of vertical aerial photographs (stereopair) or terrestrial photogrammetry using a terrestrial stereopair.

Classification of Photographs

The following paragraphs give details of classification of photographs used in different applications

(1) On the basis of the alignment of optical axis

(a) Vertical :

If optical axis of the camera is held in a vertical or nearly vertical position.

(b) Tilted :

An unintentional and unavoidable inclination of the optical axis from vertical produces a tilted photograph.

(c) Oblique : Photograph taken with the optical axis intentionally inclined to the vertical. Following are different types

of oblique photographs:

(i) High oblique: Oblique which contains the apparent horizon of the earth. (ii) Low oblique: Apparent horizon does not appear. (iii) Trimetrogon: Combination of a vertical and two oblique photographs in which the central photo is vertical and side ones are oblique. Mainly used for reconnaissance. (iv) Convergent: A pair of low obliques taken in sequence along a flight line in such a manner that both the

photographs cover essentially the same area with their axes tilted at a fixed inclination from the vertical in opposite

directions in the direction of flight line so that the forward exposure of the first station forms a stereo-pair with the

backward exposure of the next station.

Comparison of photographs

Type of photo Vertical Low oblique High oblique

Characteristics Tilt < 3o Horizon does not appear Horizon appears

Coverage Least Less Greatest

Area Rectangular Trapezoidal Trapezoidal

Scale Uniform if flat Decreases from foreground to background

Decreases from foreground to background

Difference with map Least Less Greatest

Advantage Easiest to map - Economical and illustrative

(2). On the basis of the scale

(a) Small scale - 1 : 30000 to 1 : 250000, used for rigorous mapping of undeveloped terrain and reconnaissance of vast areas. (b) Medium scale - 1 : 5000 to 1 : 30000, used for reconnaissance, preliminary survey and intelligence purpose. (c) Large scale - 1 : 1000 to 1 : 5000, used for engineering survey, exploring mines. (3). On the basis of angle of coverage

The angle of coverage is defined as the angle, the diagonal of the negative format subtends at the real node of the lens of the apex angle of the cone of rays passing through the front nodal point of the lens.

Name Coverage angle Format size (cm)

Focal length (cm)

Standard or normal angle 60o (i) 18

(ii) 23 (i) 21 (ii) 30

Wide angle 90o (i) 18

(ii) 23 (i) 11.5 (ii) 15

Super wide or ultra wide angle 120o (i) 18

(ii) 23 (i) 7

(ii) 8.8

Narrow angle < 60o

Information recorded on photographs

The following information is recorded on a typical aerial photograph 1. Fiducial marks for determination of principal points. 2. Altimeter recording to find flying height at the moment of exposure. 3. Watch recording giving the time of exposure. 4. Level bubble recording indicating tilt of camera axis. 5. Principal distance for determining the scale of photograph. 6. Number of photograph, the strip and specification no. for easy handling and indexing. 7. Number of camera to obtain camera calibration report. 8. Date of photograph

Figure 1: Typical aerial photograph

Types of projections

1. Parallel : The projecting rays are parallel. 2. Orthogonal : Projecting rays are perpendicular to plane of projection. This is a special case of parallel projection. Maps

are orthogonal projection. The advantage of this projection is that the distances, angles, and areas in plane are independent of elevation differences of objects.

3. Central : Central projection is the starting point for all photogrammetry. In this projection rays pass through a point called the projection center or perspective center. The image projected by a lens system is treated as central projection although in strictest senses it is not so.

Figure 2: Various types of projections

Introductory definitions for photographs Vertical photograph

A photograph taken with the optical axis coinciding with direction of gravity. Tilted or near vertical

Photograph taken with optical axis unintentionally tilted from vertical by a small amount (usually < 3) Focal length (f)

Distance from front nodal point to the plane of the photograph (from near nodal point to image plane). Exposure station (point L)

Position of frontal nodal point at the instant of exposure (L) Flying height (H)

Elevation of exposure station above sea level or above selected datum.

Click on the figure for a larger view

Figure 3: Aerial photographs showing various elements as defined (a) Elements of vertical photograph (b) Section of imaging geometry showing various elements

X-axis of photo

Line on photo between opposite collimation marks, which most nearly parallels the flight direction. Y-axis

Line normal to x-axis and join opposite collimation marks. Principal point (o)

The point where the perpendicular dropped from the front nodal point strikes the photograph or the point in which camera axis pierces the image plane. Camera axis

It is a ray of light incident at front nodal point in the object space and at right angles to the image plane. Fiducial marks or collimation marks Index marks usually four in number, rigidly connected with the camera lens through the camera body and forming images on the photographs to which the position on the photograph can be referred. Photographs center

The geometrical center of the photograph as defined by the intersection of the lines joining the fiducial marks. Format

It is the planar dimension of photograph (9" x 9", 7" x 7", 23 cm x 23 cm, 18 cm x 18 cm, 15 cm x 15 cm). Photogram

Photograph taken with a photogrammetric camera having fixed distance between negative plane and lens and equipped with fiducial or collimating marks. For photograms the bundle of rays on the object side at the moment of exposure can be reproduced. To achieve this the following data known as the elements of interior orientation must be known:

Calibrated focal length

Lens distortion data

Location of the principal point with reference to the photograph center (normally these two coincide)

Hence, a photogram is a photograph with known interior orientation Difference between near vertical photographs and map

1. Production : Quickest possible and most economical method of obtaining information about areas of interest. Boon for difficult areas. Enlarging and reducing easier in case of photographs than maps.

2. Content : Map gives an abstract representation of surface with a selection from nearly infinite number of features on ground. Photograph shows images of surface itself. Maps often represent non-visible phenomenon (like text) This may make interpretation difficult for photograph. Special films like color and infrared films can bring about special features of terrain.

3. Metric accuracy: Map is geometrically correct representation, photos are generally not. Maps are orthogonal projections, photo is central projection. Map has same scale throughout photo has variable scale. Bearing on photographs may not be true.

