Pramod Lakshmi Narasimha

An integrated growing-pruning method for feedforward network training

In order to facilitate complexity optimization in feedforward networks, several algorithms are developed that combine growing and pruning. First, a growing scheme is presented which iteratively adds new hidden units to full-trained networks. Then, a non-heuristic one-pass pruning technique is presented, which utilizes orthogonal least squares. Based upon pruning, a one-pass approach is developed for generating the validation error versus network size curve. A combined approach is described in which networks are continually pruned during the growing process. As a result, the hidden units are ordered according to their usefulness, and the least useful units are eliminated. Examples show that networks designed using the combined method have less training and validation error than growing or pruning alone. The combined method exhibits reduced sensitivity to the initial weights and generates an almost monotonic error versus network size curve. It is shown to perform better than two well-known growing methods-constructive backpropagation and cascade correlation.

An efficient hidden layer training method for the multilayer perceptron

Abstract The output-weight-optimization and hidden-weight-optimization (OWO–HWO) training algorithm for the multilayer perceptron alternately solves linear equations for output weights and reduces a separate hidden layer error function with respect to hidden layer weights. Here, three major improvements are made to OWO–HWO. First, a desired net function is derived. Second, using the classical mean square error, a weighted hidden layer error function is derived which de-emphasizes net function errors that correspond to saturated activation function values. Third, an adaptive learning factor based on the local shape of the error surface is used in hidden layer training. Faster learning convergence is experimentally verified, using three training data sets.

Upper Bound on Pattern Storage in Feedforward Networks

Starting from the strict interpolation equations for multivariate polynomials, an upper bound is developed for the number of patterns that can be memorized by a nonlinear feedforward network. A straightforward proof by contradiction is presented for the upper bound. It is shown that the hidden activations do not have to be analytic. Networks, trained by conjugate gradient, are used to demonstrate the tightness of the bound for random patterns. Based upon the upper bound, small multilayer perceptron models are successfully demonstrated for large support vector machines.

Convergent design of piecewise linear neural networks

Piecewise linear networks (PLNs) are attractive because they can be trained quickly and provide good performance in many nonlinear approximation problems. Most existing design algorithms for piecewise linear networks are not convergent, non-optimal, or are not designed to handle noisy data. In this paper, four algorithms are presented which attack this problem. They are: (1) a convergent design algorithm which builds the PLN one module at a time using a branch and bound technique; (2) two pruning algorithms which eliminate less useful modules from the network; and (3) a sifting algorithm which picks the best networks out of the many designed. The performance of the PLN is compared with that of the multilayer perceptron (MLP) using several benchmark data sets. Numerical results demonstrate that piecewise linear networks are adequate for many approximation problems.

Letters: Upper bound on pattern storage in feedforward networks

An upper bound on pattern storage is stated for nonlinear feedforward networks with analytic activation functions, like the multilayer perceptron and radial basis function network. The bound is given in terms of the number of network weights, and applies to networks having any number of output nodes and arbitrary connectivity. Starting from the strict interpolation equations and exact finite degree polynomial models for the hidden units, a straightforward proof by contradiction is developed for the upper bound. Several networks, trained by conjugate gradient, are used to demonstrate the tightness of the bound for random patterns.

An improved real time superresolution FPGA system

In numerous computer vision applications, enhancing the quality and resolution of captured video can be critical. Acquired video is often grainy and low quality due to motion, transmission bottlenecks, etc. Postprocessing can enhance it. Superresolution greatly decreases camera jitter to deliver a smooth, stabilized, high quality video. In this paper, we extend previous work on a real-time superresolution application implemented in ASIC/FPGA hardware. A gradient based technique is used to register the frames at the sub-pixel level. Once we get the high resolution grid, we use an improved regularization technique in which the image is iteratively modified by applying back-projection to get a sharp and undistorted image. The algorithm was first tested in software and migrated to hardware, to achieve 320x240 -> 1280x960, about 30 fps, a stunning superresolution by 16X in total pixels. Various input parameters, such as size of input image, enlarging factor and the number of nearest neighbors, can be tuned conveniently by the user. We use a maximum word size of 32 bits to implement the algorithm in Matlab Simulink as well as in FPGA hardware, which gives us a fine balance between the number of bits and performance. The proposed system is robust and highly efficient. We have shown the performance improvement of the hardware superresolution over the software version (C code).

Improved target tracking in aerial video using particle filtering

In this paper, we present an improved target tracking algorithm in aerial video. An adaptive appearance model is incorporated in Sequential Monte Carlo framework to infer the deformation (or tracking) parameter best describing the differences between the observed appearances of the target and the appearance model. The appearance model of the target is adaptively updated based on the tracking result up to the current frame, balancing a fixed model and the dynamic model with a pre-defined forgetting parameter. For targets in the aerial video, an affine model is accurate enough to describe the transformation of the targets across frames. Particles are formed with the elements of the affine model. To accommodate the dynamics embedded in the video sequence, we employ a state space time series model, and the system noise constrains the particle coverage. Instead of directly using the affine parameters as elements of particles, each affine matrix is decomposed into two rotation angles, two scales and the translation parameter, which form the particles with more geometrical meaning. Larger variances are given to the translation parameter and the rotation angles, which greatly improve the tracking performance compared with treating these parameters equally, especially for the fast rotating targets. Experimental results show that our approach provides high performance for target tracking in aerial video.

A pseudospectral fusion approach to fingerprint matching

A prototype fingerprint verification system is described which combines the direction and density images into a complex pseudo-spectrum. Two methods for extracting the direction and density images are presented. The proposed feature extraction method is shown to be fast, efficient and robust Verification is achieved by correlation matching.

An improved multi-frame super-resolution technique

We propose an improvement on the existing super-resolution technique that produces high resolution video from low quality low resolution video. Our method has two steps: (1) motion registration and (2) regularization using back-projection. Sub-pixel motion parameters are estimated for a group of 16 low resolution frames with reference to the next frame and these are used to position the low resolution pixels on high resolution grid. A gradient based technique is used to register the frames at the sub-pixel level. Once we get the high resolution grid, we use an improved state-of-the-art regularization technique where the image is iteratively modified by applying back-projection to get a sharp and undistorted image. This technique is based on bilateral prior and deals with different data and noise models. This computationally inexpensive method is robust to errors in motion/blur estimation and results in images with sharp edges. The proposed system is faster than the existing ones as the post-processing steps involved only simple filtering. The results show the proposed method gives high quality and high resolution videos and minimizes effects due to camera jerks. This technique can easily be ported to hardware and can be developed into a product.

Summarization and visualization of target trajectories from massive video archives

Video, especially massive video archives, is by nature dense information medium. Compactly presenting the activities of targets of interest provides an efficient and cost saving way to analyze the content of the video. In this paper, we propose a video content analysis system to summarize and visualize the trajectories of targets from massive video archives. We first present an adaptive appearance-based algorithm to robustly track the targets in a particle filtering framework. It provides high performance while facilitating implementation of this algorithm in hardware with parallel processing. Phase correlation algorithm is used to estimate the motion of the observation platform which is then compensated in order to extract the independent trajectories of the targets. Based on the trajectory information, we develop the interface for browsing the videos which enables us to directly manipulate the video. The user could scroll over objects to view their trajectories. If interested, he/she could click on the object and drag it along the displayed path. The actual video will be played in synchronous to the mouse movement.