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

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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

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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

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

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

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

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

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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

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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

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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

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

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