4. Training requirement: A little training and familiarity with the particular legend used in the map enables proper use of map. Photo-interpretation requires special training although initially it may appear quite simple as it gives a faithful representation of ground.

Perspective geometry of vertical photographs

The figure shows camera axis SP of a camera, perpendicular to the photographic plane ABCD, tilted at angle from the vertical at exposure so that the plane of the photograph itself is inclined by an angle to the horizontal plane CDEF, representing a level ground. S represents perspective center as defined by the inner or rear node of the lens system.

Figure 1: Perspective geometry of aerial photo

One can identify pair of points v and V (ground and photo nadir point), i and I (ground and photo isocentre), p and P (ground and photo principal point) on photographic plane and ground plane respectively. These point pairs are called homologous pair. In fact any corresponding point pair on photo and ground plane is a homologue pair.

Perspective Axis

Line CD where the two plane meet is called the perspective axis or horizontal trace.

Principal lines

A line UP drawn perpendicular to the perspective axis along the photograph plane. This projects as Up on ground plane (CDEF) and is also perpendicular to perspective axis. These lines are called the photo and ground principal lines respectively.

Principal plane

A plane containing P, V, and S is called the principal plane. Photo principal line (VP) and ground principal lines (vp) are contained in this plane.

Plate parallels or plate horizontals

Horizontal lines drawn in the photo plane are called plate parallels or plate horizontals. Line iI is the bisector of tilt angle . It meets photo plane at i and ground plane at I. These points are known as photo isocentre and ground isocentre respectively.

For a truly vertical photograph taken from exposure station S, various photo plate parallels are lines I'I", P'P", etc. The plate parallel through I is also called isometric plate parallel.

Scale of a vertical photograph

Due to perspective geometry of photographs, the scale of photograph varies as a function of focal length, flying height, and the reduced level of terrain over a certain reference datum. In figure 2, for a vertical photograph, L is exposure station, f is its focal length, H is the flying height above datum, h represents the height of ground point A above datum. Point A is imaged as a in the photograph. From the construction and using similar triangles Loa and LOAA, we can write the following relations (Wolf and Dewitt, 2000)

Figure 2: Scale for vertical photo

havg = Average terrain elevation Savg =Best single scale to use for a photo or group of photographs

Determination of Scale of photograph

Scale of photograph can be determined by various methods such as 1. By using known full length and altimeter reading, the datum scale can be found. 2. Any scale can be determined if havg known. havg can be obtained from a topographic map. 3. By comparing length of the line on the photo with the corresponding ground length. To arrive at fairly representative

scale for entire photo, get several lines in different area and the average of various scales can be adopted. 4. Use the formula

Scale along plate parallels Referring to figure 1, the scale along various plate parallels are as follows:

1. Scale through the plate parallels passing through principal point, P with q as tilt angle

2. Scale along an isometric parallel through nadir point, V

3. Scale along an isometric parallel through isocentre I

This shows that the scale along plate parallel through isocentre of a tilted photo is same as that over the whole surface of a vertical photo if ground surface is plane. For any other plate parallel, scale will depend on the tilt angle. Also, the scale along any plate parallel is constant

Ground co-ordinates for vertical photographs In figure 3, X and Y are ground co-ordinates with respect to a set of axes whose directions are parallel with the photographic axes and whose origin is directly below the exposure station, x and y indicate x and y photo coordinates with respect to the photo coordinate system with origin at o axes as shown. Using similar triangles, we can write the following relations:

Click on the image for larger view

Figure 3: Ground coordinates from vertical photographs

Flying height for vertical photographs

The flying height can be calculated by two approaches

Direct

Indirect

Direct Method

In this method, if the ground coordinates of two points, A and B are given (XA, YA ) and (XB, YB ), then a quadratic equation can be formed to derive the flying height as given below:

Indirect Method

In this method, one can find the flying height by an iterative approach. For this one can use equations (1) and (2) where hAB = average elevation of points A, B, H app is approximate height and AB = known ground distance Get H app by equation

1. Using Eq. (1), get Happ. 2. Using Happ, get XA, X B, YA, YB using formulae for measurement of coordinates. 3. Get computed AB using XA, XB, YA, YB. 4. Again use Eq. (2) to get new H value. 5. If the required precision been obtained (i.e. old Happ and new H values have converged and do not differ by more than a

threshold value), then stop else go to (b) and repeat.

Relief displacement on Vertical photographs

In figure, L is the perspective center of the camera system. A is the point on ground at an elevation of h with respect to the datum. a is the image of ground point on photograph. a' is the location of projected point A' on the datum. These figures indicate that although point A is vertically above point B, their images are not coinciding and are displaced on photographic plane due to relief.

Figure 4: (a) Relief displacement on vertical photo (b) Radial nature of relief displacement (Moffit, 1959)

The displacement of the point a on the photograph from its true position, due to height, is called the height or relief displacement or relief distortion (RD). This distortion is due to the perspective geometry.

It can also be noticed form these figures that the relief displacement is radial from nadir point. In case of vertical photographs, the nadir point and the principal point coincide. Hence, in this case relief displacement can be considered to be radial from the principal point also. The following derivation using figure 4(a) provides the magnitude of relief distortion

Differentiating d with respect to H gives From these equations, the following observations can be made:

1. For a given elevation, RD of a point increases as the distance from principal point increases. 2. Other things being equal, an increase in H decreases RD of a point. (This point is important for mosaicing or combining

photographs along common features). For the same reason, for satellite imagery, RD is very small since H is large. 3. If ground point is above datum then RD will be outward or positive; if point below datum then h has negative sign and

RD will be inward or negative. 4. RD is radial from nadir point regardless of unintentional or accidental tilt of the camera. This is a fundamental concept of

photography. It has important implication for photo rectification (this concept will not be discussed in this course). 5. Large relief displacement is objectionable in pure plannimetric mapping by graphical methods but advantageous in

contouring with stereoplotting instruments. Most effective way to control RD is to select proper flying height.

