In this note, we analyze the geometric active contour models proposed in [10, 31] from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and efficiently to the desired feature. Moreover, we consider some 3-D active surface models based on these ideas. Key words: Active vision, shape and object representation, object recognition, active contours, snakes, visual tracking, edge detection, segmentation, gradient flows, Riemannian metrics, geometric heat equations, curve and surface evolution. Gradient Flows and Geometric Active Contour Models Abstract In this note, we analyze the geometric active contour models proposed in [10, 31] from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new m...

Leonard McMillan Jr. An Image-Based Approach to Three-Dimensional Computer Graphics (Under the direction of Gary Bishop) The conventional approach to three-dimensional computer graphics produces images from geometric scene descriptions by simulating the interaction of light with matter. My research explores an alternative approach that replaces the geometric scene description with perspective images and replaces the simulation process with data interpolation. I derive an image-warping equation that maps the visible points in a reference image to their correct positions in any desired view. This mapping from reference image to desired image is determined by the center-of-projection and pinhole-camera model of the two images and by a generalized disparity value associated with each point in the reference image. This generalized disparity value, which represents the structure of the scene, can be determined from point correspondences between multiple reference images. The image-warpi...

High contrast scenes are difficult to depict on low contrast displays without loss of important fine details and textures. Skilled artists preserve these details by drawing scene contents in coarseto-fine order using a hierarchy of scene boundaries and shadings. We build a similar hierarchy using multiple instances of a new low curvature image simplifier (LCIS), a partial differential equation inspired by anisotropic diffusion. Each LCIS reduces the scene to many smooth regions that are bounded by sharp gradient discontinuities, and a single parameter K chosen for each LCIS controls region size and boundary complexity. With a few chosen K values (K1>K2>K3:::) LCIS makes a set of progressively simpler images, and image differences form a hierarchy of increasingly important details, boundaries and large features. We construct a high detail, low contrast display image from this hierarchy by compressing only the large features, then adding back all small details. Unlike linear filter hierarchies such as wavelets, filter banks, or image pyramids, LCIS hierarchies do not smooth across scene boundaries, avoiding “halo ” artifacts common to previous contrast reducing methods and some tone reproduction operators. We demonstrate LCIS effectiveness on several example images.

Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a two-dimensional (2-D) surface in three-dimensional (3-D) space for gray-level images, and 2-D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms. Index Terms — Color image processing, image enhancement, image smoothing, nonlinear image diffusion, scale-space. I.

This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designing reaction-diusion equations for image processing. We start by studying the statistics of natural images including the scale invariant properties, then generic prior models were learned to duplicate the observed statistics, based on the minimax entropy theory studied in two previous papers. The resulting Gibbs distributions have potentials of the form U(I; ; S) = P K I)(x; y)) with S = fF g being a set of lters and = f the potential functions. The learned Gibbs distributions con rm and improve the form of existing prior models such as line-process, but in contrast to all previous models, inverted potentials (i.e. (x) decreasing as a function of jxj) were found to be necessary. We nd that the partial dierential equations given by gradient descent on U(I; ; S) are essentially reaction-diusion equations, where the usual energy terms produce anisotropic diusion while the inverted energy terms produce reaction associated with pattern formation, enhancing preferred image features. We illustrate how these models can be used for texture pattern rendering, denoising, image enhancement and clutter removal by careful choice of both prior and data models of this type, incorporating the appropriate features. Song Chun Zhu is now with the Computer Science Department, Stanford University, Stanford, CA 94305, and David Mumford is with the Division of Applied Mathematics, Brown University, Providence, RI 02912. This work started when the authors were at ...

Despite significant improvements in image quality over the past several years, the full exploitation of magnetic resonance image (MRI) data is often limited by low signal to noise ratio (SNR) or contrast to noise ratio (CNR). In implementing new MR techniques, the criteria of acquisition speed and image quality are usually paramount. To decrease noise during the acquisition either time averaging over repeated measurements or enlarging voxel volume may be employed. However these methods either substantially increase the overall acquisition time or scan a spatial volume in only coarse intervals. In contrast to acquisition-based noise reduction methods we propose a postprocess based on anisotropic diffusion. Extensions of this new technique support 3-D and multi-echo MRI, incorporating higher spatial and spectral dimensions. The procedure overcomes the major drawbacks of conventional filter methods, namely the blurring of object boundaries and the suppression of fine structural details. T...

In this paper, we present Brook for GPUs, a system for general-purpose computation on programmable graphics hardware. Brook extends C to include simple data-parallel constructs, enabling the use of the GPU as a streaming coprocessor. We present a compiler and runtime system that abstracts and virtualizes many aspects of graphics hardware. In addition, we present an analysis of the effectiveness of the GPU as a compute engine compared to the CPU, to determine when the GPU can outperform the CPU for a particular algorithm. We evaluate our system with five applications, the SAXPY and SGEMV BLAS operators, image segmentation, FFT, and ray tracing. For these applications, we demonstrate that our Brook implementations perform comparably to hand-written GPU code and up to seven times faster than their CPU counterparts.

Abstract—Diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, analyzing images at multiple scales, and enhancing discontinuities. A number of diffusions of image brightness have been defined and studied so far; they may be applied to scalar and vector-valued quantities that are naturally associated with intervals of either the real line, or other flat manifolds. Some quantities of interest in computer vision, and other areas of engineering that deal with images, are defined on curved manifolds; typical examples are orientation and hue that are defined on the circle. Generalizing brightness diffusions to orientation is not straightforward, especially in the case where a discrete implementation is sought. An example of what may go wrong is presented. A method is proposed to define diffusions of orientation-like quantities. First a definition in the continuum is discussed, then a discrete orientation diffusion is proposed. The behavior of such diffusions is explored both analytically and experimentally. It is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge-process and anisotropic diffusion. A number of open questions are proposed at the end. Index Terms—Orientation analysis, texture analysis, diffusions, scale-space.

In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.

We address the problem of building watertight 3D models from surfaces that contain holes---for example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation algorithms. Our solution begins by constructing a signed distance function, the zero set of which defines the surface. Initially, this function is defined only in the vicinity of observed surfaces. We then apply a diffusion process to extend this function through the volume until its zero set bridges whatever holes may be present. If additional information is available, such as known-empty regions of space inferred from the lines of sight to a 3D scanner, it can be incorporated into the diffusion process. Our algorithm is simple to implement, is guaranteed to produce manifold non-interpenetrating surfaces, and is efficient to run on large datasets because computation is limited to areas near holes. By showing results for complex range scans, we demonstrate that our algorithm produces hole-free surfaces that are plausible, visually acceptable, and usually close to the intended geometry.