We present a new learning rule for intralayer connections in neural networks. The rule is based on Hebbian learning principles and is derived from information theoretic considerations. A simple network trained using the rule is shown to have associative memory like properties. The network acts by building connections between correlated data points, under constraints.

We present a neural network capable of separating inputs in an unsupervised manner. Oja's rule and Self-Organizing map principles are used to construct the network. The network is tested using 1) straight lines 2)MNIST database. The results demonstrate that the network can operate as a general clustering algorithm, with neighboring neurons responding to geometrically similar inputs.

Recognition of animals via images of their footprints is a non-invasive technique recently adopted by researchers interested in monitoring endangered species. One of the challenges that they face is the extraction of features from these images, which are required for this approach. These features are points along the boundary curve of the footprints. In this paper, we propose an innovative technique for extracting these curves from depth images. We formulate the problem of identification of the boundary of the footprint as a pattern recognition problem of a stochastic process over a manifold. This methodology has other applications on segmentation of biological tissue for medical applications and tracking of extreme weather patterns. The problem of pattern identification in the manifold is posed as a shortest path problem, where the path with the smallest cost is identified as the one with the highest likelihood to belong to the stochastic process. Our methodology is tested in a new dataset of normalized depth images of tiger footprints with ground truth selected by experts in the field.

Filtering in digital images via Integral Image yields fast computation times for uniform filtering. The extension by Heckbert to perform filtering via repeated integration provides a way for non-uniform filtering, but has its own limitations. A recent method by Hussein et al. provides non-uniform filtering by Euler expansion of filtering kernels, and is called kernel integral method. We propose a simplification for non-uniform filtering by stacking of box filters from a single integral image. Results show speedups of as much as 40:1, similar to run time performance gains in kernel integral method, when comparing to naïve nonuniform filtering, while at the same time reducing the setup time drastically.

This paper proposes a monocular vision solution to simultaneous detection of multiple lanes in navigable regions/urban roads using accumulator voting. Unlike other approaches in literature, this paper first examines the extent of lane parameters required for continuous control of any vehicle manually or autonomously. The accumulator-based algorithm is designed using this fundamental control knowledge to vote for the required lane parameters (position of lanes and steering angle required) in the image plane. The novel accumulator voting scheme is called "Parametric Transform for Multi-lane Detection". This paper not only adapts predictive control in the image plane, but also detects multiple lanes in the scene concurrently in the form of multiple peaks in the accumulator. This method is robust to shadows and invariant to color, texture, and width of the road. Finally, the method is designed for dashed/continuous lines.

When objects in images are small or blurred enough, geometric features are inadequate for reliable pattern recognition. We introduce the Pattern Recognition by Cluster Accumulation (PRCA) method to show that pattern recognition performance can be improved in this situation by using radiometric features for object detection. In addition, PRCA uses clustering to provide feature selection and dimensionality reduction. It uses accumulation to provide robustness against translation, rotation, cluster shape distortion, and inappropriate splitting or merging of clusters. We find that PRCA performs faster than normalized cross correlation and faster than mutual information methods.

A new strategy is proposed to defend against colluding malicious nodes in a sensor network. The new strategy is based on a new relaxation labeling algorithm to classify nodes into benign or malicious ones. Only reports from benign nodes can then be used to perform localization and obtain accurate results. Experimental results based on simulations and field experiments illustrate the performance of the algorithm.

Target tracking is a canonical issue in sensor networks research. However, tracking security has gained little or no attention. Once a sensor node is compromised, it will be able to inject false location information into the network, and those nodes receiving such information will suffer greatly in terms of tracking precision. This paper, to the best of our knowledge, is the first to explore the topic of security in the context of Bayesian tracking for sensor networks. We propose to activate more than one nodes at each time step, and use a relaxation labeling algorithm to detect malicious nodes whose reports are then removed. Simulations based on both linear and nonlinear motion models demonstrate that out algorithm works better than simply averaging over the results based on the redundant sets of nodes.

