volume visualisation

8/12/2019 Volume Visualisation

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Volume Visualization

[email protected]

Visualization Building Blocks

Viz ElementsGlyphs (e.g. Alphabets,

Arrows)

Lines

Triangles

Voxels* (volume element)

*Cannot be directly

represented on

displays

Viz AttributesTransforms

(Position, Rotation, Scale)

Color

Opacity

View AttributesViewpoint

Projection

(Orthographic, Perspective)

Canvas

Viz ReinforcementTexture

Light

Distortion(e.g. Displacement)

Motion (e.g. Camera ,time steps)

Filter (e.g. threshold, resample, subset, slice, clip)

Add Context(e.g. Connectivity, Mao Overlay)


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Geometric Visualization Process

Identify regions of same scalarvalue

Utility

2D:Contours

3D:Isosurfaces(Marching Cube,Marching Tetra)

Volume Visualization

To create two-dimensional graphical

representations from scalar datasets that are

defined on three-dimensional grids. E.g.

seismic data to fluid dynamics.

shape (given by the geometry of the grid)

appearance (given by the scalar values or color,

texture, lighting conditions, etc.) Type

Direct volume rendering (DVR)

Direct mapping of voxels on pixels of a 2D image

plane

Indirect volume rendering- or surface-fitting(SF)

Surfaces Creation & used for interactive display


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How to Visualize the volume dataset?Four Common Methods

Point Cloud Slicing Plane

Isosurface Volume Render

Point Cloud Map each data value to a color. This mapping is called a Color Map.

Display each data value as a point.

Often leads to occlusion. Here is an example that shows only data valuesgreater than 0.3.

0.0 1.0

Color Map

Point cloud of foot dataset


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Slicing Plane Display a 2D plane as a slice through the 3D dataset.

The 2D plane could be a regular grid, where each pointcorresponds to a point in the 3D space which it slices.

Linearly interpolate the triangles to color the entire 2D slice.

0.0 1.0

One slice of the foot dataset

Color Map

An axis-aligned slicing plane

Isosurface

Select a data value, called an isovalue.

Draw the 3D contour of this value.

A contour simply joins all the points having this samedata value. In 2D, a contour is a line.

In 3D, a contour is a surface, called an isosurface.

Method: Marching cubes The 3D regular grid is considered to be made of atomic

cubes.

Each cube has 8 corners. Each corner corresponds to adata point, and has a value.


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Marching Cubes AlgorithmVertex Identification

For each corner, mark the corner is 1 if the data value at that corner ishigher than the isovalue, 0 otherwise.

Then, draw surfaces separating the 1 corners from the 0 corners.

There are 16 cases.

Generate triangles for each cube. They will all join together to form anisosurface (assuming we take care of the ambiguous cases).

Example Marching Cube cases

Marching Cubes AlgorithmVertex Value

Linear interpolation between vertices.

Suppose, Data value at v0 is d0,

Data value at v1 is d1

Isovalue is d, and d0 < d < d1

Then, the triangle vertex on this edge v0v1 that is part of the isosurface is:v = (d-d0)/(d1-d0) x v1 + (d1-d)/(d1-d0) x v0

v0

v

v1


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Optimization: Octree

Marching cubes algorithm is very slow. You have to go through the entire dataset to search for cubes that contain

the isosurface.

To speed things up, use some data structure to help search.

One such data structure is the octree.

Continuously sub-divide dataset into 2x2x2 cubes. In each cube, store themaximum and minimum value.

When drawing an isosurface of value v, traverse the octree. Whenever youreach a node whose range does not contain v, you need to search nofurther down this node.

Volume Rendering

Treat volume as a translucent object.

For every pixel, shoot ray into the 3D volume.

Sample the each ray at small, regular intervals.

At each sample, calculate color and composite.


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How do you calculate color?

How do you composite?

1. At each sample, get the data value.

Data value obtained by tri-linear interpolation.

2. After getting data value, get color and opacity.

Color obtained from color map.

Opacity obtained from opacity map.

3. Get the normal

Normal approximated by data gradient

Data gradient approximated by central difference

4. Calculate color using lighting

5. Composite. Update the accumulated opacity.

The following slides will elaborate each of these steps

1. Tri-linear Interpolation to get Data Value

a

b

c

d

m

n

P

1

2What is the data value at point P?

First, find the data values at a, b, c and d.

The value at a, for example, is obtained from

linearly interpolating the values at point 1 and

point 2.

Then linearly interpolate a and b to get m.

Similarly, obtain the data value at n.

Finally, linearly interpolate m and n to get the

final data value at P.


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2. What is an Opacity Map?

Have an opacity value associated with each data value. User specifies a more opaque value for the data value that he/she is

interested in.

For example, if the value for bone is around 0.4, and the value for skin isaround 0.1, the user may wish to use the following opacity map to see thebone through translucent skin.

Opacity

1.0

Data value1.00.1 0.4

3. Approximate surface normal

Surface normal is usually in the direction of thechange of data value.

To get the direction of change of data value, usecentral difference.

Vz+1

Vy-1

Vx-1

Vy+1

Vz-1

Vx+1P

To find the normal at point P:

Consider the six adjacent data points.

Let the value at the next point along the x axis be denoted as V x+1.

Similar notation for the other five points.

Then, the normal at point P is N = (Vx+1-Vx-1,Vy+1-Vy-1,Vz+1-Vz-1).


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4. Calculate lighting

Calculate lighting using the lighting equations.

We have the color from the color map, C.

