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The article deals with the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected (for example, rotation, translation, scaling, orthographic, and semiperspective projections), and possible occlusion. It presents a fast algorithm for estimating the B-spline control points that is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure based on the B-spline knot points introduced by Cohen et al. (1991). This method, however, can neither handle the affine transformation between the curves nor the occlusion. Solutions to these two problems are presented through the use of a new class of weighted B-spline curve moments that are well defined for both open and closed curves. The method has been applied to classifying affine-transformed aircraft silhouettes, and appears to perform well.

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There have been many techniques for curve shape representation and analysis, ranging from Fourier descriptors, to moments, to implicit polynomials, to differential geometry features, to time series models, to B-splines, etc. The B-splines stand as one of the most efficient curve (surface) representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controllability, and invariance to affine transformations. These properties made them very attractive for curve representation, and consequently, they have been extensively used in computer-aided design and computer graphics. Very little work, however, has been devoted to them for recognition purposes. One possible reason might be due to the fact that the B-spline curve is not uniquely described by a single set of parameters (control points), which made the curve matching (recognition) process difficult when comparing the respective parameters of the curves to be matched. This paper is an attempt to find matching solutions despite this limitation, and as such, it deals the problem of using B-splines for shape recognition and identification from curves, with an emphasis on the following applications: affine invariant matching and classification of 2-D curves with applications in identification of aircraft types based on image silhouettes and writer-identification based on handwritten text.

The role of neuroanatomical atlases is undergoing a significant redefinition as digital atlases become available. These have the potential to serve as more than passive guides and to hold the role of directing segmentation and multimodal fusion of experimental data. Key elements needed to support these new tasks are registration algorithms. For images derived from histological procedures, the need is for techniques to map the two-dimensional (2-D) images of the sectional material into the reference atlas which may be a full three-dimensional (3-D) data set or one consisting of a series of 2-D images. A variety of 2-D-2-D registration methods are available to align experimental images with the atlas once the corresponding plane of section through the atlas has been identified. Methods to automate the identification of the homologous plane, however, have not been previously reported. In this paper we use the external section contour to drive the identification and registration procedure. For this purpose, we model the contours by B-splines because of their attractive properties the most important of which are: 1) smoothness and continuity; 2) local controllability which implies that local changes in shape are confined to the B-spline parameters local to that change; 3) shape invariance under affine transformation, which means that the affine transformed curve is still a B-spline whose control points are related to the object control points through the transformation. In this paper we present a fast algorithm for estimating the control points of the B-spline which is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure that depends directly on the parameters of the B-spline. Performance tests are reported using histological material from rat brains.

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The aim of this work is to draw the attention of the biophotonics community to a stochastic decomposition method (SDM) to potentially model 2-D scans of light scattering data from epithelium mucosa tissue. The emphasis in this work is on the proposed model and its theoretical pinning and foundation. Unlike previous works that analyze scattering signal at one spot as a function of wavelength or angle, our method statistically analyzes 2-D scans of light scattering data over an area. This allows for the extraction of texture parameters that correlate with changes in tissue morphology, and physical characteristics such as changes in absorption and scattering characteristics secondary to disease, information that could not be revealed otherwise. The method is tested on simulations, phantom data, and on a limited preliminary in-vitro animal experiment to track mucosal tissue inflammation over time, using the area Az under receiver operating characteristics (ROC) curve as a performance measure. Combination of all the features results in an Az value up to 1 for the simulated data, and Az > 0.927 for the phantom data. For the tissue data, the best performances for differentiation between pairs of various levels of inflammation are 0.859, 0.983, and 0.999.