Image-Guided Fracture David Mould University of Saskatchewan

Graphics Interface 2005 May 11, 2005 Fracture Simulation ► Early graphics criticized for "perfect" images – smooth surfaces, no dirt or imperfections ► In the real world – things break ► Desire to simulate chipping, tearing, erosion, and cracks

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Previous Work ► Physical simulation:  mass-spring models  continuum mechanics ► Ad hoc methods:  crack primitives crawling across surface  Voronoi diagrams

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Hierarchical Path Planning

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Modified Voronoi diagram ► Regular Voronoi diagram: each point on a plane assigned to a region based on proximity (Euclidean distance) ► Modified Voronoi diagram: each node in a graph assigned to a region based on proximity (shortest path through graph)

Graphics Interface 2005 May 11, 2005 Modifying the Graph ► When edges have unit cost, reverts to regular Voronoi diagram (with Manhattan or octile distance) ► When edges have arbitrary cost, results in Voronoi-like regions, but with boundaries perturbed

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Controlling the Graph ► Can put information into the graph edges ► For example, read from image, place higher weights on edges where image has higher intensity  produces crack pattern where cracks align with edges from original image

Graphics Interface 2005 May 11, 2005 after "English Words", art by Jiro Takamatsu

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Crack Modeling ► Define graph connectivity  4- or 8-connected grid convenient ► Define edge weights  completely random, or contribution from image ► Place Voronoi sites ► Compute Voronoi diagram in graph ► Crack locations are region boundaries  Output: binary map

Graphics Interface 2005 May 11, 2005 Variations ► Multiscale cracks  Draw one set of cracks, use the resulting edges to modify weights, and make a new set of cracks ► Alter the distribution of Voronoi centres  Enforce even distribution, or place extra sites where more cracks are desired ► Use a dynamic map  Change the weights wrt time in some predictable way

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Dynamic Images ► Image embedded in a graph with weighted edges:  w i = a*I i + b*R i  some contribution from Image, some Random ► Can obtain coherent image sequences with greater or smaller influence from image by modifying a, b continuously

Graphics Interface 2005 May 11, 2005 Dynamic images

Graphics Interface 2005 May 11, 2005 Dynamic images

Graphics Interface 2005 May 11, 2005 Dynamic images

Graphics Interface 2005 May 11, 2005 Dynamic images

Graphics Interface 2005 May 11, 2005 Interpolating between Images

Graphics Interface 2005 May 11, 2005 Interpolating between Images

Graphics Interface 2005 May 11, 2005 Interpolating between Images

Graphics Interface 2005 May 11, 2005 Interpolating between Images

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Rendering Cracks ► Procedural texture ► Bump and displacement mapping ► Image-based approaches ► Image Analogies (Hertzmann et al. 2001)

Graphics Interface 2005 May 11, 2005 Image Analogies ► Automatically solve A:A'::B:?? given A, A', B  all elements are images ► Learn the filter which transforms A to A', and apply it to B

Graphics Interface 2005 May 11, 2005 Image Analogies

Graphics Interface 2005 May 11, 2005 Image Analogies in Cracks

Graphics Interface 2005 May 11, 2005 Image Analogies in Cracks start with this

Graphics Interface 2005 May 11, 2005 Image Analogies in Cracks obtain crack map

Graphics Interface 2005 May 11, 2005 Image Analogies in Cracks extract crack map from photo

Graphics Interface 2005 May 11, 2005 Image Analogies in Cracks use IA to get final crack image A:A'::B:B'

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005

Graphics Interface 2005 May 11, 2005 Summary ► Modified Voronoi diagram has crack-like boundaries ► Boundary locations guided by input images ► A number of handles for further control (e.g., site placement and distribution) ► Method produces crack maps ► Image analogies a possibility for rendering

Graphics Interface 2005 May 11, 2005 Future Work ► More attention to rendering ► Crack computation on polygonal models ► Exploration of additional phenomena  e.g., lightning ► Ability to produce more nuanced images  not just line art – small cracks used for shading

Graphics Interface 2005 May 11, 2005 Questions?