Morphing,

Cartographic Applications

and

DefinitionMorphing is a special technique that creates a smooth, controlled transformation of one image into another.

Transforming Shape

Warping vs MorphingWarping

•Single object

•Specification of original and deformed states

Morphing

•Two objects

•Specification of initial and final states

Warping and Morphing

Warping• Source object• No target object

Morphing• Source object• Target object

Warping versus Morphing Warping

Morphing

Specification of TransformationsGlobal Transformations

Affine MapsProjective MapsNon-Linear Maps

Specification

DefinitionsCorrespondence

association between two regions defines original and final states

Specification set of correspondences

Warping x MorphingWarping

Single objectSpecification of original and deformed states

Morphing (metamorphosis)Two objectsSpecification of initial and final states

Types of SpecificationParametricPartition-basedFeature-basedAutomatic or semi-automatic

Parametric Specification

Specification by PartitionRegions cover the entire objectRegular x Irregular partitionsSame topology: original and final sets

Partition Examples

Specification by FeaturesRegions do not cover the objectDimension of features £ object dimensionExamples: points, vectors, planes, boxes,...

Feature (Vector) Examples

Transforming Attributes

Texture, Color

Linear BlendingA and B objects in a vector space

c(t) = (1 - t) A + t Bc(0) = A, c(1) = B

Functions (attributes)Subsets of space (shape)Also Bilinear, Trilinear and Affine Blending

Shape Warp + Attribute Blending

Linear Color Interpolation(cross dissolve)

Some Guidelines for a good morphing

Feature preservationSmoothness preservationAvoid linearities

use adaptive methods

Avoid leakage

Select and warp foreground only

Example of Morphing and Attribute Transformation form Fantamorph

Geometry DeformationChange of Coordinate Systems

AnimationEmphasisStretchSquashDistortion plus Motion

AnimationKeyframesTweens

MotionShape

The World according to Aaron “Garp” Arthur

Types of Warps

Warping Techniques

Barycentric mappingField-based mappingRadial basis functions - RBFFree-form deformation - FFDMulti-pass spline meshPhysically-based warping

Parametric (global) warping

translation rotation aspect

affineperspective

cylindrical

Examples

xT = xs (cos(+ ys (sin())yT = ys (cos()) - xs (sin())

Rotation

Scale Change

xT = mxs

yT = nys

Scaling coefficient m usually is the same as n

Translation

xs = xs + Dxys = ys + Dy

Bilinear Coordinate Transformation

Bilinear Coordinate TransformationTransformation Equations are:

xT = axs + bys + cxsys + dyT = exs + fys + gxsys + h

Which are solved simultaneouslyFrom a minimum of 4 points whoseCoordinates are known in both systems.

Forward warpingSend each pixel f(x,y) to its corresponding location

(x’,y’) = T(x,y) in the second imageif pixel lands “between” two pixels distribute color among neighboring pixels (x’,y’), known as “splatting”

f(x,y) g(x’,y’)x x’

T(x,y)y y’

Origin Target

Inverse WarpingGet each pixel g(x’,y’) from its corresponding location

(x,y) = T-1(x’,y’) in the first imageif pixel comes from “between” two pixels, Interpolate color value from neighbors

nearest neighbor, bilinear, Gaussian, bicubic

Inverse warping usually better because it eliminates holes, but it is not always possible.

f(x,y) g(x’,y’)xy

x x’

T-1(x,y)y’

Origin Target

ApplicationsGenesis in the graphic arts, moviesYet, Morphing is not just a special effect:Lens distortion correctionGraphical objects modelingMotion capture data interpolationAccelerated Rendering

ApplicationsMapping “significance”

Area = the relative significance of states based on electoral college votes

Applications: Interpolation of AnimationExample: Glacial Metamorphosis

Considerations: Frame time resolutionSpeed of motionRealistic shapes

Georegister Maps: Example Rubber Sheeting in ArcGIS

For two raster maps in separate layers in ArcGIS. Look up procedure in Help under “georeferencing.”

Work with tools in georeferencing menu bar

httpChina Historical GIS: georeferencing

Applications: PhotorectificationExample: Leica Photogrammetry SuiteCorrects for camera, camera angle, and relief distortions.

Applications: Showing ChangeNot just areal change, but also warping of a surface to show change in mapped parameters, such as population density or temperature.

Terragen: Mount St. Helens Morph

Is this morph realistic?

Software used in different types of morphingImage morphing software

Morpheous Photo Morpher www.morpheoussoftware.net

Winmorph http://debugmode.com/winmorph

Abrosoft Fantatmorph www.fantamorph.com

Terrain imaging softwareTerragen http://www.planetside.co.uk

Bryrce 5.5 http://bryce.daz3d.com/55index.php

Other software capable of morphingAutodesk Map 3D 2007 www.autodesk.com

Esri Arcview 9.1 www.esri.com

Flash 8 www.macromedia.com

Landscapes done in Bryce

‘Canyon Walls’ by Burpee ‘Hidden Valley‘ by Andy Simmons

Landscape created in terragen

By: Giancarolo http://www.timster.net/terragenasart/site/giancarlo-flight2.html