Curvature Representation And Decomposition Of Shape

Shape plays a key role in human visual system and it is the key feature for object recognition.Because of the nonlinearity of shape and the subjectivity of human visual system, thegap of the recognition precision between shape based machine recognition system and humanvisual system is large. Fortunately, the rapid progress of hardware and software makeit possible to shorten this gap.Shape representation is the first step towards shape related application, and it is also themost critical step. The information lost in this step can not be recovered at the following step;at the same time, the noise introduced in this step is also hard to remove at the following step.A good shape representation can greatly improve the effect of shape related application.However, because of the diversity of the form of real objects and the complexity of sur-roundingenvironment, the shape of the same object varies greatly. The fundamental aim ofshape representation is to represent the invariant and most discriminative features of an object.Thus, when need to distinguish between invariant information and variant informationof shape, which is a big challenge.The works of this dissertation concentrate on shape representation techniques. We didresearch on local and global shape representation techniques, including multi-scale curvaturefor planar curves,multi-scale normal and principal curvature for 3D surfaces and convexshape decomposition for arbitrary dimension objects.The contributions of the dissertation are:1. Propose the concept of visual curvature and build its theory. Analyze the relationbetween visual curvature and classical curvature, and also analyze the relation betweenvisual curvature and turn angle,prove that on regular curves, classical curvatureis the limit of visual curvature and on polygonal curves, turn angle is a specialcase of visual curvature. Propose the definition of global scale measure, based onit, propose the multi-scale visual curvature. Analyze the properties of multi-scalevisual curvature and demonstrates its power in some applications.2. Research on the principal curvature of surfaces. Based on visual curvature of planarcurves, propose and prove the min max principle, which can estimate the surfacenormal and principal curvature simultaneously. The experimental results demonstratethat such method is very robust to noise.3. Research on the relationship between the line segment connecting two points withinthe object and the object itself, propose the concept of mutex. Constructing the mu- tex pair set and candidate cut set, transform the convex shape decomposition probleminto a linear programming problem. The solution of this linear programmingproblem is just the optimal decomposition scheme.The reason why multi-scale visual curvature is robust is that a global scale measureis introduced,this idea is also suitable for robust estimation of other local measure. Thecentral point of obtaining optimal decomposition scheme is transforming the convex shapedecomposition problem into a linear programming problem, since linear programmingproblem can be solved efficiently, thus we are guaranteed to obtain optimal decompositionscheme efficiently.