Most of the recent work on inhomogeneous diffusion in image filtering focuses on diffusing the isotope curve. We present a less familiar approach to the development of inhomogeneous diffusion algorithms in which the image is regarded as a surface in three-space. The magnitude of the surface normal controls a diffusion that evolves the image surface at the speed proportional to its mean curvature. A discrete algorithm to implement this proposed diffusion is introduced and we show experimentally that the algorithm develops singularities that reveal, preserve, and enhance the underlying signal. If the imput signal is an isolated noisy edge, this leads to complete noise removal and enhancement without affecting the edge locality.

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 decent surface minimization. At edges, it swithches to a nondiffusion state due to two factors: the Laplacian of position vanishes and the magnitude of the surface normal attains a local maximum.

Representing the image as a surface, an inhomogeneous diffusion algorithm is developed, evolving the surface at a speed proportional to its mean curvature, reducing noise while preserving image structure. An adaptive scaling parameter increases the speed of the diffusion. The properties of a discrete algorithm are demonstrated experimentally

In previous work, we have 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 pre-processing 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 pre-processing 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.

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 that the original.

For high quality applications, we have developed a coding technique that produces no visible degradation, that we denote as perceptually transparent. A compression significantly higher than error free codes is achieved. In a progressive scheme, a reduced resolution image is used for the transmission of high quality still images. To use the lower resolution images effectively, analysis based interpolation provides the estimate of the higher resolution image and reduces the incremental information transmitted. This approach may also lead to compressed images of higher quality that the original.

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. One 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.