Numerical problems 1. The distance on a map between two road intersections in flat terrain measures 12.78 cm. The distance between the

same two points is 9.25 cm on vertical photograph. If the scale of the map is 1: 24,000, what is the scale of the photograph?

2. Fifteen photographs were taken in a strip each covering an area equal to 25.75 sq. km. If the longitudinal overlap is 60%, find the total ground area covered by the strip.

3. A aircraft takes photographs at a scale of 1:10,000. Photo size is 23x23 cm. Overlaps are: longitudinal 65% and lateral 30%. The photography consists of 5 strips of 21 photographs each. Calculate: (a) Ground area covered by a single photograph. (b) Ground area covered by the first strip. (c) Ground area covered by the whole photography.

4. A vertical photograph was taken with H above datum = 2400 m and f = 210 mm. The highest, lowest, and average elevation of terrain appearing in the photograph is 1330, 617, and 960 m respectively. Calculate minimum, maximum, and average photographic scale.

5. An aircraft flying at an altitude of 4600 m above MSL photographs 5 strips of 20 photographs each of a terrain having havg = 300 m above MSL. If f = 205.53 mm, find the scale of photograph and area covered by each photograph of size 23 x 23 cm. Assuming 60% forward and 20% sidelap, find total area covered by the photography.

6. Points A and B are at elevations 273 m and 328 m above datum, respectively. The photographic coordinates of their images on a vertical photograph are: xa = -68.27 mm xb = -87.44 mm

ya = -32.37 mm yb = 26.81 mm What is the horizontal length of the line AB if the photo was taken from 3200 meters above datum with a 21 cm focal length camera?

7. An image of a hilltop is 87.5 mm from the centre of a photograph. The elevation of the hill is 665 meters and the flight altitude 4660 meters from the same datum. How much is the image displaced due to elevation of the hill?

Answers:

1.

2.

3.

4.

5.

6.

7.

Scale of a tilted photograph

Click on image for larger view

Figure 1 Tilt-swing-azimuth relationship in tilted photo (Moffit, 1959)

The figure shows a tilted photograph. In this figure, rotate y -axis till the new y -axis or the y '-axis coincides with the principal line having a positive direction no as shown (Moffit). = Amount of rotation = 180 - s s = swing angle

In the same figure, P is the point lying at an elevation hp above datum, p is its image on tilted photo, x, y ; photo-coordinates, x and y are measured with respect to axes defined by collimation marks. O - principal point, n - nadir point, s - swing angle.

Since is clockwise it must be negative. Co-ordinates in rotated system can be given below. Translating x' axis from oto w, the co-ordinates of p after translation

Construct line wk perpendicular to line Ln. This is a horizontal line (because Ln is a vertical line). Since wp is perpendicular to the principal line, it is also a horizontal line. Therefore, plane kwp is a horizontal plane.

Also, PP' = WW' = NN' = hp(from construction) and therefore, plane nwp is also horizontal. In s Lkp and LNP

But Lk = Ln - kn. = f sec t - y' sin t. Therefore,

But kp/NP = scale for a point lying in a plane kwp. Since p lies on this plane

Where St scale of a tilted photograph at a point whose elevation is h. f focal length. t tilt angle H flying height above datum. y' y -co-ordinate of the point with respect to a set of axes whose origin is at the nadir point and whose y' axis

coincides with the principal line.

Ground co-ordinates on tilted photograph

Referring to figure 1, the coordinates can be derived by assuming the following situation:

1. Y-co-ordinate axis lies in the principal plane. 2. X-co-ordinate axis passes through ground nadir point.

Therefore, ground nadir point is the origin of co-ordinates wp = x', WP = X Therefore, scale relationship between plane kwp and KWP is given by

X, Y Ground co-ordinates x', y' Co-ordinate of point with respect to axes whose origin is at the nadir point and whose y' axis coincides with the principal line t tilt Flying height for tilted photo

The flying height can be derived in a similar as that for the vertical photograph explained earlier. The procedure is given below:

1. Get photo-coordinates of the end points of control line with respect to axes defined by the collimation marks. 2. Photographic length of line is scaled directly. 3. Use ratio of photographic length to known ground length to get first approximation as

where, f - focal length h AB - Avg. elevation of A and B

AB - ground length. ab - scaled photo length. By using Happ, together with other scale data, one can solve the following equations

4. Calculate distance based on first set of ground co-ordinates. 5. Compare this computed distance for better approximation of H. Where H is new value of flying height, AB is the value of length based on first approximation height

6. Repeat the procedure till computed value of length agrees with the known ground length within the desired precision

Relief displacement on a Tilted photo

Figure 2: Relief displacement on a tilted photo

Figure 2 shows the relief displacement on a tilted photograph. It should be noted that:

1. On a tilted photo relief displacement (a'a) are radial from nadir point (n). 2. The amount of relief displacement depends upon: (i) Flying height (ii) distance from nadir point to image (iii) elevation of

ground point (iv) position of point with respect to principal line and to the axis of the tilt. 3. Compared with an equivalent relief displacement on vertical photo, the RD on a tilted photo will be

o less on the half of the photograph upward from the axis of the tilt, o identical for points lying on the axis of the tilt and o greater on downward half of the photo.

4. Image displacement due to the tilt (explained later) tends to compensate relief displacement on the upward half and will be added to RD on the downward half.

5. Because tilts in near-vertical photos rarely > 3o, therefore the value of RD is given with sufficient accuracy with following

equation. However, the radial distance should be measured from the nadir point rather than from the principal point

Tilt displacement (TD) on a Tilted photo

Figure 3: Tilt displacement on a Tilted photo (Moffit, 1959) 1. Tilted and corresponding vertical photo taken from same flying height and with same focal length will match along the axis of

the tilt (passing from the isocentre) where they intersect. 2. In the figure, image points A, B, C, D appear as images a, b, c, d on tilted photo, and as a', b', c', d' on an equivalent vertical

photo. If we rotate equivalent vertical photograph (EVP) about axis of tilt, till it is in the plane of tilted photo then for any point other than lying on the tilt axis, it will be displaced either outward or inward with respect to equivalent position on a vertical photograph:

o If point lies on the half of photo upward from the axis of tilt, it will be displaced inwards. o If lies on downward half, then displaced outward.

