This paper and its companion are concerned with the problems of 3-D object recognition and shape estimation from image curves using a 3-D object curve model that is invariant to affine transformation onto the image space, and a binocular stereo imaging system. The objects of interest here are the ones that have markings (e.g., characters, letters, special drawings and symbols, etc.) on their surfaces. The 3-D curves on the object are modeled as B-splines, which are characterized by a set of parameters (the control points) from which the 3-D curve can be totally generated. The B-splines are invariant under affine transformations. That means that the affine projected object curve onto the image space is a B-spline whose control points are related to the object control points through the affine transformation. Part I deals with issues relating to the curve modeling process. In particular, the authors address the problems of estimating the control points from the data curve, and of deciding on the "best" order B-spline and the "best" number of control points to be used to model the image or object curve(s). A minimum mean-square error (mmse) estimation technique which is invariant to affine transformations is presented as a noniterative, simple, and fast approach for control point estimation. The "best" B-spline is decided upon using a Bayesian selection rule. Finally, we present a matching algorithm that allocates a sample curve to one of p prototype curves when the sample curve is an a priori unknown affine transformation of one of the prototype curves stored in the data base. The approach is tried on a variety of images of real objects.>

For pt. I, see ibid., p.1-12 (1994). 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.>

The problem of recognizing and estimating the shape of objects with special markings (text, symbols, drawings, etc.) on their surfaces using B-spline curve modeling and a pair of binocular images is considered. As a direct consequence of the invariance of the B-splines to affine transformations the computation of the 3-D coordinates of the object curve points from a pair of stereo images becomes a straightforward task, and is obtained using minimum-mean-square-error estimation. The 3-D curve is recovered from the estimated object curve control points, and is subsequently used for the object shape estimation and classification.>