In this paper, we extend the idea of using mosaicked color filter array (CFA) in color imaging, which has been widely adopted in the digital color camera industry, to the use of multispectral filter array (MSFA) in multispectral imaging. The filter array technique can help reduce the cost, achieve exact registration, and improve the robustness of the imaging system. However, the extension from CFA to MSFA is not straightforward. First, most CFAs only deal with a few bands (3 or 4) within the narrow visual spectral region, while the design of MSFA needs to handle the arrangement of multiple bands (more than 3) across a much wider spectral range. Second, most existing CFA demosaicking algorithms assume the fixed Bayer CFA and are confined to properties only existed in the color domain. Therefore, they cannot be directly applied to multispectral demosaicking. The main challenges faced in multispectral demosaicking is how to design a generic algorithm that can handle the more diversified MSFA patterns, and how to improve performance with a coarser spatial resolution and a less degree of spectral correlation. In this paper, we present a binary tree based generic demosaicking method. Two metrics are used to evaluate the generic algorithm, including the root mean-square error (RMSE) for reconstruction performance and the classification accuracy for target discrimination performance. Experimental results show that the demosaicked images present low RMSE (less than 7) and comparable classification performance as original images. These results support that MSFA technique can be applied to multispectral imaging with unique advantages.

Active contours have been widely used as image segmentation methods. The use of level set theory has provided more flexibility and convenience for the implementation of active contours. However, traditional active contour models have some limitations on the segmentation of complicated images whose sub-regions consist of multiple components. The segmentation of multispectral images is even a more difficult problem. We propose an advanced active contour model using the statistics of image intensity based on a multivariate mixture density model. The proposed active contour model shows a robust segmentation capability on the images that traditional segmentation methods cannot properly partition. Numerical experiments with synthetic and real images are presented.

The technology of color filter arrays (CFA) has been widely used in the digital camera industry since it provides several advantages like low cost, exact registration, and strong robustness. The same motivations also drive the design of multi-spectral filter arrays (MSFA), in which more than three color bands are used (e.g. visible and infrared). Although considerable research has been reported to optimally reconstruct the full-color image using various interpolation algorithms, studies on the intrinsic properties of these filter arrays as well as the underlying design principles have been very limited. In this paper, we identify the properties a CFA should possess and extend the design philosophy to MSFA. Based on these discussions, we develop a generic MSFA generation method starting from a checkerboard pattern with both rectangular and hexagonal tessellations. By manipulating this pattern through a combination of decomposition and subsampling steps, we can generate MSFAs that satisfy all the design requirements. We show, through case studies, that most of the CFAs currently used by the industry can be derived as special cases. To evaluate the performance of MSFAs, we design a metric, referred as the static coefficient (SC), to measure the uniformity of MSFAs.

Eigenspaces are commonly used for dimensionality reduction, either for a compact encoding or for classification of high dimensional data. However in the presence of noise, the eigenspaces that were created using low-noise data, no longer explain the noise-corrupted data. In this paper, we present the notion of noise equivalent dimensions (NED) as a means of increasing the contribution of signal strength to compensate for the contribution of noise. Although the notion of NED is created with reconstruction error in mind, the additional dimensions may very well be used for classification purposes. Experiments with synthetic and real data are presented to demonstrate their use.

This paper investigates vector space methods of reconstructing a surface from a given needle map in discrete image settings. We first describe the subset of the gradient space corresponding to uniformly integrable surfaces in terms of an orthonormal. set of gradient fields. We then formulate the minimum norm solution to the surface reconstruction problem from a given set of gradients, and show that the solution corresponds to an equivalence class of surfaces. Next, we relax the uniform integrability condition to partial integrability by modifying the feasible subspace. We show that partial integrability enforced as such allows reconstruction of surfaces which are not uniformly integrable.

We propose a new approach to steganography for information hiding in digital media. We refer to it as blind consistency-based steganography (BCBS). Our main concerns in designing BCBS is high imperceptibility, high security level, and large capacity. Steganography differs from digital watermarking because both the information and the very existence of the information are hidden. Even though the discussion focuses on digital images, BCBS can be applied to any digital media. While existing steganographic approaches all have different advantages for specific applications, they also suffer a similar problem: such systems are unable to handle subterfuge attacks, i.e., they cannot deal with the opponents who not only detect a message, but also render it useless, or even worse, modify it to the opponent's favor. The breakthrough of BCBS is that it not only decodes the message exactly, it also detects if the message has been tampered without using any extra error correction. The detection is integrated into the process of decoding. Another advantage of BCBS is the "blindness" of the decoding process, meaning the decoding can be operated without access to the cover image. The encoding and decoding process are detailed in the paper, along with the analysis on imperceptibility, security, and capacity. Experimental results are provided as well.