Figure 4: Magnitude of TD (vertical section through principal line (Moffit, 1959)

The TD is a"a, b"b, c"c, d"d. These displacement occur along radial lines from isocentre.

Although a and c lie at the same distance from axis of tilt, but the displacement of a is greater than that of c. This ratio = secant of cia

Tilt displacement also depends upon the position of point with respect to both the axes of the tilt and the principal lineno.

For c lying in principal line, TD is given as c"c

is obtained by measuring the distance to the point from a line through the principal point and parallel with the axis of the tilt. When point lies on principal line, as does the point C, the distance is measured from principal point itself to the image point. This distance is then divided by focal length to obtain tan .

The following observations should also be noted for the tilt displacement:

1. Tilt displacement for a point not lying on the principal line is greater than that of a corresponding point on principal line. 2. Above ratio is equal to the secant of angle at isocentre from principal line to the point. Therefore, tilt displacement on upper

half of tilted photo is inward and is given as:

For a point lying in lower half or nadir point half is outward

I = angle measured at the isocentre from principal line to the point. t = tilt = angle in the principal plane formed at the exposure station. Another expression for tilt displacement For a point b on upper half of photo and using similar triangles Lqb and ibb'. q is intersection of horizontal line through L meeting extension of tilted line ab (Wolf and Dewitt, 2000)

Figure 5 Tilt displacement with respect to an equivalent vertical photograph ( Wolf and Dewitt, 2000 )

Using figure 5, the following derivation can be accomplished for TD given as d.

For any point a lying on lower side of photo

For any general point The above equation holds for any point lying on principal line. For any other point lying off the principal line, TD is d/cos where is angle between the line passing through off axis point and principal line at isocentre. For any off-principal line pointb, TD is given as

TD is maximum when = 0, i.e. point lies along principal line, minimum when point lies along isometric parallel.

The general equation can also be written as

Figure 6: General format for TD ( Wolf and Dewitt, 2000, ) angle in plane of photo, measured clockwise from positive end of principal line to the radial line from isocentre to imaged point d Tilt displacement. ri Radial distance from isocentre to imaged point. f Focal length. t Tilt angle Angle in plane of photo, measured clockwise from positive end of principal line to the radial line from isocentre to imaged point. 1. The algebraic sign of ri is always considered +ve. 2. The units of d will be same as those used for ri and f. 3. The correct algebraic sign of d is not obtained automatically but must be assigned. +ve : if point lies above the axis of tilt. -ve : if the point lies below the axis of tilt. For b between 0 - 90 and 270 - 360 , pt lies above axis of tilt.

Figure 7: Combined displacements of points due to relief and tilt

In figure 7, position of each point: o position marked as 1 is datum photograph position o position marked as 2 is the position after image has undergone relief displacement o position marked as 3 is the position after image has been displaced due to tilt.

For points a and b, the two displacements tend to cancel; for points c and d, these are cumulative; for point e lying on tilt axis, there is no tilt displacement. This complexity is further compounded by the fact that amounts and direction of tilts are random and difficult to be computed.

Stereoscopic vision

Method of judging depth may be classified as stereoscopic or monoscopic.

Persons with normal vision are said to have binocular vision. They can view with both eyes simultaneously. These persons are said to have stereoscopic viewing

The term monocular vision is applied to viewing with one eye only.

Depth perception

Monoscopic viewing provides only rough depth impression which is based on the following clues: o Relative size of objects o Hidden objects o Shadows o Differences in focussing of eye required for viewing objects at varying distances.

For stereoscopic depth perception usually two clues are involved o Double image phenomenon. o Relative convergence of optical axis of two eyes.

The human eye functions in a similar manner to a camera. The lens of the eye is biconvex in shape and is composed of refractive transparent medium. The separation between eyes is fixed (called eye base). Therefore, in order to satisfy the lens formula for varying object distance, the focal length of eye lens changes. For example, when a distant object is seen, the lens muscle relax, causing the spherical surface of the lens to become flatter. This increases the focal length to satisfy the lens formula and accommodate the long object distance. When close objects are viewed, a reverse phenomenon happens. The

eye's ability to focus varying object distance is called accommodation.

The figure shows two situations where eyes separated by eye base (b) are focussing on two objects A and B located at two distances dA and dB respectively.

In binocular vision, there is convergence of axes of eyes when focusing at point A and B. The corresponding angles are 1 and 2. Angle 1 tells the mind that object A is distance dA. Similarly for point B. These angle are calledparallactic angles for points. The nearer the object, the greater the parallactic angle and vice versa. Difference ( 1 - 2 ) tells the mind that the distance (depth) between two points is e = d B - d A.

For average separation of eye and distinct vision of about 10 inch, the limiting upper value of 16. Lower limiting value of ranges from 10 to 20 seconds and represents a distance of about 1700 to 1500 ft for average eye separation. It is called stereoscopic acuity of the person.

Figure 1: Binocular vision (Wolf and Dewitt, 2000)

To understand the stereoscopic vision by viewing photographs, let us replace the eyes by two cameras and take photographs as shown in figure 2 assuming that the photographic plates are between the objects and lenses. If these photographs could be placed in the same position and seen with both eyes, one would get the same depth. Since it is not possible to keep eyes at such a wide separation (called air base B), a scaled version is shown in figure (ii) where camera position are replaced by a scaled down geometrical arrangement (eyes separated by eye base-b e ), the two images are fused and the brain perceives the scaled down depth between objects.

Figure 2: Stereoscopic vision (i) object imaged with cameras (ii) scaled down version with eyes (Wolf and Dewitt, 2000)

Stereoscope

If two photographs taken from two exposure stations L1 and L2 are laid on table so that left photograph is seen by left eye and the right photo is seen with right eye, a 3D-model is obtained. However, viewing in this arrangement is quite difficult due to following reasons:

o Eye strain and focusing difficulty due to close range. o There is disparity in viewing. The eyes are focused at short range on photos lying on table where as the brain

perceives parallactic angles which tends to form the stereoscopic model at some depth below the table.

