Showing papers on "Kernel (image processing) published in 2002"

Background and foreground modeling using nonparametric kernel density estimation for visual surveillance

Abstract: Automatic understanding of events happening at a site is the ultimate goal for many visual surveillance systems. Higher level understanding of events requires that certain lower level computer vision tasks be performed. These may include detection of unusual motion, tracking targets, labeling body parts, and understanding the interactions between people. To achieve many of these tasks, it is necessary to build representations of the appearance of objects in the scene. This paper focuses on two issues related to this problem. First, we construct a statistical representation of the scene background that supports sensitive detection of moving objects in the scene, but is robust to clutter arising out of natural scene variations. Second, we build statistical representations of the foreground regions (moving objects) that support their tracking and support occlusion reasoning. The probability density functions (pdfs) associated with the background and foreground are likely to vary from image to image and will not in general have a known parametric form. We accordingly utilize general nonparametric kernel density estimation techniques for building these statistical representations of the background and the foreground. These techniques estimate the pdf directly from the data without any assumptions about the underlying distributions. Example results from applications are presented.

Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions

Abstract: We present an efficient algorithm to solve a class of two- and 25-dimensional (2-D and 25-D) Fredholm integrals of the first kind with a tensor product structure and nonnegativity constraint on the estimated parameters of interest in an optimization framework A zeroth-order regularization functional is used to incorporate a priori information about the smoothness of the parameters into the problem formulation We adapt the Butler-Reeds-Dawson (1981) algorithm to solve this optimization problem in three steps In the first step, the data are compressed using singular value decomposition (SVD) of the kernels The tensor-product structure of the kernel is exploited so that the compressed data is typically a thousand fold smaller than the original data This size reduction is crucial for fast optimization In the second step, the constrained optimization problem is transformed to an unconstrained optimization problem in the compressed data space In the third step, a suboptimal value of the smoothing parameter is chosen by the BRD method Steps 2 and 3 are iterated until convergence of the algorithm We demonstrate the performance of the algorithm on simulated data

Space and Space-Time Modeling using Process Convolutions

Abstract: A continuous spatial model can be constructed by convolving a very simple, perhaps independent, process with a kernel or point spread function. This approach for constructing a spatial process offers a number of advantages over specification through a spatial covariogram. In particular, this process convolution specification leads to computational simplifications and easily extends beyond simple stationary models. This paper uses process convolution models to build space and space-time models that are flexible and able to accommodate large amounts of data. Data from environmental monitoring is considered.

Kernels for Semi-Structured Data

Abstract: Semi-structured data such as XML and HTML is attracting considerable attention. It is important to develop various kinds of data mining techniques that can handle semistructured data. In this paper, we discuss applications of kernel methods for semistructured data. We model semi-structured data by labeled ordered trees, and present kernels for classifying labeled ordered trees based on their tag structures by generalizing the convolution kernel for parse trees introduced by Collins and Duffy (2001). We give algorithms to efficiently compute the kernels for labeled ordered trees. We also apply our kernels to node marking problems that are special cases of information extraction from trees. Preliminary experiments using artificial data and real HTML documents show encouraging results.

Path Kernels and Multiplicative Updates

Abstract: We consider a natural convolution kernel defined by a directed graph. Each edge contributes an input. The inputs along a path form a product and the products for all paths are summed. We also have a set of probabilities on the edges so that the outflow from each node is one. We then discuss multiplicative updates on these graphs where the prediction is essentially a kernel computation and the update contributes a factor to each edge. Now the total outflow out of each node is not one any more. However some clever algorithms re-normalize the weights on the paths so that the total outflow out of each node is one again. Finally we discuss the use of regular expressions for speeding up the kernel and re-normalization computation. In particular we rewrite the multiplicative algorithms that predict as well as the best pruning of a series parallel graph in terms of efficient kernel computations.

Spectral Partitioning with Indefinite Kernels Using the Nyström Extension

Abstract: Fowlkes et al. [7] recently introduced an approximation to the Normalized Cut (NCut) grouping algorithm [18] based on random subsampling and the Nystrom extension. As presented, their method is restricted to the case where W, the weighted adjacency matrix, is positive definite. Although many common measures of image similarity (i.e. kernels) are positive definite, a popular example being Gaussian-weighted distance, there are important cases that are not. In this work, we present a modification to Nystrom-NCut that does not require W to be positive definite. The modification only affects the orthogonalization step, and in doing so it necessitates one additional O(m3) operation, where m is the number of random samples used in the approximation. As such it is of interest to know which kernels are positive definite and which are indefinite. In addressing this issue, we further develop connections between NCut and related methods in the kernel machines literature. We provide a proof that the Gaussian-weighted chi-squared kernel is positive definite, which has thus far only been conjectured. We also explore the performance of the approximation algorithm on a variety of grouping cues including contour, color and texture.