Optimal missing data estimation algorithms including deblurring and denoising are designed to restore images captured from large CCD sensor arrays using a butting technique, where 1 to 2 columns of data are missed at the butting edge. We developed a consistency method with separable deblurring to estimate the missing data. This method converts an ill-posed restoration problem into a well-posed one by making few assumptions based on regularization theory. Under the condition that no noise is inserted, and the separable blur kernel is exactly known, the consistency method can deblur the original image and at the same time estimate the missing columns(s) exactly. However, this algorithm becomes unstable when large noise is inserted or inaccurate estimation of the blur kernel is made. Conditioning analysis is used to quantify the amount of ill condition of the blur kernel when the assumptions are relaxed to different levels, which provides a solid measurement on how stable the system will remain knowing the signal-to-noise ratio and the inaccuracy of the blur kernel estimation. Experimental results from different approaches are compared.

Anisotropic diffusion is a powerful method for image feature extraction in which blurring is allowed to occur except at edges. Mean field annealing (MFA) is an image optimization technique which is used to find the best estimation of a blurred, noisy corrupted image. We show that MFA is versatile enough to be used for image feature extraction as well. Furthermore, the two major problems in anisotropic diffusion (white noise and geometric interpretation) can be solved by few modifications of the MFA equation. Finally, experiments and results are presented.

This paper documents how two mobile robots can share knowledge about their environment. The two mobile robots we use have different sensor configurations, drive systems and other physical attributes including weight and size. "Knowledge" is generated by the region-feature neural network (RFNN), and can be transferred on two general levels: (1) a complete transfer of a matured neural network; and (2) a transfer of matured features. This transferred knowledge can also be "tuned" with and without locking the feature level synaptic weights. We examine the impact and feasibility of sharing (on both levels, with and without locking features) neural network modules trained on actual sonar data in the global self-localization (GSL) problem. Significant reductions in training time are realized and presented. We also describe the neural network architecture and our general approach to solving the GSL problem in a time-, translation- and rotation-invariant way.

In this paper we show how a self-organizing Kohonen neural network can use hyperellipsoid clustering (HEC) to build maps from actual sonar data. Since the HEC algorithm uses the Mahalanobis distance, the elongated shapes (typical of sonar data) can be learned. The Mahalanobis distance metric also gives a stochastic measurement of a data point's association with a node. Hence, the HEC Kohonen can be used to build topographical maps and to recognize its own topographical cites for self-localization. The number of nodes can also be regulated in a self-organizing manner by using the Kolmogorov-Smirnov (KS) test for cluster compactness. The KS test determines whether a node should be divided (mitosis) or pruned completely. By incorporating principal component analysis, the HEC Kohonen can handle problems with several dimensions (3D, time-series, etc.). The HEC Kohonen is also multifunctional in that it accommodates compact geometric motion planning and self-referencing algorithms. It can also be used to solve a host of other pattern recognition problems.

The techniques of a posteriori image restoration and iterative image feature extraction are described and compared. Image feature extraction methods known as graduated nonconvexity (GNC); variable conductance diffusion (VCD), anisotropic diffusion, and biased anisotropic diffusion (BAD), which extract edges from noisy images, are compared with a restoration/feature extraction method known as mean field annealing (MFA). All are shown to be performing the same basic operation: image relaxation. This equivalence shows the relationship between energy minimization methods and spatial analysis methods and between their respective parameters of temperature and scale. As a result of the equivalence, VCD is demonstrated to minimize a cost function, and that cost is specified explicitly. Furthermore, operations over scale space are shown to be a method of avoiding local minima.>

Mean field annealing using a piecewise linear model was applied to gated cardiac nuclear medicine images as a preprocessing tool for image smoothing and noise reduction. A second derivative operator was then used to extract the edges for ventricle boundary estimation. Combined with the user input initial boundary estimate, the extracted edge information was used to find a minimum cost boundary, which was optimum with regards to boundary smoothness and the boundary edge strength.>

