Shape Discrimination Using Fourier Descriptors
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This paper is the second part of a 3-D object recognition and shape estimation system that identifies particular objects by recognizing the special markings (text, symbols, drawings, etc.) on their surfaces. The shape of the object is identified from the image curves using B-spline curve modeling as described in Part I, as well as a binocular stereo imaging system. This is achieved by first estimating the 3-D control points from the corresponding curves in each image in the stereo imaging system. From the 3-D control points, the 3-D object curves are generated, and these are subsequently used for estimating the 3-D surface parameters. A Bayesian framework is used for classifying the image into one of c possible surfaces based on the extracted 3-D object curves. This is complemented by a neural network (NN) that recognizes the surface as a particular object (e.g., a Pepsi can versus a peanut butter jar), by reading the text/markings on the surface. To reduce the amount of training the NN has to undergo for recognition, the object curves are "unwarped" into planar curves before the matching process. This eliminates the need for templates that are surface shape dependent and results in a planar curve that might be a rotated, translated, and scaled version of the template. Hence, for the matching process we need to use measures that are invariant to these transformations. One such measure is the Fourier descriptors (FD) derived from the control points associated with the unwarped parent curves. The approach is tried on a variety of images of real objects and appears to hold great promise.