The paper deals with grouping of edges to contours of shapes using only local symmetry and continuity. Shape skeletons are used to generate the search space for a version of the Markov Chain Monte Carlo approach utilizing particle filters to find the most likely skeleton. Intuitively this means that grouping of edge segments is performed by walking along the skeleton. The particle search, which is an adapted version of a successful algorithm in robot mapping, is assisted by a reference model of a shape, which is expressed as the sequence of sample points and radii of maximal skeleton disks. This model is sufficiently flexible to represent non-rigid deformations, but restrictive enough to perform well on real, noisy image data. The order of skeleton points (and their corresponding segments) found by the particles defines the grouping.

We present a realistic mathematical model of a digitized edge which handles both blurring and arbitrary thresholding. We show that a thresholded digital image of a blurred half-plane obtained for some unknown threshold value is equal to the image of a perfectly focused half-plane with the same slope obtained by object boundary quantisation. This result implies that recovering the slope of a blurred half-plane, given its image obtained for some unknown threshold value, reduces to recovering the slope of a perfectly focused half-plane under object boundary quantization. Therefore, the previous results and algorithms for the recovery of straight lines, which mainly assumed object boundary quantization, are also valid if we assume this more realistic digitization model.

Generalized cylinders are a flexible, loosely-defined class of parametric shapes capable of modeling many real-world objects. Straight homogeneous generalized cylinders are an important subclass of generalized cylinders, whose cross-sections are scaled versions of a reference curve. Although there has been considerable research into recovering the shape of SHGCs from their contour, this work has almost exclusively involved methods that couple contour and heuristic constraints. A rigorous approach to the problem of recovering solid parametric shape from a single intensity view should involve at least two stages: (1) deriving the contour constraints, and (2) determining if additional image constraints, e.g., intensity, can be used to uniquely determine the 3D object shape. In this paper, the authors follow the approach just described. This methodology is also important for the recovery of object classes like tubes, where contour and heuristic constraints are shown to be insufficient for shape recovery. First, the authors prove that SHGC contours generated under orthography have exactly two degrees of freedom. Next, the authors show that the remaining free parameters can be resolved using reflectance-based constraints, without knowledge of the number of light sources, their positions, intensities, the amount of ambient light; or the surface albedo. Finally, the reflectance-based recovery algorithm is demonstrated on both synthetic and real SHGC images.

Recovering the 3-D shape of an object from its 2-D image contour is an important problem in computer vision. In this correspondence, the author motivates and develops two object-based heuristics. The structured nature of objects is the motivation for the nonaccidental alignment criterion: parallel coordinate axes within the object's bounding contour correspond to object-centered coordinate axes. The regularity and symmetry inherent in many man-made objects is the motivation for the orthogonal basis constraint. An oblique set of coordinate axes in the image is presumed to be the projection of an orthogonal set of 3-D coordinate axes in the scene. These object-based heuristics are used to recover shape in both real and synthetic images.>

A description is given of the construction of a symmetry analyzer. Examples using SYMAN on both real and synthetic images are shown. SYMAN's combination of both global and local methods is discussed. The derivation of a global analytic solution for the skew axes when the degree of skew symmetry is known is described. A local tangent-based algorithm which has advantages over previous methods is presented.>

A general method is presented for recovering straight homogeneous generalized cylinders from monocular intensity images. In this method, it is assumed that the generalized cylinder being recovered has purely diffuse reflectance and that the diffuse reflectance coefficient is constant. It is demonstrated that contour information alone is insufficient to recover a straight homogeneous generalized cylinder uniquely. It is shown that the sign and magnitude of the Gaussian curvature at a point vary among members of a contour-equivalent class. The contour image fails to constrain two parameters of the underlying generalized cylinder, the 3D axis tilt and translation. A method for ruling straight homogeneous generalized cylinder images is described. Once the rulings of the image have been recovered, all parameters derivable from contour alone can be recovered, all parameters derivable from contour alone can be recovered. To recover the two remaining parameters (modulo scale) not constrained by image contour, additional information must be incorporated into the recovery process, e.g. intensity information. A method for recovering the tilt of the object using the ruled contour image and intensity values along extremal cross-section curves is derived, along with a method for recovering the location of the object's 3D axis from intensity values along meridians of the surface. The methods outlined constitute an algorithm for recovering all the shape parameters (modulo scale).>

Consideration is given to two membership tests for straight homogeneous generalized cylinders to determine if an object in the image is a member of the shape class. It is shown that contour information alone is insufficient to recover a straight homogeneous generalized cylinder uniquely. It is then shown that the sign and magnitude of the Gaussian curvature at a point vary among members of a contour-equivalent class. Next, a method of ruling straight homogeneous generalized cylinder images is developed. This ruling of the surface serves two functions. First, the ruling algorithm provides a heuristic test of whether or not the image is consistent with that of a straight homogeneous generalized cylinder. Secondly, the ruling makes explicit certain parameters of the underlying straight homogeneous generalized cylinder that the authors use in their second membership test. The second membership test is an intensity-based method which assumes that the surface has geodesics and that the albedo is constant. The method compares intensity values at corresponding meridian points along cross-sectional geodesics.>

Parametric models of objects are becoming increasingly more impor- tant in computer vision. In the past few years, a number of researchers have investigated the recovery of a class of parametric models by the minimization of an error of fit measure. The measures used have typ- ically been chosen in an ad hoc fashion. This paper looks at how these measures affect the performance of a recovery system. This research can be divided into two parts. The first studies the biases of the po- tential error-of-fit measures with respect to the parameters recovered and examines the cross-sectional shape of their respective error of fit surfaces. This study is done in simulation by holding all but one pa- rameter constant. The second part of the research compares two of the better error of fit measures by using them in a recovery system. Both the number of iterations and the quality of the reconstruction are considered.