Cartographic Applications Morphing, and Warping Blending Cartographic Applications

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

Transforming Shape

Warping vs Morphing Warping Single object Specification of original and deformed states Morphing Two objects Specification of initial and final states

Warping and Morphing Warping Morphing • Source object • No target object Morphing • Target object

Warping versus Morphing Warping Morphing

Specification of Transformations Global Transformations Affine Maps Projective Maps Non-Linear Maps

Specification Definitions Correspondence Specification association between two regions defines original and final states Specification set of correspondences

Warping x Morphing Warping Morphing (metamorphosis) Single object Specification of original and deformed states Morphing (metamorphosis) Two objects Specification of initial and final states

Types of Specification Parametric Partition-based Feature-based Automatic or semi-automatic

Parametric Specification

Specification by Partition Regions cover the entire object Regular x Irregular partitions Same topology: original and final sets

Partition Examples

Specification by Features Regions do not cover the object Dimension of features £ object dimension Examples: points, vectors, planes, boxes,...

Feature (Vector) Examples

Transforming Attributes Texture, Color

Linear Blending A and B objects in a vector space c(t) = (1 - t) A + t B c(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 preservation Smoothness preservation Avoid linearities use adaptive methods

Avoid leakage Select and warp foreground only

Example of Morphing and Attribute Transformation form Fantamorph

Geometry Deformation Change of Coordinate Systems

Animation Emphasis Stretch Squash Distortion plus Motion

Animation Keyframes Tweens Motion Shape

The World according to Aaron “Garp” Arthur

Types of Warps

Warping Techniques Barycentric mapping Field-based mapping Radial basis functions - RBF Free-form deformation - FFD Multi-pass spline mesh Physically-based warping

Parametric (global) warping Examples aspect translation rotation perspective affine cylindrical

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

Scale Change xT = mxs yT = nys Scaling coefficient m usually is the same as n

Translation xs = xs + Dx ys = ys + Dy

Bilinear Coordinate Transformation

Bilinear Coordinate Transformation Transformation Equations are: xT = axs + bys + cxsys + d yT = exs + fys + gxsys + h Which are solved simultaneously From a minimum of 4 points whose Coordinates are known in both systems.

Forward warping Send each pixel f(x,y) to its corresponding location (x’,y’) = T(x,y) in the second image if pixel lands “between” two pixels distribute color among neighboring pixels (x’,y’), known as “splatting” Origin Target T(x,y) y y’ x x’ f(x,y) g(x’,y’)

Inverse Warping Get each pixel g(x’,y’) from its corresponding location (x,y) = T-1(x’,y’) in the first image if 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. Origin Target T-1(x,y) y y’ x x x’ f(x,y) g(x’,y’)

Applications Genesis in the graphic arts, movies Yet, Morphing is not just a special effect: Lens distortion correction Graphical objects modeling Motion capture data interpolation Accelerated Rendering

Applications Mapping “significance” Area = the relative significance of states based on electoral college votes

Applications: Interpolation of Animation Example: Glacial Metamorphosis Considerations: Frame time resolution Speed of motion Realistic 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: Photorectification Example: Leica Photogrammetry Suite Corrects for camera, camera angle, and relief distortions.

Applications: Showing Change Not 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 morphing Image morphing software Morpheous Photo Morpher www.morpheoussoftware.net Winmorph http://debugmode.com/winmorph Abrosoft Fantatmorph www.fantamorph.com Terrain imaging software Terragen http://www.planetside.co.uk Bryrce 5.5 http://bryce.daz3d.com/55index.php Other software capable of morphing Autodesk 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