This paper presents a method of optimal boundary smoothing for curvature estimation and a method of corner detection for consistent representation of objects for computer vision applications. The existing methods for curvature estimation have a common problem in determining a unique smoothing factor. We propose a constrained regularization (CR) approach to overcome that problem. The curvature function computed on the preprocessed boundary, which is obtained by the CR approach, gives consistent corner detection results. Ideal corners rarely exist for a real boundary. They are often rounded due to the smoothing effects of the preprocessing. In addition, a human recognizes both sharp corners and slightly rounded segments as corners. Hence, we establish a criterion, called "corner sharpness", which is qualitatively similar to a human's capability to detect corners.>

A novel method for obtaining dense displacement fields from a sequence of frames is presented. The algorithm is based on modeling the displacement field as a Markov random field, hence making it possible to use the equivalence of a Markov random field and a Gibbs distribution. The Gibbs distribution is used to define a mean field probability density function, and the displacement field is found using a mean field annealing algorithm. Mean field annealing is a technique which finds the global or near global minima in nonconvex optimization problems. Analysis of the algorithm and experimental results are presented.>

Motion estimation is cast as a problem in energy minimization. This is achieved by modeling the displacement field as a Markov random field. The equivalence of a Markov random field and a Gibbs distribution is then used to convert the problem into one of defining an appropriate energy function that describes the motion and any constraints imposed on it. The energy function is then minimized using the mean field annealing algorithm, a technique which finds the global or near-global minima in nonconvex optimization problems. Analysis of the algorithm and experimental results are presented.>

Computing a curvature function on a digitized boundary is an ill-posed problem due to the discrete nature of the boundary. The authors use a constrained regularization technique to obtain the optimal smooth boundary before computing the curvature function. A corner sharpness is defined for robust corner point detection. Matching results in the presence of occlusion using a 2-D Hopfield neural network are also shown to produce excellent results using this boundary representation. The human cognition system recognizes both ideal corner points and slightly rounded segments as corner points. A criterion to mimic a human's capability of detecting corner points and to compensate for the smoothing effect of the preprocessing in detecting corner points in the curvature function space is established.>

Optimization problems are approached using mean field annealing (MFA), which is a deterministic approximation, using mean field theory and based on Peierls's inequality, to simulated annealing. The MFA mathematics are applied to three different objective function examples. In each case, MFA produces a minimization algorithm that is a type of graduated nonconvexity. When applied to the ;weak-membrane' objective, MFA results in an algorithm qualitatively identical to the published GNC algorithm. One of the examples, MFA applied to a piecewise-constant objective function, is then compared experimentally with the corresponding GNC weak-membrane algorithm. The mathematics of MFA are shown to provide a powerful and general tool for deriving optimization algorithms.

A numerical method for finding the global minimum of nonconvex functions is presented. The method is based on the principles of simulated annealing, but handles continuously valued variables in a natural way. The method is completely general, and optimizes functions of up to 30 variables. Several examples are presented. A general-purpose program, INTEROPT, is described, which finds the minimum of arbitrary functions, with user-friendly, quasi-natural-language input.>

A principle source of noise in X-ray and emission computer tomography is at the detectors that measure the projection of the object. The noise can be approximated by additive, signal-independent white Gaussian statistics by ignoring the negligible effects of scattering and diffraction of the source beam. The back-projection filter that is used significantly alters power spectral density of the noise, such that the back-projected noise at each reconstructed point is no longer white. However, to effectively restore the reconstructed image using maximum a posteriori techniques via mean field annealing (MFA), a reasonable estimate of the autocorrelation of the back-projected noise is necessary. This work derives the autocorrelation and power spectra of the reconstructed noise for parallel, fan, and cone beam projections and also shows some preliminary results of MFA restorations.>

Motion artifacts due to heart motion and blood flow within the heart chambers are a significant barrier to accurate interpretation of cardiac magnetic resonance images (MRI). The post-processing techniques of Wiener filtering, alternating projections onto convex sets (POCS), and mean field annealing (MFA) to remove these artifacts are studied. Removal of noise from the images is accomplished with MFA by setting up a restoration problem whose objective function encapsulates both data-dependent and a priori knowledge about the image. Two important aspects of MFA are the use of a penalty rather than a constraint, and the fact that it converges twenty times as rapidly as normal simulated annealing. Images of the results of Wiener filtering and MFA are shown, and the methods of POCS and MFA are briefly explained.>