By using stereoscope, these problems can be alleviated. Different types of stereoscopes are available for different purposes - from pocket (inexpensive) for viewing small area to mirror (expensive) for viewing larger area.

Figure 3: Photograph showing mirror stereoscope (Wolf and Dewitt, 2000)

Figure 4: Principle of stereoscope (Wolf and Dewitt, 2000) (a) pocket (b) mirror

Conditions of good stereo viewing

1. The two images must be obtained from two different positions of the camera. 2. The left photo and right photo should be presented to the left and right eye in the same order. 3. Photographs of the object should be obtained from nearly the same distance, i.e. scales of the two adjacent photographs

should be nearly same. Normal eye can accommodate 5 to 15% variations in scale of photograph. 4. During stereovision, keep the area under vision in near vertical epipolar planes as far as possible. The plane containing

optical centers for eyes (S1 S2), object point A and corresponding images a and a' on left and right photographs respectively is called the epipolar plane. Thus camera axes should be approximately in one plane, though the eyes can accommodate the differences to a limited degree. The term epipolar planes is used if it refers to eyes; the term basal planes is used if it refers to cameras.

5. For a good stereovision, the pair of photos should be in the same orientation with each other as they were at the time of photography.

6. The brightness of both the photographs should be similar. 7. The ratio B/H should be appropriate. If this ratio is too small say smaller than 0.02, we can obtain the fusion of two pictures,

but the depth impression will not be stronger than if only one photograph was used. The ideal value of B/H is not known, but is probably not far from 0.25. In photogrammetry values up to 2.0 are used.

Geometry of overlapping vertical photos

Figure 5 shows two photographs taken from two exposure stations L 1 (left) and L2 (right). Ground point A appears in these two photos at a and a' in left and right photos. The image coordinates of these photo points a and a' are (xa, ya ) and (x'a, y'a ) respectively.

A pair of vertical photographs which have some common area imaged is known as a stereopair. This stereopair can be used for estimation of depth by measurement of parallax which will explained next.

Figure 5: Geometry of overlapping vertical photos

Figure 6: A stereopair

Parallax

It is the central concept to the geometry of overlapping photographs and is defined as the apparent shift in the position of a body with respect to a reference point caused by a shift in the point of observation

In photogrammetry, it refers to the relative difference in position of an image point that appears in each of the overlapping photo.

Absolute Parallax:

Absolute X parallax (P X ) is given by (x l - x r ),

where x l and x r are x coordinates on left and right photographs respectively P x = x l - x r

Other names: X-parallax, horizontal parallax, linear parallax, absolute stereo parallax, or just parallax For the following photograph pair, the parallax is given as follows. P x = x b - (-x b' ) It can be noted that the value of parallax has been used with sign

Figure 7: Parallax in photograph pair Parallax and its relation to height

From figure 5, the absolute parallax PA at point A is given as follows where B is air base.

Similarly for another point B, we can write

Height differences between two points ( dh BA = h B - h A ) is given by:

dP BA = P B - P A is the difference in absolute parallaxes between two points. Above equation can be modified to give

where dp BA = p B - p A is the difference in parallax bar readings between two points. Thus the above equation says that dPBA = dpBA under the assumption that flying height for both photographs is same (i.e. H1 = H2 = H) and photograph is truly vertical.

It may, however, be noted that for a given point, there may be parallax in both directions X and Y. The Y-parallax is caused due to the following reasons:

o Unequal flying height o Photographic tilt

o Misalignment of flight line o Misalignment of stereoscope o Great difference in parallax between adjacent images (in highly mountainous/rugged terrain)

Other forms of parallax equation If the principal point are assumed to have same elevation as known point A, then the parallax of principal point is the same as the

parallax of point A i.e. P A = b m, the mean principal base. Using this assumption

dp = absolute parallax of unknown point - absolute parallax of known point

If dp is small then

Some other forms of parallax equation are given in adjacent formats

Sources of errors in using parallax equation

Locating and marking the flight line on photo.

Orientation of stereopair for parallax measurement.

Parallax and photo co-ordinate measurements.

Shrinkage and expansion of photographs.

Unequal flying height.

Tilted photo.

Error in ground control.

Camera lens distortion, atmospheric refraction etc.

Measurement with Parallax bar and floating marks

From the parallax equation, we note that o parallax of any point is directly related to its elevation o parallax is greater for point which are higher in elevation

If we could measure the parallax of the point, its height could be measured easily. Unfortunately there is no device for this. However, difference in absolute parallaxes which can be related to height differences. Therefore, if the elevation of one point is known, the elevation of other point can be measured.

Parallax bar (figure 8) or stereometer is used to measure the difference in parallaxes between corresponding points on stereopair which have been oriented as they were at the time of photography.

Figure 8: Parallax bar (Wolf and Dewitt, 2000)

If the two photographs are placed in a properly oriented position (this process is known as base lining) on a table and viewed through stereoscope, the distances between corresponding (conjugate) points on left and right photos can be measured by parallax bar in terms of parallax bar reading. The difference between two measured distances will provide parallax differences between two points. The measurement by stereometer is called parallax bar reading.

While measuring the parallax, the stereometer uses the principle of floating mark.

Floating mark is used to carry out quantitative measurements on stereo photographs. It is made up of two identical half marks or dots which are placed over conjugate images on the two overlapping photographs

The dots may be black circular spots or crosses (etched on two clear glass plates), for example parallax bars used with stereoscopes or many stereoplotters. The dots may also be luminous circular spots, crosses or annuli which are used in stereoplotters, stereocomparators and particularly the digital image display.

The floating marks are placed on the photographs such that the right mark is on the right photo and the left mark is on the left photo.

Within a stereomodel, the floating mark will appear to lie on the surface of the terrain (fused form) when the dots are placed exactly on conjugate or corresponding images.

If the dots are moved slightly closer together, the floating mark will appear to rise or float off the surface.

