Shape grammar implementation with vision Iestyn Jowers University of Leeds Design Computing and Cognition 2010 Workshop on Shape Grammar Implementation 11 th July 2010

Analytical subshape detection Typically, subshape detection has relied on analytical methods, and as a result : - subshape detection is restricted according to specific geometric elements e.g. lines - subshape detection depends on embedding properties of geometric elements rather than visual similarity Iestyn Jowers, University of Leeds

Implementation with vision Using results from computer vision it is possible to teach a system to “see” shapes For example, the Hausdorff distance is a distance metric for point sets, and has been used for object recognition to find a template image in a test image H(A,B) = max(h(A,B), h(B,A)) where Iestyn Jowers, University of Leeds

Implementation with vision Let shapes be defined as raster images Iestyn Jowers, University of Leeds

Implementation with vision Then shapes are defined as point sets Iestyn Jowers, University of Leeds

Implementation with vision H(A,B) = 0 The similarity of shapes can be measured according to the Hausdorff distance: Iestyn Jowers, University of Leeds

Implementation with vision The similarity of images can be measured according to the Hausdorff distance: H(A,B) = 2 Iestyn Jowers, University of Leeds

Implementation with vision If the second image is a sub-shape of the first then its directed Hausdorff distance will be 0 h(B,A) = 0 h(A,B) = 18 Iestyn Jowers, University of Leeds

Can consider the directed Hausdorff distance under transformation Implementation with vision Sub-shape?h(B T,A) = 5h(B T,A) = 2 h(B T,A) = 1 h(B T,A) = 2 h(B T,A) = 0 Sub-shape!!! Iestyn Jowers, University of Leeds

A shape grammar interpreter The Hausdorff distance has been used to implement a shape grammar interpreter: - shapes are defined as raster images - shapes have no restriction on geometry - Hausdorff distance provides a more “visual” measure of shape similarity Iestyn Jowers, University of Leeds

A shape grammar interpreter Demo… Iestyn Jowers, University of Leeds