Abstract: To seek for an isometry-invariant 2D shape descriptor, we encode 2D shapes from 3D perspective,and propose a novel shape classification approach based on heat kernel. First, we build triangulation for the regionenclosed by the contour. Then, we transform the 2D shape into a 3D closed/smooth surface through a setof optimization techniques. Finally, the heat kernel signature of the 3D counterpart is extracted to identify theoriginal 2D shape. Extensive experimental results on the MPEG-7 and Animal Shapes benchmarks exhibit anadvantage of classification in terms of accuracy and robustness.