Todd R. Reed

A Gaussian derivative-based transform

The article describes a new image transform that decomposes an image using a set of Gaussian derivatives. The basis functions themselves have been shown to effectively model the measured receptive fields of simple cells in the mammalian visual cortex. Based on these functions, it can be expected that this transform can provide a mechanism for exploiting the properties of the human visual system in image processing algorithms.

On the Computation of Optical Flow using the 3-D GaborTransform

The motion of brightness patterns in an image sequence (optical flow) is most intuitively considered as a spatiotemporal phenomenon. It has been shown, however, that motion has a characteristic signature in the spatiotemporal-frequency (Fourier) domain. This fact can be exploited for the computation of optical flow. However, for cases which involve a number of regions in a sequence with different motions, as in scenes with one or more objects moving against a stationary or moving background, the global nature of the Fourier transform makes it unsuitable for this task. The signatures of the different motions cannot be resolved in the Fourier domain, nor associated with their respective regions in the image sequence. Local frequency representations provide a means to address this problem. In this paper, we consider the application of a 3-D version of the widely used Gabor transform to the computation of optical flow.

An uncertainty analysis of some real functions for image processing applications

There are many benefits to be gained in image processing and compression by the use of analyzing functions which are local in both space and spatial frequency. It is often assumed that these benefits are in some way proportional to the degree of joint locality of the functions being used. Within the limits imposed by the uncertainty principle, there can be great variation in this joint locality across different local function families. While there is no generally accepted joint locality metric appropriate for visual applications, Gabors joint uncertainty is often cited to justify the use of a set of functions. It has been shown that complex Gabor functions optimize this metric. There is some debate however regarding which, of the restricted class of real functions, has the lowest joint uncertainty. In this paper we examine three families of real functions and directly evaluate the Gabor metric for joint uncertainty. In contrast to previous attempts to prove the optimality of any one function, this analysis provides an explicit numerical basis for comparison of these real functions.

A performance analysis of fast Gabor transform methods

Abstract Computation of the finite discrete Gabor transform can be accomplished in a variety of ways. Three representative methods (matrix inversion, Zak transform, and relaxation network) were evaluated in terms of execution speed, accuracy, and stability. The relaxation network was the slowest method tested. Its strength lies in the fact that it makes no explicit assumptions about the basis functions; in practice it was found that convergence did depend on basis choice. The matrix method requires a separable Gabor basis (i.e., one that can be generated by taking a Cartesian product of one-dimensional functions), but is faster than the relaxation network by several orders of magnitude. It proved to be a stable and highly accurate algorithm. The Zak–Gabor algorithm requires that all of the Gabor basis functions have exactly the same envelope and gives no freedom in choosing the modulating function. Its execution, however, is very stable, accurate, and by far the most rapid of the three methods tested.

Compression of still images using segmentation-based approximation

This paper describes a segmentation-based approach for image compression. The image to be compressed is represented as regions and a contour map, with each coded separately. The proposed method is applicable to monochrome, color, and mixed image data.

Perceptually based coding of monochrome and color still images

The authors describe a human visual perception approach and report some results for this problem. The approach is based on the differential quantization of images, in which smooth approximations are subtracted from the image prior to quantization. They consider two such approximations. The first one is an approximation by splines obtained from a sparse and fixed subsampled array of the image. The second one segments the image into piecewise constant regions on the basis of the local activity of the image. Both these approximations result in remainders of residual images where large errors are localized in portions of the image of high activity. Because of visual masking the remainder image can now be coarsely quantized without visual impairment to the reconstructed image. The coarsely quantized remainder is now encoded in an error free manner. In such a perceptually based encoding method the mean square error is now dependent on the activity of the image.<<ETX>>

The analysis of motion in natural scenes using a spatiotemporal/spatiotemporal-frequency representation

It has been shown that motion can be characterized in the spatiotemporal-frequency (Fourier) domain, and that this phenomenon can be exploited for the computation of optical flow. However in practical (natural) sequences, the signatures of the different motions cannot be resolved in the Fourier domain, nor associated with their respective regions in the image sequence. In this paper we consider the application of a spatiotemporal/spatiotemporal frequency representation (a 3-D version of the widely used Gabor transform) to the computation of optical flow in natural scenes.

Motion analysis using the 3-D Gabor transform

It has long been known that motion in a sequence of images has a characteristic signature in the spatiotemporal-frequency (Fourier) domain. For sequences which involve multiple objects in motion, however the global nature of the Fourier transform makes it unsuitable as a mechanism for motion analysis. In general, the signatures of the different motions cannot be resolved. Local frequency representations provide a means to address this difficulty. In the past, both the use of windowed Fourier analysis and the Wigner distribution have been proposed for this task. We consider the application of this 3-D Gabor (1946) transform to motion analysis.

On the compression of still images using the derivative of Gaussian transform

The derivative of Gaussian transform was introduced by the authors as a technique to locally represent image frequency information using functions which have also been used to model certain aspects of human vision. This paper presents the application of this transform to still image compression. A set of basis selection criteria are used in order to minimize the leakage and edge artifacts which can be introduced by quantization of the transform coefficients. A quantization mask is derived which is based on a model of the contrast sensitivity function of the human visual system and is appropriately extended for the DGT basis functions.

Segmentation-based nonlinear image smoothing

One of the most commonly used image enhancement techniques is noise removal. The goal of a noise removal method is to remove noise while preserving the image structure. In this paper a segmentation-based image enhancement method is presented which confines image smoothing to the region interiors. Since the structure in the image is captured by segmentation, confining image smoothing to the region interiors does not cause any significant loss of this structure. In fact, region confined averaging enhances the contrast between boundaries, and hence sharpens the image at these boundaries. The result is an image with reduced noise, but that appears sharper than the original.<<ETX>>