CVGIP: Graphical Models and Image Processing最新文献

The human face is an elastic object. A natural paradigm for representing facial expressions is to form a complete 3D model of facial muscles and tissues. However, determining the actual parameter values for synthesizing and animating facial expressions is tedious; evaluating these parameters for facial expression analysis out of gray-level images is ahead of the state of the art in computer vision. Using only 2D face images and a small number of anchor points, we show that the method of radial basis functions provides a powerful mechanism for processing facial expressions. Although constructed specifically for facial expressions, our method is applicable to other elastic objects as well.

Expansion matching (EXM) is a novel method for template matching that optimizes a new similarity measure called discriminative signal-to-noise ratio (DSNR). Since EXM is designed to minimize off-center response, it yields results with very sharp matching peaks. EXM yields superior performance to the widely used correlation matching (also known as matched filtering), especially in conditions of noise, superposition, and severe occlusion. This paper presents an extended EXM formulation that matches multiple templates in the complex image domain. Complex template matching is useful in matching frequency domain templates and edge gradient images, and can be extended to multispectral images as well. Here, a single filter is designed to simultaneously match a set of given complex templates with optimal DSNR, while eliciting user-defined center responses for each template. It is shown that when the complex case is simplified to the case of matching a single real template, the result reduces exactly to the minimum squared error (MSE) restoration filter assuming the template as the blurring function. Here, we introduce a new generalized MSE restoration paradigm based on the analogy to multiple-template EXM. Furthermore, the output of the single-template EXM filter is also shown to be equivalent to a nonorthogonal expansion of the image with basis functions that are all shifted versions of the template. Experimental results prove that EXM is robust to minor rotation and scale distortions.

The most common approach for incorporating discontinuities in visual reconstruction problems makes use of Bayesian techniques, based on Markov random field models, coupled with stochastic relaxation and simulated annealing. Despite their convergence properties and flexibility in exploiting a priori knowledge on physical and geometric features of discontinuities, stochastic relaxation algorithms often present insurmountable computational complexity. Recently, considerable attention has been given to suboptimal deterministic algorithms, which can provide solutions with much lower computational costs. These algorithms consider the discontinuities implicitly rather than explicitly and have been mostly derived when there are no interactions between two or more discontinuities in the image model. In this paper we propose an algorithm that allows for interacting discontinuities, in order to exploit the constraint that discontinuities must be connected and thin. The algorithm, called E-GNC, can be considered an extension of the graduated nonconvexity (GNC), first proposed by Blake and Zisserman for noninteracting discontinuities. When applied to the problem of image reconstruction from sparse and noisy data, the method is shown to give satisfactory results with a low number of iterations.

This paper explores the local form of actual feature types contained in real images. The local energy feature detector is used to locate points in an image where features are found. An unsupervised neural network is trained to capture the mean luminance values and standard deviations of the luminance values in a small neighborhood of these feature points. This local luminance information is called a feature template. After culling and normalization, we arrive at a catalog of local feature forms for the image. Our experiments indicate that the feature forms are self-similar over different images and across scales. When described by their phase angle, features also show some clustering around a small number of types. The size of the feature catalog is small, and shows promising applications in the area of image compression and reconstruction. Quantization of phase angles around the central angles of clusters yields a catalog of synthetic feature templates that further improves the fidelity of the reconstructed images.

In this paper we examine the problem of reconstructing a (possibly dynamic) ellipsoid from its (possibly inconsistent) orthogonal silhouette projections. We present a particularly convenient representation of ellipsoids as elements of the vector space of symmetric matrices. The relationship between an ellipsoid and its orthogonal projections in this representation is linear, unlike the standard parameterization based on semiaxis length and orientation. This representation is used to completely and simply characterize the solutions to the reconstruction problem. The representation also allows the straightforward inclusion of geometric constraints on the reconstructed ellipsoid in the form of inner and outer bounds on recovered ellipsoid shape. The inclusion of a dynamic model with natural behavior, such as stretching, shrinking, and rotation, is similarly straightforward in this framework and results in the possibility of dynamic ellipsoid estimation. For example, the linear reconstruction of a dynamic ellipsoid from a single lower-dimensional projection observed over time is possible. Numerical examples are provided to illustrate these points.