We have the normal from the central difference, N.

Assume that the light is white, and is in the direction

L.

Assume that we use only diffuse lighting.

Then, the color seen by the camera is: Cx N.L

5. Consider opacity

We have to diminish the color at each sample point because itis translucent.

To do this, we accumulate color and opacity.

In the beginning,

Coloraccumulatedis set to (0,0,0), and

Opacityaccumulatedis set to 0.0

At each sample point, update Coloraccumulatedby:Coloraccumulated+= (1Opacityaccumulated) xax C x N.L

At each sample point, update Opacityaccumulatedby:

Opacityaccumulated+= (1Opacityaccumulated) xa

whereais the opacity of the sample point from the Opacity Map,

C is the color of the sample point from the Color Map,

N is the unit normal at the sample point from central difference, and

L is the unit vector from the sample point to the light source.


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Techniques for examining sub-section

of Volume

Slicing

To examine scalar fields

2 dimensional slice plane

Isosurfacing

Isosurfaces are 2D

surfaces

Transparency

Volume materialattenuates reflected

Modern 3D maps

Computer-generated perspective views with

cartographic content are called 3D maps.


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Design Variables of 3D Maps

Modelling Modelling of digital terrain model objects

Modelling of (topographic) map objects

Modelling of orientating map objects

Symbolization

Graphic appearance

Special graphic aspects

Textures

Text objects

Object animation

Visualization

Perspective (projection)

Camera (viewing) Lighting

Shading and shadow

Atmospheric effects and natural phenomenon

3D Design Requirements


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3D Visualization pipeline

View-dependent, multi-perspective view


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LoD

LoDs are mainly determined in relation tothe resolution of sensor data, the precisionof semantic information and the relevantapplication

LoDs for settlements and buildings-Thiemann, (2004) LoD1 = aggregated settlement blocks with a

uniform height

LoD2 = block of the individual buildingswithout roof form

LoD3 = LoD2 enhanced with a simplified roofform

LoDs for individual buildings-Netlexikon vonakademie.de LoD1 = Popping up of the ground plan to a

uniform height

LoD2 = LoD1 enhanced with a texture

LoD3 = External hull of the building with aroof form and small surface elements

LoD4 = LoD3 enhanced with external textures

LoD5 = LoD4 enhanced with internalstructures

LoDs of 3D landscapes-Grger et al., (2004) LOD 0 = A digital terrain model with draped

orthophoto and classification of land use,

LOD 1 = Popping up of the ground plan to auniform height,

LOD 2 = LoD1 enhanced with roof textures,roof structures and vegetation features,

LOD 3 = Architecture models with vegetation

features and street furniture LOD 4 = Indoors architecture models.

3D Buildings

3D buildings is

essentially a linear

continuum

an arbitrary number of

milestones can be said

to exist referred to asLevels of Detail (LoD)

there are no generally

agreed LoDs for 3D

buildings


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3D Building Generalization

Need

3D building models are too time intensive and

expensive for 3D data acquisition and updating.

high maintenance cost and difficulties for the user

in conducting multi-scale spatial analysis

Modelgeneralization

graphic (or

cartographic)

generalization

3D

Generalization

3D Building Generalization steps

Model generalization

Is a data-to-data transformation that deals with modelobjects, their geometric and semantic precision and theirtopological consistency in the scale space.

Generalized building models are either distributed as dataservices for integration with thematic information of

comparable resolution or regarded as a prior stage tographic generalization

Graphic (or cartographic) generalization

focuses on the visual impression of model objects togetherwith 3D graphic artifacts in relation to the selectedprojection, visualisation style, camera position etc.


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Description Models of 3D Buildings

Voxel model Parametric description

3D building is constructed through a number of primitivebodies such as cuboid, sphere, cylinder, cone and pyramid-sub components of the structure called geons

absolute position of the building is defined by six furtherparameters of rotation and translation

Constructive solid geometry (CSG) 3D building is constructed through Boolean operations

such as intersection, difference, union or inversion ofelementary building parts

sequence of operations is stored in a CSG tree

Description Models of 3D Buildings

CSG-tree of a building

Boundary Representation

3D building is described by itsboundary surface usingtopological elements such asmesh, edge and vertex.e.g.TIN,VRML

Solid representation (SRep)

3D building is described by aTetrahedral Network

(TEN) composed of theregular or irregulartopological elements:tetrahedron, triangle,edgeand vertex


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3D building Structure

LOD based- Successive refinement of 3Dbuilding structures based on viewing

distance

The nearer the building objects, the more

details they reveal

Individual- Structural components of

a typical building


Segmentation of

building structures

polyhedron

segmentation-feature-

finding

Recognition of 3Dbuilding structures

Segmentation of a sample building with split

planes

Types of ground plan in the top row; Roof types in the middle

and bottom row


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Building Clustering

Hirachial approach classification of

neighbourhood relationshipsand the detection of buildingclusters

Model generalization of 3Dbuildings simplification ofbuilding

data, is introduced

Simplification of parallelstructures

Squaring of inclined roof-facets

Automatically recognised 3D building clusters

Parallel facets under a certain distance are

shifted towards each other

Squaring of roof


simplification based on parallel shifts

Results of the roof-squaring procedure


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Graphic generalization

of 3D buildings

Invasive simplification of

3D buildings

reducing and adjusting

the geometric details of

3D buildings

Non-invasive

simplification of 3D

buildings

Presentation based on standard illumination

(left), presentation based on expressive line

drawing (right)

volume visualisation

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