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Mean curvature diffusion is shown to be a position vector diffusion, tending to scalar diffusion as a flat image region is approached, and providing noise removal by steepest descent surface minimization. At edges, it switches to a nondiffusion state due to two factors: the Laplacian of position vanishes and the magnitude of the surface normal attains a local maximum.

A high-resolution study of breast tissue motion during cardiac systole and respiration is presented. An experimental system was designed to achieve a velocity resolution on the order of 1 mm/s with high spatial resolution. The peak velocity of tissue motion estimated during cardiac systole ranged from 0.2 mm/s to 5.6 mm/s among the subjects studied. It is shown that motion due to the cardiac cycle is less significant when the subject is positioned on the side rather than supine. The mean tissue velocity among subjects in the supine position is 2.88 mm/s and drops to 0.81 mm/s for the side position, with a corresponding spatial displacement of 0.095 mm, dropping to 0.027 mm. The velocity profiles indicate that 100 ms is required for the entire ribcage contraction-relaxation process to occur. Experiments using a prone biopsy table show the almost complete elimination of tissue motion due to cardiac systole, suggesting that the use of the table eliminates this motion, thus allowing for high-resolution blood velocity estimates. Features resulting from respiratory motion are also presented. We found this motion to be of a much longer time duration, and of a much higher magnitude, with velocities as high as 29 mm/s. The implications of the study on the high-resolution estimation of blood velocity and high-resolution breast imaging are discussed.

The encoding of images at high quality is important in a number of applications. We have developed an approach to coding that produces no visible degradation and that we denote as perceptually transparent. Such a technique achieves a modest compression, but still significantly higher than error free codes. Maintaining image quality is not important in the early stages of a progressive scheme, when only a reduced resolution preview is needed. In this paper, we describe a new method for the progressive transmission of high quality still images, that efficiently uses the lower resolution images in the encoding process. Analysis based interpolation is used to estimate the higher resolution image, and reduces the incremental information transmitted at each step. This methodology for high quality image compression is also aimed at obtaining a compressed image of higher perceived quality than the original.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In previous work, we reported on the benefits of noise reduction prior to coding of very high quality images. Perceptual transparency can be achieved with a significant improvement in compression as compared to error free codes. In this paper, we examine the benefits of preprocessing when the quality requirements are not very high, and perceptible distortion results. The use of data dependent anisotropic diffusion that maintains image structure, edges, and transitions in luminance or color is beneficial in controlling the spatial distribution of errors introduced by coding. Thus, the merit of preprocessing is for the control of coding errors. In this preliminary study, we only consider preprocessing prior to the use of the standard JPEG and MPEG coding techniques.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We have recently proposed the use of geometry in image processing by representing an image as a surface in 3-space. The linear variations in intensity (edges) were shown to have a nondivergent surface normal. Exploiting this feature we introduced a nonlinear adaptive filter that only averages the divergence in the direction of the surface normal. This led to an inhomogeneous diffusion (ID) that averages the mean curvature of the surface, rendering edges invariant while removing noise. This mean curvature diffusion (MCD) when applied to an isolated edge imbedded in additive Gaussian noise results in complete noise removal and edge enhancement with the edge location left intact. In this paper we introduce a new filter that will render corners (two intersecting edges), as well as edges, invariant to the diffusion process. Because many edges in images are not isolated the corner model better represents the image than the edge model. For this reason, this new filtering technique, while encompassing MCD, also outperforms it when applied to images. Many applications will benefit from this geometrical interpretation of image processing, and those discussed in this paper include image noise removal, edge and/or corner detection and enhancement, and perceptually transparent coding.

In the perceptually transparent coding of images, we use representation and quantization strategies that exploit properties of human perception to obtain an approximate digital image indistinguishable from the original. This image is then encoded in an error free manner. The resulting coders have better performance than error free coding for a comparable quality. Further, by considering changes to images that do not produce perceptible distortion, we identify image characteristics onerous for the encoder, but perceptually unimportant. Once such characteristic is the typical noise level, often imperceptible, encountered in still images. Thus, we consider adaptive noise removal to improve coder performance, without perceptible degradation of quality. In this paper, several elements contribute to coding efficiency while preserving image quality: adaptive noise removal, additive decomposition of the image with a high activity remainder, coarse quantization of the remainder, progressive representation of the remainder, using bilinear or directional interpolation methods, and efficient encoding of the sparse remainder. The overall coding performance improvement due to noise removal and the use of a progressive code is about 18%, as compared to our previous results for perceptually transparent coders. The compression ratio for a set of nine test images is 3.72 for no perceptible loss of quality.

The inadequacy of the classic linear approach to edge detection and scale space filtering lies in the spatial averaging of the Laplacian. The Laplacian is the divergence of the gradient and thus is the divergence of both magnitude and direction. The divergence in magnitude characterizes edges and this divergence must not be averaged if the image structure is to be preserved. We introduce a new nonlinear filtering theory that only averages the divergence of direction. This averaging keeps edges and lines intact as their direction is nondivergent. Noise does not have this nondivergent consistency and its divergent direction is averaged. Higher order structures such as corners are singular points or inflection points in the divergence of direction and also are averaged. Corners are intersection points of edges of nondivergent direction (or smooth curves of small divergence in direction) and their averaging is limited. This approach provides a better compromise between noise removal and preservation of image structure. Experiments that verify and demonstrate the adequacy of this new theory are presented.