Compact and parametric shape representation by a tree of sigmoid functions for automatic shape modeling

摘要

A modeling method to represent an object shape by a tree of sigmoid functions, and a gradient-descent-based searching procedure to estimate shape parameters are described. The model's unique feature is that it can produce a shape parameterized with a gain parameter determining the resolution of the represented shape. With a large gain value, the model represents a detailed shape with a sharp edge, which is described by a piecewise combination of lines and curves. With a small gain value, it generates a blurred shape, which has explicit (analytic) forms of partial derivaties with respect to parameters describing the shape. Using the model's differentiable property, the gradient-descent-based searching method updates the shape parameters and the gain parameter simultaneously so that an optimal set of shape parameters which makes the model fit to a target shape is found through a coarse-to-fine search. Previous shape description techniques were either contour-based (spline, active contour, wireframe, polygon and so on) or expansion-based (wavelet, radial basis function, eigenfunction and so on). The method has a dual modal nature with its capability of dealing with sharp edges and its differentiable and resolution adjustable nature. The model's performance was evaluated by some coarse-to-fine shape modeling simulations and its efficiency and robustness were verified.