Shape complexity measure of an object is an inimitable intuitive perception power of the human vision system. Is it possible to quantify this perception property of the most powerful and most complicated human vision system by assigning a complexity metric? Can the intuitive quality of the human eye to distinguish objects based on shape be executed as a computer vision algorithm? These questions have interested researchers in a wide range of applications spanning computer vision, cell biology, medical imaging, satellite imagery, neuron morphology, and computer graphics.

As computer vision engineers,the goal of this project is to investigate the robustness of the algorithm in applications,such as object discrimination (man made and natural objects), 3D surface registration and surface ruggedness measure. We are interested in 3D shape similarity of mechanical automotive parts for the task of under vehicle robotic inspection, and shape description for the task of reverse engineering.

We use an algorithm to measure the shape complexity for discrete approximations of planar curves in 2D images and manifold surfaces for 3D triangle meshes.  We based our algorithm on shape curvature, and thus we compute shape information as the entropy of curvature.  We present definitions to estimate curvature for both discrete curves and surfaces, and then formulate our theory of shape information from these definitions.  We demonstrate our algorithm with experimental results.