If the mark floats too far above the surface then stereofusion will be broken because the eyes can not accommodate the range in convergence, and a double image of the terrain will result

If the dots are moved slightly apart the floating mark will split into two separate dots as the brain of the observer can not imagine seeing the floating mark beneath the surface

Again if the dots are moved too far apart a double image of the terrain will result.

Figure 9: Floating mark

Base lining

In order to get fused 3D images, the orientation relationship between the two photographs and stereoscopic lenses should be same as that between the photographed ground and the camera lenses at the time of photography. Base lining is the process to achieve such orientation. The step by step procedure to achieve base lining is as follows:

o Find out the photographic center of the first photograph by joining the opposite fiducial marks and getting the intersecting lines. Let it be A. Mark a corresponding point A' on the other photo of the stereopair.

o Find the photograph center of the second photo B and locate corresponding point B' on the first photograph of the stereopair.

o Join A, B' to get AB' and B and A' to get BA'. o Fix a white sheet (called the base sheet) on table and draw a straight line on this sheet in the middle. o Set up stereoscope on this sheet such that the line is midway between stereoscope legs. o Put the first photograph in such a way that the line AB' coincides with the line on the base sheet. o Now by trial and error, and viewing through the stereoscope, put the second photograph (right photograph) in

such a way that the image of point A coincides with A' and B coincides with B' i.e line AB' coincides with A'B. o This arrangement will give 3D view of stereopair. o Now with the help of stereometer, the floating mark of left plate is put over a well defined point on the left

photograph. Now by giving lateral and longitudinal motion to the other plate (with the help of stereometer drum), we try to bring the floating mark of other glass plate on the corresponding point of second photograph. When the images of left and right floating marks are fused, the reading on the parallax bar can be recorded as the parallax bar reading for that point.

Numerical examples 1. Two ground points A and B appear on a pair of overlapping photographs, which have been taken from a height of 3650

m above MSL. The base lines as measured on the two photographs are 89.5 and 90.5 mm respectively. The mean parallax bar reading from A and B are 29.32 mm and 30.82 mm respectively. If the elevation of A above MSL is 230.35 m, compute the elevation B.

2. In the above problem if the lengths of base lines are not known and the absolute parallax of A is measured to be 89.80 mm, compute the elevation of B. Also, find the height of another point C whose parallax bar reading is 32.32 mm.

Answers

1.

2.

Base lining

The flight planning is the process of making all relevant preparations and taking certain decisions for taking photographs to satisfy certain application requirements. This may include the following:

o deciding about flying height above datum o spacing between successive exposures o separation between flight lines

After careful decision about these elements, the flight lines are carefully laid on the map of the study area to be photographed. This map is called the flight map.

Computation of flight plan

The following information is required for effective flight planning (Tiwari and Badjatia, 1985; Sadasivam, 1988): o Camera focal length o Photographic scale o Flying height above datum o Permissible scale variation o Relief displacement o Tilt of photographs o Size of photograph o Area to be photographed or ground coverage o Air base o Base-height ratio

o Flight line spacing o Number of flight lines o Forward or longitudinal overlap o Side or lateral overlap o Ground speed of the aircraft o Number of photographs per flight line o Drift angle o Exposure interval, maximum exposure time

Focal length (f)

It is the most important parameter for flight planning and must be determined by proper calibration.

Photographic scale (S)

It is specified to ensure that the user can resolve the smallest objects to be identified. Choice of scale is a function of project at hand and the experience. This is a function of the focal length (f) and altitude of aircraft (H) at the exposure time. Scales vary from large to small. Very large scales are used for cadastral surveys and small scale for topographic mapping. The larger the scale, the better and more accurate the interpretation and plotting. But this will result in too many photographs and hence more time and money for covering the same area.

It is often more convenient to use an average scale corresponding to the average elevation in the study area o (Sa = f / ( H - ha ).

Flying height (H)

This is the height of the camera exposure station and recorded by altimeter (aneroid barometer) and sometimes with a statoscope. It is recorded on the picture itself for easy reference.

For a given focal length, average scale, and focal length, the flying height H is fixed. Several interrelated factors affect choice of flying height. For example, scale, relief displacement, and tilt.

Permissible scale variation

Scale variation is caused by combination of change in ground elevation or flying height. Scale variation affect ground coverage. Large scale variation also affect the capability to view images in stereo mode.

Relief displacement

Large relief displacement create difficulty in forming continuous interrupted picture. Relief displacement decrease with height although increase in height reduces scale. Hence, these two effects have to be balanced.

Tilt of photograph

The tilt in a photograph can be resolved into two components: x-tilt and y-tilt, along x and y directions respectively. In a photo with y-tilt, the forward overlap will be higher on one side and lower on opposite side. The x-tilt causes the side lap to decrease on one side and to increase on another. Large x-tilt affects flight line spacing.

Crab and Drift

Crab is the angle formed between flight line and the edges of the photographs in the direction of flight. It reduces the effective width of photographic coverage. This can be rectified by rotating the camera about the vertical axis of camera mount.

Drift is caused by failure of the aircraft to stay on predetermined flight line. It leads to serious gaps between adjacent flight lines.

Ground coverage

After choosing scale and camera format, the ground coverage with a single photograph can be calculated. If the longitudinal and lateral overlaps are known, the ground coverage by a stereomodel can be calculated. This coverage is important since it provides approximate mapping area.

Airbase (B)

This is the distance between two adjacent exposure stations. On photographs, it is the distance between successive principal points which is also called the 'advance'.

Base-height ratio (B/H ratio)

The ratio of airbase (B) and flying height (H) is called B/H ratio. Normally the vertical scale of stereo model than the horizontal scale. This scale disparity, which helps determination of heights and identification of objects better is calledvertical exaggeration.

