This paper presents an axiomatic approach to corner detection. In the first part of the paper we review five currently used corner detection methods (Harris-Stephens, Forstner, Shi-Tomasi, Rohr, and Kenney et al ) for graylevel images. This is followed by a discussion of extending these corner detectors to images with different pixel dimensions such as signals (pixel dimension one) and tomographic medical images (pixel dimension three) as well as different intensity dimensions such as color or LADAR images (intensity dimension three). These extensions are motivated by analyzing a particular example of optical flow in pixel and intensity space with arbitrary dimensions. Placing corner detection in a general setting enables us to state four axioms that any corner detector might reasonably be required to satisfy. Our main result is that only the Shi-Tomasi (and equivalently the Kenney et al. 2-norm detector) satisfy all four of the axioms.

A RANSAC based procedure is described for detecting inliers corresponding to multiple models in a given set of data points. The algorithm we present in this paper (called multiRANSAC) on average performs better than traditional approaches based on the sequential application of a standard RANSAC algorithm followed by the removal of the detected set of inliers. We illustrate the effectiveness of our approach on a synthetic example and apply it to the problem of identifying multiple world planes in pairs of images containing dominant planar structures.

In this paper we present a new physically motivated curve descriptor based on the solution of Helmholtz’s equation. The descriptor satisfies the six principles set by MPEG-7: it has a good retrieval accuracy, it is compact, it can be applied in general contexts, it has a reasonable computational complexity, it is robust and provides an hierarchical representation of the curve from coarse to fine. Moreover this descriptor generalizes straightforwardly to three dimensional surfaces. We tested the performance of the descriptor in the context of affine invariant curve matching using the multiview curve dataset (MCD), which consists of 40 curves (extracted from the MPEG-7 shape dataset) imaged under 14 different points of view. The results we obtained show that the proposed descriptor satisfies the MPEG-7 requirements and presents some advantages over some of the commonly used curve descriptors. 1

In this paper, we propose, an affine-invariant-method for describing and matching curves. This is important since affine transformations are often used to model perspective distortions. More specifically, we propose a new definition of the shape of a curve that characterizes a curve independently of the effects introduced by affine distortions. By combining this definition with a rotation-invariant shape descriptor, we show how it is possible to describe a curve in an intrinsically affine-invariant manner. To validate our procedure we built a database of shapes subject to perspective distortions and plotted the precision-recall curve for this dataset. Finally an application of our method is shown in the context of wide baseline matching.

A novel scheme for image segmentation is presented. An image segmentation criterion is proposed that groups similar pixels together to form regions. This criterion is formulated as a cost function. Using gradient-descent methods, which lead to a curve evolution equation that segments the image into multiple homogenous regions, minimizes this cost function. Homogeneity is specified through a pixel-to-pixel similarity measure, which is defined by the user and can be adaptive based on the current application. To improve the performance of the system, an edge function is also used to adjust the speed of the competing curves. The proposed method can be easily applied to vector valued images such as texture and color images without a significant addition to computational complexity.

Selecting salient points from two or more images for computing correspondence is a well-studied problem in image analysis. This paper describes a new and effective technique for selecting these tiepoints using condition numbers, with application to image registration and mosaicking. Condition numbers are derived for point-matching methods based on minimizing windowed objective functions for 1) translation, 2) rotation-scaling-translation (RST), and 3) affine transformations. Our principal result is that the condition numbers satisfy K/sub Trans/ /spl les/ K/sub RST/ /spl les/ K/sub Affine/. That is, if a point is ill-conditioned with respect to point-matching via translation, then it is also unsuited for matching with respect to RST and affine transforms. This is fortunate since K/sub Trans/ is easily computed whereas K/sub RST/ and K/sub Affine/ are not. The second half of the paper applies the condition estimation results to the problem of identifying tiepoints in pairs of images for the purpose of registration. Once these points have been matched (after culling outliers using a RANSAC-like procedure), the registration parameters are computed. The postregistration error between the reference image and the stabilized image is then estimated by evaluating the translation between these images at points exhibiting good conditioning with respect to translation. The proposed method of tiepoint selection and matching using condition number provides a reliable basis for registration. The method has been tested on a large number of diverse collection of images - multidate Landsat images, aerial images, aerial videos, and infrared images. A Web site where the users can try our registration software is available and is being actively used by researchers around the world.