A fluence-convolution method to calculate radiation therapy dose distributions that incorporate random set-up error.

Abstract: The International Commission on Radiation Units and Measurements Report 62 (ICRU 1999) introduced the concept of expanding the clinical target volume (CTV) to form the planning target volume by a two-step process. The first step is adding a clinically definable internal margin, which produces an internal target volume that accounts for the size, shape and position of the CTV in relation to anatomical reference points. The second is the use of a set-up margin (SM) that incorporates the uncertainties of patient beam positioning, i.e. systematic and random set-up errors. We propose to replace the random set-up error component of the SM by explicitly incorporating the random set-up error into the dose-calculation model by convolving the incident photon beam fluence with a Gaussian set-up error kernel. This fluence-convolution method was implemented into a Monte Carlo (MC) based treatment-planning system. Also implemented for comparison purposes was a dose-matrix-convolution algorithm similar to that described by Leong (1987 Phys. Med. Biol. 32 327–34). Fluence and dose-matrix-convolution agree in homogeneous media. However, for the heterogeneous phantom calculations, discrepancies of up to 5% in the dose profiles were observed with a 0.4 cm set-up error value. Fluence-convolution mimics reality more closely, as dose perturbations at interfaces are correctly predicted (Wang et al 1999 Med. Phys. 26 2626–34, Sauer 1995 Med. Phys. 22 1685–90). Fluence-convolution effectively decouples the treatment beams from the patient, and more closely resembles the reality of particle fluence distributions for many individual beam-patient set-ups. However, dose-matrix-convolution reduces the random statistical noise in MC calculations. Fluence-convolution can easily be applied to convolution/superposition based dose-calculation algorithms.

Implementation of steerable spatiotemporal image filters on the focal plane

Abstract: This paper presents an architectural overview of a pseudogeneral image processor (GIP) chip for realizing steerable spatial and temporal filters at the focal-plane. The convolution of the image with programmable kernels is realized with area-efficient and real-time circuits. The chip's architecture allows photoreceptor cells to be small and densely packed by performing all analog computations on the read-out, away from the array. The size, configuration, and coefficients of the kernels can be varied on the fly. In addition to the raw intensity image, the chip outputs four processed images in parallel. The convolution is implemented with a digitally programmable analog processor, resulting in very low-power consumption at high-computation rates. A 16/spl times/16 pixels prototype of the GIP has been fabricated in a standard 1.2-/spl mu/m CMOS process and its spatiotemporal capabilities have been successfully tested. The chip exhibits 1 GOPS/mW at 20 kft/s while computing four spatiotemporal convolutions in parallel.

Face recognition using kernel fisherfaces

Abstract: A face recognition system and method project an input face image and a set of reference face images from an input space to a high dimensional feature space in order to obtain more representative features of the face images. The Kernel Fisherfaces of the input face image and the reference face images are calculated, and are used to project the input face image and the reference face images to a face image space lower in dimension than the input space and the high dimensional feature space. The input face image and the reference face images are represented as points in the face image space, and the distance between the input face point and each of the reference image points are used to determine whether or not the input face image resembles a particular face image of the reference face images.

On the equivalence of local-mode finding, robust estimation and mean-shift analysis as used in early vision tasks

Abstract: In this paper we show the equivalence of three techniques used in image processing: local-mode finding, robust-estimation and mean-shift analysis. The computational common element in all these image operators is the spatial-tonal normalized convolution, an image operator that generalizes the bilateral filter.

Estimation of blur and noise parameters in remote sensing

Abstract: In this paper we propose a new algorithm to estimate the parameters of the noise related to the sensor and the impulse response of the optical system, from a blurred and noisy satellite or aerial image. The noise is supposed to be white, Gaussian and stationary. The blurring kernel has a parametric form and is modeled in such a way as to take into account the physics of the system (the atmosphere, the optics and the sensor). The observed scene is described by a fractal model, taking into account the scale invariance properties of natural images. The estimation is performed automatically by maximizing a marginalized likelihood, which is achieved by a deterministic algorithm whose complexity is limited to O (N), where N is the number of pixels.

Properties of the Catadioptric Fundamental Matrix

Abstract: The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the subject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear constraint on transformed image coordinates in two parabolic catadioptric views involving what we call the catadioptric fundamental matrix. We prove that the angle between corresponding epipolar curves is preserved and that the transformed image of the absolute conic is in the kernel of that matrix, thus enabling a Euclidean reconstruction from two views. We establish the necessary and sufficient conditions for a matrix to be a catadioptric fundamental matrix.