The average adult eye base (b) is about 6.5 cm, the corresponding variable h is difficult to measure. Experiments have provided an approximate value of 42.5 cm. This gives approximate b/h value as 0.15. The vertical exaggeration V is defined as V = (B/H) x (h/b)

Spacing of flight line spacing

It is defined as the distance between two adjacent flight lines or strips, at the photographic scale or ground scale. The direction of flight lines is also important. If there are number of ridges and valleys, it is better to fly parallel to the ridges. The strips are arranged in N-S or E-W direction keeping in mind the movement of sun throughout the day and effects of shadows.

It is better to run the strips in E-W course, as the dip of the magnetic north towards north (or south) makes accurate course of flight difficult if navigation is with compass only.

Number of flight lines

It depends on total width of area to be photographed. To avoid any possible gap in the flight line spacing and extra line can be added at ends

Number of photographs per flight line

It depends upon the total length of flight line and is given by the length of the line divided by airbase. Generally, additional two additional photographs are taken at the end of line for factor of safety.

Exposure interval

This is the time interval between two successive exposures and is a function of longitudinal overlap and aircraft velocity. It is equal to the time taken by aircraft to cover airbase. This can be done with a device known as intervalometer, which automatically make an exposures at fixed interval of time.

Maximum exposure time

Larger diaphragm opening (f - stop setting) allows more light to enter the camera, giving better image. A low shutter speed allows light for long time. The time interval which is small fraction of a second, during which the diaphragm is kept open is called exposure time. A small value of exposure time results in poor illumination and darker image. But a higher value is also problematic since it gives streak in an image instead of a point while imaging. So one needs just sufficient exposure time (shorter) without any appreciable image movement.

Assuming a permissible image movement of about 0.02 mm, the maximum exposure time can be calculated. The image movement allowed on the photograph, when converted to ground scale and divided by the aircraft speed gives exposure time, and is normally expressed as 1/t seconds.

Examples The overall flight planning procedure can be understood by a few simple examples that follow. Example 1 : An area 45 km long and 36 km wide is to be photographed to an average scale of 1:12000, using an aerial camera of f = 21 cm. The speed of the aircraft is 200 km/h. The photographs are 23 cm square, with a longitudinal overlap of at least 60% and lateral overlap of 30%, average elevation of the terrain is 500 m above MSL. Calculate the following:

The flying height above mean sea level (MSL).

Distance between successive exposures

Distance between flight lines for successive strips.

Flight line spacing on flight map at a scale of 1 cm = 600 m

Interval between successive exposures

Number of photographs per strip taking one extra photograph at either end

Number of strips with only one extra strip as a safety factor

Total number of photographs

Solution:

The flying height (H) can be calculated by using

Spacing of the flight line (W)

Number of flight lines (N fl ) required

Actual spacing between flight lines

Spacing of the flight lines on a flight map

Ground distance between exposures

Exposure interval

Since required overlap is at least 60%, hence exposure interval can be kept as 19 seconds.

Adjusted ground distance between exposures L = 55.55 x 19 = 1055.45 m

No. of photographs per flight line (N p )

Allowing two extra photographs at each end, the total photographs per flight lines = 44 + 2 + 2 = 48.

Hence, total no. of photographs = 48 x 20 = 960

Example 2: The following data is given for flight planning:

Format 18 x 18 cm

Focal length = 21 cm

Scale = 1/20,000

Longitudinal overlap = 60%

Lateral overlap = 20%

East-west terrain length = 100 km

North-south terrain width = 50 km

Flight direction: East to west

Aircraft velocity = 296 km

Permissible image movement = 0.02 mm

Wind velocity = 10 m /s from SSE direction

Calculate the following

Exposure interval

maximum exposure time

Ground speed of aircraft

Drift angle

Solution

Airbase = 0.4 x 18 cm at photo scale. On ground

Exposure interval

Image movement = 0.02 mm on photo. On ground,

Time taken to cover this distance = maximum exposure time (shutter speed)

Wind speed = 10 m/s = 36km/hr; flying speed = 296 km/hr. The ground speed of the aircraft and the angle of drift can be found out by vector operations. Effective ground speed = (296

2 + 36

2 - 2x296x36xcos67.5)

1/2 = 284.176 km/hr.

Drift angle ( ) is given as

Developments in photogrammetry

In a typical photogrammetric process, the information is obtained by establishing rigorously a geometric relationship between the model created by images and the object, as it existed at the time of the imaging event (Mikhail and Bethel, 2001).

The geometric relationship can be established by various means, which are broadly classified as: o analog photogrammetric methods o analytical photogrammetric methods o digital photogrammetric methods

Further, based on the type of platform used for the data acquisition, photogrammetry can be classified intotopographical photogrammetry and non-topographical photogrammetry (also known as close-rangephotogrammetry). Topographical photogrammetry uses satellite and/or airborne imagery, whereas non-topographical photogrammetry uses imagery from ground based platforms (Mikhail and Bethel, 2001).

Data processing system is used for data reduction from geometric information (e.g., image coordinates of targets) on the image to object space information.

Depending on the type of input used and the desired output, there are three alternatives for the data reduction: analog, analytical and digital.

Analog methods use optical, mechanical and electronic components for modeling and processing. In this mode of processing, the data reduction is carried out using analog instruments (e.g., plotters such as Kelsh K-480 stereoplotter). A typical instrument using this principle is shown in figure 1.

Analytical methods use mathematical modeling assisted with digital processing. In this mode, the image coordinates are obtained using monocomparators or stereocomparators (equipments to measure coordinates) and further processing is done through computer. Images used in both the above methods are in hard copy form (e.g., on film). A typical instrument known as analytical stereoplotter which uses this principle is shown in figure 2.

In recent times, with the advent of digital scanners and digital cameras, images in digital form are used instead of hard copy form. In digital methods, the modeling is based on analytical principles except that they use digital images as input. Hence, digital photogrammetric methods use strengths of both analytical and image processing methods for stereoplotting and related photogrammetric works. In digital mode of processing, the entire process is carried out using computer programs. These programs constitute digital photogrammetric software. A typical instrument known as digital photogrammetric work station (DPWS) is shown in figure 3.