A simple technique to visualize the isosurfaces extracted from a cell-based volumetric dataset using the Marching Cubes algorithm is proposed. The technique exploits the intrinsic ordering of the triangles produced by the surface extraction algorithm by adopting a Back-to-Front visualization technique. The use of the technique together with the adoption of a simple shading algorithm permits the rendering of high resolution volumetric datasets in computational environments with limited capabilities in terms of memory and graphics hardware.

Pattern models for the analysis, visualization, and compression of experimental 2-D flow imagery are developed. These models are based on the 2-D linear phase portrait, and consist of a superposition of flow primitives that are equivalent to the canonical form of phase portraits. The phase portrait is a compact flow descriptor specified by a 2 × 2 A matrix, and it provides for classification into one of six possible patterns based on the matrix eigenvalues. The modeling requires computation of the orientation field, critical point detection, and estimation of the associated phase portraits as preliminary analysis steps. Existing methods to compute the orientation field that are appropriate for highly textured images are employed, but a technique for its computation in weakly textured imagery is included. Critical points are located with a detector that is based on the index (or winding number) of a vector field. A performance analysis of the detector is included. A linear least-squares method of estimating the phase portrait A matrix from the orientation field is presented. Flows are then modeled as a superposition of primitives, where their associated strengths are determined from the orientation field. This modeling works well for flows that exhibit nearly ideal behavior. Finally, the derived models are employed to compress scalar images that exhibit little or gradual variation along the flow streamlines. Compression ratios on the order of 100: 1 are achieved.

Nonuniform B-splines are usually computed using the traditional recurrence relation $\text{B}{}_{\mathrm{i,r}}\text{(}\text{u}\text{) =}\text{u}{}_{\mathrm{i}}\text{−}\text{u}\text{u}{}_{\mathrm{i+r-1}}\text{−}\text{u}{}_{\mathrm{i}}\text{Bi,}{}_{\mathrm{r-1}}\text{(}\text{u}\text{) +}\text{u}{}_{\mathrm{i+r}}\text{−}\text{u}\text{u}{}_{\mathrm{i+r}}\text{−}\text{u}{}_{\mathrm{i+1}}\text{B}{}_{\mathrm{i+1,r-1}}\text{(}\text{u}\text{).}$We derive a recurrence relation which relates the rth derivative of B_i,r(ū) to the (r − 1)th derivatives of B_i,r−1($\text{u}$) and B_{i + 1, r − 1}$\text{u}$[formula]B^(r)_{i, r}($\text{u}$) is comprised of r + 1 impulses (Dirac functions) at the knots [ū_i, ū_{i + 1}, . . . , ū_{i + r}]. The amplitudes of the impulses are found from the recurrence. We show that equally spaced samples of the continuous B-spline function B_{i, r}(ū) can be computed exactly using recursive summation.

The existence of the implicit equation of rational surfaces can be proved by three techniques: elimination theory, undetermined coefficients, and the theory of field extensions. The methods of elimination theory and undetermined coefficients also reveal that the implicit equation can be written with coefficients from the coefficient field of the parametric polynomials. All three techniques can be implemented as implicitization algorithms. For each method, the theoretical limitations of the proof and the practical advantages and disadvantages of the algorithm are discussed. Our results are important for two reasons. First, we caution that elimination theory cannot be generalized in a straightforward manner from rational plane curves to rational surfaces to show the existence of the implicit equation; thus other rigorous methods are necessary to bypass the vanishing of the resultant in the presence of base points. Second, as an immediate consequence of the coefficient relationship, we see that the implicit representation involves only rational (or real) coefficients if a parametric representation involves only rational (or real) coefficients. The existence of the implicit equation means every rational surface is a subset of an irreducible algebraic surface. The subset relation can be proper and this may cause problems in certain applications in computer aided geometric design. This anomaly is illustrated by an example.

We present the algebraic specification of a prototype interactive geometric modeler for 3D objects, whose topologies are represented by 3-dimensional generalized maps. After a reminder of some topological models, particularly maps and extensions, we begin with the more general frame of n-dimensional hypermaps. We specify algebraically a hierarchy of operations on hypermaps and generalized maps, which are embedded in a 3-dimensional Euclidean space. We make precise the modeling area and give the main functionalities of the modeler. We detail high-level operations on 3D objects, and some technical features of this software. Some constructions are explained using pictures. We show that hypermaps and algebraic specification constitute an efficient formal frame for developing large pieces of software in the area of boundary representation.