Image Kernels

Abstract: In this paper we discuss the mathematical properties of a few kernels specifically constructed for dealing with image data in binary classification and novelty detection problems. First, we show that histogram intersection is a Mercer's kernel. Then, we show that a similarity measure based on the notion of Hausdorff distance and directly applicable to raw images, though not a Mercer's kernel, is a kernel for novelty detection. Both kernels appear to be well suited for building effective vision-based learning systems.

Convolution surfaces for line skeletons with polynomial weight distributions

Abstract: Convolution surfaces generalize point-based implicit surfaces to incorporate higher-dimensional skeletal elements; line segments can be considered the most fundamental skeletal elements since they can approximate curve skeletons. Existing analytical models for line-segment skeletons assume uniform weight distributions, and thus they can produce only constant-radius convolution surfaces. This paper presents an analytical solution for convolving line-segment skeletons with a variable kernel modulated by a polynomial function, allowing generalized cylindrical convolution surfaces to be modeled conveniently. Its computational requirement is competitive with that of uniform weight distribution. The source code of the field computation is available online.

Implementation of algorithm to decode two-dimensional barcode PDF-417

Abstract: We present a barcode reader to decode two-dimensional symbology PDF-417 and propose a novel method to extract the bar-space patterns directly from the gray-level barcode image, which employs the location and the distance between extreme points of each row of the barcode image. This algorithm proves to be very robust for high convolution distortion environments such as defocussing and warping, even under bad illumination conditions. If the scanned barcode image is a result of the convolution of a Gaussian-shaped point spread function with a bilevel image, popular image segmentation methods such as image thresholding cannot distinguish between very narrow bar-space patterns which are a couple of pixels wide. The proposed algorithm shows improved performance over current barcode readers.

Convolution surfaces for arcs and quadratic curves with a varying kernel

Abstract: A convolution surface is an isosurface in a scalar field defined by convolving a skeleton, comprising of points, curves, surfaces, or volumes, with a potential function. While convolution surfaces are attractive for modeling natural phenomena and objects of complex evolving topology, the analytical evaluation of integrals of convolution models still poses some open problems. This paper presents some novel analytical convolution solutions for arcs and quadratic spline curves with a varying kernel. In addition, we approximate planar higher-degree polynomial spline curves by optimal arc splines within a prescribed tolerance and sum the potential functions of all the arc primitives to approximate the field for the entire spline curve.

High speed signal enhancement using pixons

Abstract: Input data comprising a video signal is processed using a combination of a known image processing method to deblur, or sharpen, the image and convolution with Pixon™ kernels for smoothing. The smoothing process utilizes a plurality of different size Pixon™ kernels which operate in parallel so that the input data are convolved with each different Pixon™ kernel simultaneously. The smoothed image is convolved with the point response function (PRF) to form data models that are compared against the input data, then the broadest Pixon™ kernel that fits the input data within a predetermined criterion are selected to form a Pixon™ map. The data are smoothed and assembled according to the Pixon™ map, then are deconvolved and output to a video display or other appropriate device, providing a clearer image with less noise.

A GPU-Based, Three-Dimensional Level Set Solver with Curvature Flow

Abstract: Author(s): Lefohn, Aaron; Whitaker, Ross T. | Abstract: Level set methods are a powerful tool for implicitly representing deformable surfaces. Since their inception, these techniques have been used to solve problems in fields as varied as computer vision, scientific visualization, computer graphics and computational physics. With the power and flexibility of this approach; however, comes a large computational burden. In the level set approach, surface motion is computed via a partial differential equation (PDE) framework. One possibility for accelerating level-set based applications is to map the solver kernel onto a commodity graphics processing unit (GPU). GPUs are parallel, vector computers whose power is currently increasing at a faster rate than that of CPUs. in this work, we demonstrate a GPU-based, three-dimensional level set solver that is capable of computing curvature flow as well as other speed terms. Results are shown for this solver segmenting the brain surface from an MRI data set.

Method and apparatus implementing an overlay adaptive frequency hopping kernel in a wireless communication system

Abstract: A novel method and apparatus for implementing an overlay adaptive frequency-hopping kernel in a wireless communication system is described. The present inventive method and apparatus selects hopping frequencies based on channel conditions. Hopping frequencies are selected using an inventive overlay adaptive frequency-hopping (OAFH) kernel that maps bad channels to good channels while retaining the pseudo-random properties of the original frequency-hopping sequence. The OAFH kernel uses existing FH kernels to initially select hopping frequencies. If the initially selected hopping frequency has bad channel condition characteristics, the OAFH kernel maps the initially selected hopping frequency to a substitute hopping frequency having good channel condition characteristics.

