Fernand S. Cohen

Classification of rotated and scaled textured images using Gaussian Markov random field models

Consideration is given to the problem of classifying a test textured image that is obtained from one of C possible parent texture classes, after possibly applying unknown rotation and scale changes to the parent texture. The training texture images (parent classes) are modeled by Gaussian Markov random fields (GMRFs). To classify a rotated and scaled test texture, the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the GMRF. For the rotated and scaled image, a bona fide likelihood function that shows the explicit dependence of the likelihood function on the GMRF parameters, as well as on the rotation and scale parameters, is derived. Although, in general, the scaled and/or rotated texture does not correspond to a finite-order GMRF, it is possible nonetheless to write down a likelihood function for the image data. The likelihood function of the discrete Fourier transform of the image data corresponds to that of a white nonstationary Gaussian random field, with the variance at each pixel (i,j) being a known function of the rotation, the scale, the GMRF model parameters, and (i,j). The variance is an explicit function of the appropriately sampled power spectral density of the GMRF. The estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete Fourier transform of the image data. Cramer-Rao error bounds on the scale and rotation estimates are easily computed. A modified Bayes decision rule is used to classify a given test image into one of C possible texture classes. The classification power of the method is demonstrated through experimental results on natural textures from the Brodatz album. >

Automated inspection of textile fabrics using textural models

The authors discuss the problem of textile fabric inspection using the visual textural properties of the fabric. The problem is to detect and locate the various kinds of defects that might be present in a given fabric sample based on an image of the fabric. Stochastic models are used to model the visual fabric texture. The authors use the Gaussian Markov random field to model the texture image of nondefective fabric. The inspection problem is cast as a statistical hypothesis testing problem on statistics derived from the model. The image of the fabric patch to be inspected is partitioned into nonoverlapping windows of size N*N where each window is classified as defective or nondefective based on a likelihood ratio test of size alpha . The test is recast in terms of the sufficient statistics associated with the model parameters. The sufficient statistics are easily computable for any sample. The authors generalize the test when the model parameters of the fabric are assumed to be unknown. >

Invariant matching and identification of curves using B-splines curve representation

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.

Affine-invariant B-spline moments for curve matching

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.

Image registration and object recognition using affine invariants and convex hulls

This paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations and under possible occlusion and/or appearance of new objects. It presents a set of local absolute affine invariants derived from the convex hull of scattered feature points (e.g., fiducial or marking points, corner points, inflection points, etc.) extracted from the image. The affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices (quadruplets) of the convex hull, and hence do make direct use of the area invariance property associated with the affine transformation. Because they are locally constructed, they are very well suited to handle the occlusion and/or appearance of new objects. These invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them. A point matching approach for recognition follows this. The time complexity for registering L feature points on the test image with N feature points of the reference image is of order O(N x L). The method has been tested on real indoor and outdoor images and performs well.

Cross-weighted moments and affine invariants for image registration and matching

A framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross-weighted moments with fractional weights is presented. The fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise. Moreover, it makes it possible to arrive at low order (zero order) affine invariants that are more robust than those derived from higher order regular moments. The affine transformation parameters are recovered from the zero and the first order cross-weighted moments without requiring any feature point correspondence information. The equations used to find the affine transformation parameters are linear algebraic. The sensitivity of the cross-weighted moment invariants to noise, missing data, and perspective effects is shown on real images.

3-D face structure extraction and recognition from images using 3-D morphing and distance mapping

We describe a novel approach for creating a three-dimensional (3-D) face structure from multiple image views of a human face taken at a priori unknown poses by appropriately morphing a generic 3-D face. A cubic explicit polynomial in 3-D is used to morph a generic face into the specific face structure. The 3-D face structure allows for accurate pose estimation as well as the synthesis of virtual images to be matched with a test image for face identification. The estimation of a 3-D persons face and pose estimation is achieved through the use of a distance map metric. This distance map residual error (geometric-based face classifier) and the image intensity residual error are fused in identifying a person in the database from one or more arbitrary image view(s). Experimental results are shown on simulated data in the presence of noise, as well as for images of real faces, and promising results are obtained.

Maximum likelihood unsupervised textured image segmentation

Abstract This paper presents an algorithm for segmenting an image that is composed of an unknown number of regions c. In each region n, the image data gn are viewed as a realization from a homogeneous parametric random field with a class conditional density function p(gn|γn), where γnis an unknown parameter set. The number of regions c and the segmentation Sc are treated as unknown constants that are estimated using the maximum likelihood (ML) estimation principle. The ML estimates for c and Sc are obtained by maximizing log{p(g|Sc)} over all possible c and Sc. p(g|Sc) has the desirable property of unbiasedness; i.e., ESctrue{log{p(g|Sc)}} ≤ ESctrue {log{p(g|Sctrue)}. Unfortunately, it suffers from two limitations: (i) a closed-form analytic expression for p(g|Sc) for a given fixed c cannot be obtained in general, and (ii) in order to arrive at the optimum ( c ∗ , S c ∗ ) we must evaluate p(g|Sc) for all possible c and Sc, a most formidable task. This paper presents a solution to both problems that results into an optimum number of classes c ∗ ; an “optimum” window-based coarse segmentation S c ∗ of the image; and a ML estimate of the parameters Γ S ∗ c ∗ = (γ 1 , γ 2 , …, γ c ∗ ) of the c ∗ regions induced by S c ∗ . From this knowledge, the mixed windows (windows that fall between regions) are segmented further in a supervised mode (known parameter case) using the ML high-resolution segmentation developed by Cohen and Cooper (IEEE Trans. Pattern Anal. Mach. Intelligence Mar., 1987). The ML algorithm is applied to the problem of unsupervised segmentation of textured images of natural outdoor scenes.

Tissue characterization using the continuous wavelet transform. II. Application on breast RF data

For pt.I see ibid., vol.48, no.2, p.356-63 (2001). In the first part of this work (Georgiou and Cohen 2000), a wavelet-based decomposition algorithm of the RF echo into its coherent and diffuse components was introduced. In this paper, the proposed algorithm is used to estimate structural parameters of the breast tissue such as the number and energy of coherent scatterers, the energy of the diffuse scatterers, and the correlation between them. Based on these individual parameters, breast tissue characterization is performed. The database used consists of 155 breast scans from 42 patients. The results are presented in terms of empirical receiver operating characteristics (ROC) curves. The results of this study are discussed in relation to the tissue microstructure. Individual estimated parameters are able to differentiate reliably between normal and fibroadenoma or fibrocystic or cancerous tissue (area under the ROC A/sub z/>0.93). Also, the differentiation between malignant and benign (normal, fibrocystic, and fibroadenoma) tissue was possible (A/sub z/>0.89).

A maximum likelihood approach to segmenting range data

The problem of segmenting a range image into homogeneous regions in each of which the range data correspond to a different surface is considered. The segmentation sought is a maximum-likelihood (ML) segmentation. Only planes, cylinders, and spheres are considered as presented in the image. The basic approach to segmentation is to divide the range image into windows, classify each window as a particular surface primitive, and group like windows into surface regions. Mixed windows are detected by testing the hypothesis that a window is homogeneous. Homogeneous windows are classified according to a generalized likelihood ratio test which is computationally simple and incorporates information from adjacent windows. Grouping windows of the same surface types is cast as a weighted ML clustering problem. Finally, mixed windows are segmented using an ML hierarchical segmentation algorithm. A similar approach is taken for segmenting visible-light images of Lambertian objects illuminated by a point source at infinity. >