The problem of pose determination of a surface in a range image is described as a six-degree-of-freedom optimization problem, where the surface is expressed by a quadratic equation. The tree annealing algorithm, a general-purpose technique for finding minima of functions of continuously valued variables, is presented. The technique is applied to the pose determination of analytic surfaces and is shown to be quite effective even in the presence of considerable amounts of noise in the images.>

The method of Fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point. Invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions, as is demonstrated by processing silhouettes of aircraft maneuvering in three-space.>

A planar or quadric surface can be fit to a segment of range data in a locally optimal sense by selecting the minimum eigensolution of a scatter matrix for that segment. We obtain a globally optimal fit by perturbing the local eigensystems with constraints reflecting relations among the corresponding primitives of a model. These pairwise relations define a view-invariant description of the model. For segments containing a few hundred pixels, the resulting perturbation is small enough to justify a linear treatment of the coupled system. From this globally optimal fit, we determine the pose of the object algebraically.

A general three dimensional image analysis environment is presented. The environment proved extremely flexible, and a three dimensional object recognition system was designed using this environment. The recognition system addresses all the issues associated with view independent object recognition. The particular concentration of this paper is the development of an active model matching approach called a procedural model The procedural model uses the surface geometry available in a range image to limit the amount of searching that must be done. The surface geometry is determined by solving an eigensystem, and utilized to determine the pose of the object.

In this paper, we describe the fundamental differences between three-dimensional (range) images and two-dimensional (luminance) images. A number of problems arise which are unique to range data, including in particular a strong sensitivity to quantization effects. Although range images and luminance images are both arrays of scalars, the range image conceptually represents a surface in space and cannot be naively manipulated using the conventional image processing functions such as 3 × 3 convolution kernels. If the range data are regarded as a sampling of a surface parametrized by the focal plane coordinates, it is possible to find a representation for the surface normal and for the surface curvature in terms of familiar-looking convolution kernels.

This paper describes a new technique for calculating the displacement field in a motion sequence of two-dimensional imagery generated by a moving sensor. It proposes a scheme wherein a simple algorithm for calculating single displacement vectors is applied over numerous subimages to create a displacement field. This algorithm is an application of the MDT (motion detection transform) [15,16], thus is based on the 1D (one-dimensional) Fourier transform.

A theorem is proven which shows that the position and orientation of a specular-reflecting object may be determined using a single camera and unconstrained light source. The camera and light are moved together in a straight line, and specular peaks are noted. From the changes in the location of the peaks, and knowledge of the surface function, the pose of the part may be determined. This paper includes the basic theorem and its proof. Experimental results will be presented at the conference.

The postulate is made that ``any computation which can be performed recursively can be performed easily and efficiently by iteration coupled with association.'' The ``easily and efficiently'' part of that postulate is nontrivial to prove, and is shown by examples in this paper. The use of association leads directly to potential implementation by content-addressable memories. The example addressed is region growing, often given as a classical example of the use of recursive control structures in image processing. Recursive control structures, however, are somewhat awkward to build in hardware, where the intent is to segment an image at raster scan rates. This paper describes an algorithm and hardware structure capable of per-forming region labeling iteratively at scan rates. Every pixel is individually labeled with an identifier signifying to which region it belongs. The difficulties which often justify recursion (``U''- and ``N''-shaped regions, etc.) are handled by maintaining an equivalence table in hardware, transparent to the computer, which reads the labeled pixels. The mechanism for updating the region map is explained in detail. Furthermore, simulation of the associative memory has been demon-strated to be an effective implementation of region growing in a serial computer.

In this paper we report the results of experimental studies of zero-level, one-level, and two-level search rearrangement backtracking. We establish upper and lower limits for the size problem for which one-level backtracking is preferred over zero-level and two-level methods, thereby showing that the zero-level method is best for very small problems. The one-level method is best for moderate size problems, and the two-level method is best for extremely large problems. Together with our theoretical asymptotic formulas, these measurements provide a useful guide for selecting the best search rearrangement method for a particular problem.

Two common problems in image analysis are described—the region-labeling problem and the clustering problem. Both are shown to be instances of a search-and-rename problem which can be solved in parallel by a system architecture inherently suitable for VLSI implementation.

The computational difficulty of finding the extreme points (those two points furthest from each other) in a region of an image is examined. Various approaches are described, including computation of convex hulls, sophisticated search strategies, and a statistical method. Suitability of the various methods to particular applications is discussed.