Method and system for using an image based autofocus algorithm

Abstract: An image based autofocus method and system that includes receiving image data; monitoring and analyzing the contrast between different portions of the image data in determining the location of a target wherein the different portions of the image data contain at least one type of image pixel information and the monitoring and analyzing are performed using at least one kernel filter to determine a focus measure; adjusting a focus mechanism that is focusing on the image data; observing an image quality of the image data that has been focused; and continuously outputting an image to support an image processing frame rate and adjusting the focus mechanism to obtain an improved focus image by adjusting the focus mechanism in a positive direction, a negative direction or a zero (0) direction based upon effectuating a desired change in the observed image quality of the image data.

Elastic transformation of the image pixel grid for similarity based face identification

Abstract: Nonlinear transformation of one image plane relative to another by spatially constrained elastic matching of two pixel grids is proposed as a technique of measuring image similarity for the purpose of featureless face identification. The elastic matching algorithm is devised as a combination of two dynamic programming procedures applied independently to each row and then to each column of the pixel grid. In contrast to the commonly adopted method of measuring face image similarity based on the dynamic link architecture, the proposed method is non-iterative and it avoids image segmentation. Most importantly the method provides the linear computational complexity with respect to the number of pixels without application of parallel computers.

Application-level access to kernel input/output state

Abstract: A technique for tracking a state of one or more input/output (I/O) channels associated with an application, by the application itself, comprises the steps of: (i) storing, by an operating system kernel, one or more selected elements of the state of at least a portion of the one or more I/O channels associated with the application in a memory which is shared by the application and the operating system kernel, when the one or more elements are available to the operating system kernel; (ii) acquiring, by the application, at least a portion of the stored elements through one or more memory read operations of the shared memory; and (iii) assessing, by the application, one or more of the acquired elements to determine the state of the one or more I/O channels corresponding thereto. In this manner, a need for context switching to track the state of the one or more I/O channels is thereby eliminated.

Speed versus accuracy in a fast convolution photon dose calculation for conformal radiotherapy.

Abstract: A convolution dose calculation for megavoltage photon beams is described and the compromise between speed and accuracy examined. The algorithm is suitable for treatment planning optimization, where the need is for a fast, flexible method requiring minimal beam data but providing an accurate result. The algorithm uses a simple tabular beam model, together with a discrete scatter kernel. These beam parameters are fitted either to a measured dose distribution, or to a dose distribution calculated using a more accurate dose calculation algorithm. The calculation is then applied to pelvic and thoracic conformal plans, and the results compared with those provided by a commercial radiotherapy treatment planning system (Pinnacle3, Philips Radiation Oncology Systems, Milpitas, CA), which has been verified against measurements. The calculation takes around 4 s to compute a 100 ? 100 mm field, and agreement of the dose?volume histograms with the commercial treatment planning system is to within 5% dose or 8% volume. Use of a grid resolution coarser than 5 ? 5 ? 5 mm is found to be inaccurate, whereas calculating primary dose on a coarse grid and interpolating is found to increase speed without significantly reducing accuracy. Kernel resolution influences the speed and accuracy, but using 12 discrete points provides a fast result with a limited error. Thus, the algorithm is suitable for optimization applications.

Kernel-based optimized feature vectors selection and discriminant analysis for face recognition

Abstract: In practice, face image data distribution is very complex because of pose, illumination and facial expression variation, so it is inadequate to describe it just by Fisherface or Fisher linear discriminant analysis (FLDA). In the paper a method is presented for face recognition using kernel-based optimized feature vectors selection and discriminant analysis. The kernel trick is used to select an optimized subset from the data and form a subspace into the feature space that can capture the structure of the entire data into the feature space according to geometric consideration. Then all the data are projected into this subspace and FLDA is performed in this subspace to extract nonlinear discriminant features of the data for face recognition. Another similar analysis method is kernel-based Fisher discriminant analysis (KFDA), which transforms all the data into the feature space and FLDA is performed in the feature space. The proposed method is compared with Fisherface and KFDA on two benchmarks, and experimental results demonstrate that it outperforms Fisherface and can give the same recognition accuracy as KFDA, but its computational complexity is reduced against KFDA.

Methods and apparatus for correcting scatter

Abstract: A method for removing scatter in an image includes acquiring data of an object of interest, and using an iterative equation including a thickness-dependent kernel modulation factor to reconstruct an image of the object.

5th order multi-tone Volterra simulator with component-level output

Abstract: In this paper, a Matlab software performing numerical Volterra distortion analysis of a weakly nonlinear circuit with arbitrary multiport topology is described. Due to numerical convolution of signal spectrums, the degree of nonlinearity is relatively easy to increase, and the amount of signal tones is not limited to one or two. Distortion products are displayed graphically as vector sums of all different contributions. This makes it easy to recognize the dominant distortion source and possible cancellation mechanisms, and aids the designer to improve the design.