An image segmentation scheme that utilizes image-based flow fields in a curve evolution framework is presented. Geometric curve evolution methods require an edge function and a vector field with certain characteristics that are obtained from the image itself. A vector field borrowed from the edgeflow segmentation (Ma and Manjunath 2000) method is utilized both to obtain an edge function and to guide the curve evolution towards the object boundaries. This vector field is computed from the image using intensity, texture and color features. The proposed method integrates well-tested image features with the well-studied curve evolution methods thus achieving better segmentation results.

Describes a system for automatic and semi-automatic registration/mosaic of remote sensing images. Information provided by the user can be used to speed up processing or to avoid mismatched control points. A statistical procedure is used to characterize good and bad registrations. Based on this "good fit-bad fit" statistical test the user can stop, modify the parameters, or continue the processing. Several tests have been performed by registering optical, radar, multi-sensor, high-resolution images and video sequences. We have included very difficult image registration examples in order to show the strengths and limits of our system. An online registration system demo containing several examples can be executed using a Web browser.

A compact color descriptor and an efficient indexing method for this descriptor are presented. The target application is similarity retrieval in large image databases using color. Colors in a given region are clustered into a small number of representative colors. The feature descriptor consists of the representative colors and their percentages in the region. A similarity measure similar to the quadratic color histogram distance measure is defined for this descriptor. The representative colors can be indexed in the three-dimensional (3-D) color space thus avoiding the high-dimensional indexing problems associated with the traditional color histogram. For similarity retrieval, each representative color in the query image or region is used independently to find regions containing that color. The matches from all of the query colors are then combined to obtain the final retrievals. An efficient indexing scheme for fast retrieval is presented. Experimental results show that this compact descriptor is effective and compares favorably with the traditional color histogram in terms of overall computational complexity.

Peer group image processing identifies a "peer group" for each pixel and then replaces the pixel intensity with the average over the peer group. Two parameters provide direct control over which image features are selectively enhanced: area (number of pixels in the feature) and window diameter (window size needed to enclose the feature). A discussion is given of how these parameters determine which features in the image are smoothed or preserved. We show that the Fisher discriminant can be used to automatically adjust the peer group averaging (PGA) parameters at each point in the image. This local parameter selection allows smoothing over uniform regions while preserving features like corners and edges. This adaptive procedure extends to multilevel and color forms of PGA. Comparisons are made with a variety of standard filtering techniques and an analysis is given of computational complexity and convergence issues.

A general variational framework for image approximation and segmentation is introduced. By using a continuous "line-process" to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Application is made to Mumford-Shah type functionals as well as those considered by Geman and others. Employing arbitrary Lp norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function that minimizes the associated objective functional for a given approximation function can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation (PDE) descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.

We review and present examples for two new image processing methods based on scale space evolution under partial differential operators. These operators arise from minimizing variational objective functions and from a novel approach that respects the discrete nature of real images. The first method considered is a variational approach that provides a closed-form expression for the optimal boundary function. This method gives good results with a 2-norm penalty term for approximation error and a 1-norm smoothness term; in this case there is a strong connection with total variation methods. The second method is a peer group averaging approach (developed by Hewer et al.) that smooths the image without blurring edges. This is accomplished by averaging over window pixels with nearly the same intensity; these pixels are the 'peer group' of the window's central pixel. The direct correspondence between the object characteristics and the parameters of peer group size and window diameter make the parameter selection easier for peer group averaging than for standard variational methods. These methods are used in combination with PGA providing the initial approximation for the variational descent procedure. This is applied to real image examples and compared to existing methods including a new level-set histogram modification method (developed by Caselles et al. (see Hewlett Packard Technical Report HPL97-58, 1997)) that treats connected level-sets of pixels as individual units.

A general variational framework for image approximation and segmentation is introduced in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Since the optimal boundary function, that minimizes the associated objective functional for a given approximation function, can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.