Characterizing the response of the brain to a stimulus based on functional magnetic resonance imaging data is a major challenge due to the fact that the response time delay of the brain may be different from one stimulus phase to the next and from pixel to pixel. To enhance detectability, this work introduces the use of a curve evolution approach that provides separate estimates of the response time shifts at each phase of the stimulus on a pixel-by-pixel basis. The approach relies on a parsimonious but simple model that is nonlinear in the time shifts of the response relative to the stimulus and linear in the gains. To effectively use the response time shift estimates in a subspace detection framework, we implement a robust hypothesis test based on a Laplacian noise model. The algorithm provides a pixel-by-pixel functional characterization of the brain's response. The results based on experimental data show that response time shift estimates, when properly implemented, enhance detectability without sacrificing robustness.

A system of coupled differential equations is formulated which learns priors for modelling "preattentive" textures. It is derived from an energy functional consisting of a linear combination of a large number of terms corresponding to the features that the system is capable of learning. The system learns the parameters associated with each feature by applying gradient ascent to the log-likelihood function. Update of each parameter is thus governed by the residual with respect to the corresponding feature. A feature residual is computed from its observed value and value generated by the system. The latter is calculated from a synthesized sample image, which is generated by means of a reaction-diffusion equation obtained by applying gradient descent to the energy functional.

Motivated by a need to define an object-centered reference system determined by the most salient characteristics of the shape, many methods have been proposed, all of which directly or indirectly involve an axis about which the shape is locally symmetric. Recently, a function /spl upsi/, called "the edge strength function", has been successfully used to determine efficiently the axes of local symmetries of 2-d shapes. The level curves of /spl upsi/ are interpreted as successively smoother versions of the initial shape boundary. The local minima of the absolute gradient /spl par//spl nabla//spl upsi//spl par/ along the level curves of /spl upsi/ are shown to be a robust criterion for determining the shape skeleton. More generally, at an extremal point of /spl par//spl nabla//spl upsi//spl par/ along a level curve, the level curve is locally symmetric with respect to the gradient vector /spl nabla//spl upsi/. That is, at such a point, the level curve is approximately a conic section whose one of the principal axes coincides with the gradient vector. Thus, the locus of the extremal points of /spl par//spl nabla//spl upsi//spl par/ along the level curves determines the axes of local symmetries of the shape. In this paper, we extend this method to shapes of arbitrary dimension.

Segmentation of anatomic structures of the human brain from MR images is important for assessing treatment efficacy, screening for anomalies, and improving our understanding of human development. The labor intensive nature of manual segmentation, however, makes such a technique viable only in selected cases. In this paper we present a new approach to segmentation that involves only minimal human interactions. The technique utilizes a variational formulation to obtain an edge-strength function over the region of interest, and uses curve evolution and a pre-segmented atlas to guide the actual segmentation process. The approach is demonstrated via both phantoms and actual MR images, and when applied to the lateral ventricles and caudate nucleus, showed a size accuracy error of 5%–20% with respect to manual segmentation, depending on the manual segmentation method utilized.

In recent years, curve evolution has developed into an important tool in Computer Vision and has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. The underlying principle is the evolution of a simple closed curve whose points move in the direction of the normal with prescribed velocity. A fundamental limitation of the method as it stands is that it cannot deal with important image features such as triple points. The method also requires a choice of an "edge-strength" function, defined over the image domain. Indicating the likelihood of an object boundary being present at any point in the image domain. This implies a separate preprocessing step, in essence precomputing approximate boundaries in the presence of noise. One also has to choose the initial curve. It is shown here that the different versions of curve evolution used in Computer Vision together with the preprocessing step can be integrated in the form of a new segmentation functional which overcomes these limitations and extends curve evolution models. Moreover, the numerical solutions obtained retain sharp discontinuities or "shocks", thus providing sharp demarcation of object boundaries.

This work provides a variational framework for fusing range and intensity data for recovering regularized surfaces. It is shown that this framework provides natural boundary conditions for the shape-from-shading problem, results in a new shape-from-shading formulation in the absence of range data, and provides a new fusion paradigm when range data is incorporated. The approach is demonstrated on simulated range and intensity images; error analysis with respect to the ground truth surface is presented. It is shown that the formulation performs well even in very noisy images.

Most stereo algorithms do not take into account discontinuities in disparity and the fact that there are half-occlusions consisting of areas seen by one eye but not the other. Very few are formulated using the framework of energy functionals. A formulation that lies within such a framework and addresses the discontinuities and half-occlusions is presented. The formulation follows directly from the assumption that, when matching the left and right images, the order of points must be preserved. A model consisting of two coupled energy functions, corresponding to the two eyes, is presented. They are coupled in the sense that the discontinuity locus determined by one eye also determines the occluded area in the image seen by the other eye. A nonlinear system of diffusion equations is derived by simultaneously applying gradient descent to these functionals. The diffusion equations are implemented by a finite-difference scheme.>

An algorithm that systematically uses nonuniform smoothing to find boundary components in the form of connected, regularized curves is presented. The boundary, represented by a variable continuously defined over the image domain, as well as the smoothing of the image are determined by a nonlinear system of diffusion equations. Nonlinear diffusion is used again to threshold the boundary variable to produce the actual object boundaries. Laplacians of smoothed gradients are the main tool used. Nonuniform smoothing permits the use of multiple smoothings and the use of derivatives of up to order six.>

A global model which integrates three sequential steps for segmenting an image, namely, noise-filtering, local edge-detection, and integration of local edges into object boundaries, is described. The model overcomes some of the difficulties inherent in earlier global models, particularly their tendency to oversegment, and the lack of practical numerical algorithms for implementing them. The model consists of two coupled elliptic functionals, one for smoothing out the noise, and the other for boundary detection. The latter is obtained by regularizing the usual pointwise thresholding employed for boundary detection. The first variation of these functionals leads to coupled system of diffusion equations which are implemented by a simple finite difference scheme. The scheme may easily be converted into a parallel algorithm.>

The author analyzes basic problems of image segmentation-edge detection, elimination of weak boundaries and small segments, and multiscale representation-in the context of all energy-minimizing model. He discusses two general frameworks for finding approximate solutions, the split-and-merge algorithm based on energy criteria, and nonlinear diffusion. The difficulty with the split-and-merge algorithm considered is that unless further approximations are introduced, it does not have an easy parallel implementation. The idea of the alternative approach, based on nonlinear diffusion, is to produce first only a blurred version of the discontinuities of f (the smoothed image which need not be continuous across the segmenting curve) in the hope of controlling the extent of the smoothing of small domains and then to refine the approximate solution by the method of steepest descent. Thus, the method sets thresholds only indirectly.>