Figure 1: Kern PG2 mechanical projection stereoplotter equipped with pantograph for direct manuscript plotting, and interfaced with computer for digital mapping (Wolf and Ghilani, 2002)

Figure 2: Zeiss P3 Analytical Plotter (Wolf and Ghilani, 2002)

(a) (b)

Figure 3: (a) Digital photogrammetric work station (b) Digital Video Plotter DVP (Wolf and Ghilani, 2002)

In general, a photogrammetric system is defined by its three components 1. Data acquisition 2. Data reduction 3. Data presentation

1. Data acquisition

Data acquisition systems are concerned with procuring the data or information. The data can be acquired in terms of images. The data acquisition system is generally classified into two categories: Conventional Imagery and Non-Conventional Imagery.

In conventional imagery, the imaging system has a lens and an image plane such as frame photographs, which is based on the central projection of the object onto an image plane. These can be obtained by using both metric andnon-metric cameras. In Non-conventional imagery the imaging system does not use a lens and image plane. Holograms, X-rays, T.V. systems etc. are categorized to this type of imagery.

The metric cameras are those manufactured specially for photogrammetric applications. In these types of cameras, the elements of interior orientation are known. The elements of interior orientation include: the focal length and location of the centre of the photograph. The metric cameras are further classified as single and stereometriccameras. A single metric camera is mounted on a tripod (figure 4 a) whereas a stereometric camera consists of two identical metric cameras mounted rigidly at the ends of a fixed base for photography (figure 4 b).

A non-metric camera is characterized by the off-the-shelf cameras which are often used for conventional photography (Figure 5 a and b). These are not the cameras especially made for the photogrammetric purposes. In these types of cameras, the elements of interior orientation are unknown or partially available.

(a) (b)

Figure 4: Terrestrial cameras (a) Zeiss TMK6 camera (b) Tripod mounted Zeiss SMK 40 + SMK 120 cameras

(a) (b)

Figure 5: Non-metric cameras for photogrammetric application (a) Sony video camera (b) Sony still camera

Digital close range photogrammetry (DCRP) is the latest development in photogrammetry, which is especially used to obtain 3D spatial information about objects placed near the camera. In this close range process, the cameras are generally positioned within 100 meters from the object and camera axes essentially point towards the center of the object (Atkinson, 1996). From multiple positions, the user is able to acquire imagery at many convergent angles.

The introduction of digital cameras into DCRP (as image acquisition systems) has given rise to on-line systems, which facilitate both real time and near-real time 3D coordinate measurement. With the availability of wide range of digital cameras including camcorders, CCD (charge coupled device) video cameras and digital still cameras at affordable prices, the utilization of these cameras as data acquisition systems in DCRP has increased considerably (Samson, 2003).

DCRP systems employing wide range of cameras coupled with automated image measurement and mapping have attracted wide usage over the past decade for precise deformation measurement in industrial and engineering applications. For example,

Engineering Applications o Monitoring of dam structures o Highway applications (DTM and GIS for alignment by computer) o Measurements of sand deposits in Hydraulics channel for different flow conditions

Biomedical Applications o Design of prosthesis for below knee amputees o Facial reconstruction studies o Physical education - monitoring the movements of athletes

Architectural Applications o Depicting the existing state of monuments/buildings and preparing working drawings o Studying the deformation decay and damage to buildings/structures of importance by periodic monitoring o Preserving the cultural heritage of various epochs in the form of stereo - photographs o Reconstructing and restoring and architectural monuments to their past glory o Mapping of sites and relocating/recapturing the landscape and location of monuments

Industrial Applications o Automobile industry o Shipping industry o Antenna calibration

2. Data reduction

The data reduction is concerned with the process of extracting desired information from photographs. Photogrammetric techniques have changed a lot with time.

In the earlier stages, analogue approach was used in which the imaging geometry is reconstructed by orienting two images in such a way that a three-dimensional model of the object is formed through optical or mechanical devices. With development in optics and mechanics the analogue photogrammetric instruments have improved and can attain very high accuracy.

With the evolution of computers, analogue instruments have been replaced by analytical plotters, where single or a pair of photographs is placed in X-Y measuring system which digitally records image coordinates (using mono or stereo comparators). The relations between image points and object points are described through numerical calculations based on the collinearity equations.

The collinearity condition specifies that the exposure station, ground point and its corresponding image point must all lie along a straight line. Figure 6 shows the collinearity condition. Let O be the exposure or perspective centre, P be the location of a point in object space whose corresponding point in image plane is p. Therefore, O p P represent the collinearity condition. The basic transformation equation describing the relationship between two mutually associated 3D coordinate systems is given by (Wolf and Dewitt, 2000)

Figure 6: Collinearity equations

Where,

x, y coordinates of the image point,

X, Y & Z coordinates of the object point,

f focal length of the camera,

m11,.. m33 elements of rotation matrix,

X L, Y L and Z L coordinates of exposure station in XYZ system

The introduction of digital photogrammetry has changed the world of photogrammetry completely. The advances in electronics and computer science have permitted new approaches to obtain photogrammetric solutions more effectively, while the basic mathematics, optical theory and many of the basic practices remain same.

3. Data presentation

It consists of preparing and presenting the results in a suitable form. The final output can be in the form of contour maps, pictorial representation of objects, digital model, three-dimensional (3D) spatial coordinates etc.

The developments in digital photogrammetry has resulted in digital photogrammetric work stations (DPWS). In the late eighties, the International Society for Photogrammetry and Remote Sensing (ISPRS) had defined a DPWS as "hardware and software to derive photogrammetric products from digital imagery". Some of the well known DPWS are Autometric, LH Systems, Z/I Imaging, and ERDAS.

A typical DPWS comprise standard hardware components such as stereo viewing devices and a three-dimensional mouse with a core of specialized photogrammetric software. Majority of DPWS are PCs with windows operating systems though UNIX based systems are also there. Such systems carry our various operations such as vector, raster and attribute data storage and processing, image handling, compression, processing and display, and several photogrammetric applications such as image orientation, generation of digital terrain models (DTM) or the capture of structured vector data, and the user interface level (Heipcke, 2003)