Morris Goldberg

Hierarchy in picture segmentation: a stepwise optimization approach

A segmentation algorithm based on sequential optimization which produces a hierarchical decomposition of the picture is presented. The decomposition is data driven with no restriction on segment shapes. It can be viewed as a tree, where the nodes correspond to picture segments and where links between nodes indicate set inclusions. Picture segmentation is first regarded as a problem of piecewise picture approximation, which consists of finding the partition with the minimum approximation error. Then, picture segmentation is presented as an hypothesis-testing process which merges only segments that belong to the same region. A hierarchical decomposition constraint is used in both cases, which results in the same stepwise optimization algorithm. At each iteration, the two most similar segments are merged by optimizing a stepwise criterion. The algorithm is used to segment a remote-sensing picture, and illustrate the hierarchical structure of the picture. >

Image Sequence Coding Using Vector Quantization

In this paper, a new interframe coding technique based upon vector quantization is presented. This algorithm has as its basis twodimensional block vector quantization, at the frame level, onto which is grafted the concept of adaptive codebook replenishment and frame replenishment. This algorithm includes three strategies: label replenishment, label replenishment with mean shift, and label replenishment with mean shift and selective codeword replacement. The last two strategies efficiently update the codebook to track the changes in local statistics on a frame basis. Compared with three-dimensional block vector quantization [16], for bit rates between 0.5 and 0.65 the normalized mean Squared error (NMSE) is reduced by a factor ranging between 2 and 2.5 by the use of replenishment.

Image Compression Using Adaptive Vector Quantization

The paper demonstrates the application of adaptive vector quantization techniques to the coding of monochromatic and color pictures. Codebooks of representative vectors are generated for different portions of the image. By means of extensive simulations, the performance of the coder for monochrome images is estimated as a function of the various coding parameters-vector dimensionality, number of representative vectors, and degree of adaptivity. It is shown that for a vector size of dimension 4, there is a zone of operation, ranging from 1.0 to 1.5 bits/pixel, where adaptive vector quantization is advantageous. Despite the simplicity of the decoder, the performance of the adaptive vector quantizer is found to be comparable with block transform coding schemes for both monochrome and color pictures.

Comparative performance of pyramid data structures for progressive image transmission

A review of various pyramid data structures for progressive image transmission, focusing on the steps involved in forming the pyramid and the performance comparisons, is presented. The simple mean pyramid, its variants including the truncated mean, reduced-sum, difference, reduced-difference and S-transform pyramids, and the more general Laplacian pyramid are discussed. It is also shown that the use of an interpolation function improves the quality of the full-resolution approximations both objectively and subjectively. >

An Expert System for Remote Sensing

The Canada Centre for Remote Sensing has developed two hierarchical expert systems, the Analyst Advisor and the Map Image Congruency Evaluation (MICE) advisor. These expert systems are built upon our Remote-Sensing Shell (RESHELL) written in Logicwares MPROLOG. A shell is a programming environment that specifically caters to expert system development. Knowledge is represented in the production rules and frames database. Numerical processing takes place using the extensive FORTRAN code of the Landsat Digital Image Analysis System (LDIAS). The LDIAS includes several DEC VAX computers, image displays, specialized processors, and DEC Al VAXstations. The paper describes the architecture of the expert system to compare maps and images (MICE) and the expert system to advise on the extraction of resource information from remotely sensed data, the Analyst Advisor. Details are given concerning the structure of RESHELL and our methods of interfacing symbolic reasoning in PROLOG on the Al VAX stations with numeric processing in FORTRAN on several different computers. The first prototype of the Analyst Advisor will be released for internal use at CCRS in March 1987.

Image Segmentation with Directed Trees

This correspondence presents a simple algorithm to detect and label homogeneous areas in an image, using directed trees for region labeling. The scheme constructs directed trees with the image points as nodes, guided by an edge value computed at every point. These directed trees segment the image into disjoint regions. Because of a valley seeldng property of the tree construction procedure, the boundaries separating the resultant segments pass through the center of the edges. The algorithm thus performs wel1 with thick and wide edges of varying height, because no thresholding of the edge image is involved. The properties of the resultant segments are stated in terms of the edge image. The algorithm is shown to be simple, efficient, and effective for detecting homogeneous segments in the presence of noise. Results of application in the algorithm to segment a LANDSAT multispectral scene of an agricultural area are included.

A Clustering Scheme for Multispectral Images

A clustering scheme using a multidimensional histogram stored in a table is described and tested on four-dimensional data derived from LANDSAT imagery. By doing all clustering operations on the histogram rather than on the original measurement vectors, it is possible to reduce the computations by a large factor and handle the large sample sizes that are typically encountered in image processing. The clustering algorithm first isolates and delineates the peaks in the multidimensional histogram. These peaks are then used as cluster centers, and all the other measurement vectors in the histogram are assigned to the nearest center. The scheme initially identifies the most separable clusters in the data. It then runs on an interactive basis allowing the user to split specific clusters into subclusters at the expense of less separability. The histogram approach lends itself to statistical analysis using parametric models and the likelihood ratio test. As a starting point, it is assumed that the observed distribution is a mixture of several multivariate Gaussian distributions with unknown mean vectors, covariance matrices, and a priori probabilities. Estimates of the Gaussian parameters are determined ignoring the overlap of the neighboring distributions. The theoretical histogram is then calculated by integrating numerically the probability density function in each of the cells of the histogram, and the likelihood ratio test is applied to measure the departure of the model from the observed data. A statistical measure taking into account the number of degrees of freedom is defined and used to choose between alternative models.

Progressive image transmission by transform coefficient residual error quantization

A progressive image transmission scheme based on iterative transform coding structure is proposed for application in interactive image communication over low-bandwidth channels. The scheme not only provides progressive transmission, but also guarantees lossless reproduction combined with a degree of compression. The image to be transmitted undergoes an orthogonal transform, and the transform coefficients are quantized (scalar or vector) before transmission. The novelty is that the residual error array due to quantization is iteratively fedback and requantized (scalar or vector); the coded residual error information is progressively transmitted and utilized in reconstructing the successive approximations. It is shown that the average reconstruction error variance converges to zero as the number of iterative stages approaches infinity. In practice, lossless reproduction can be achieved with a small number of iterations by using an entropy coder on the final residual-error image. Computer simulation results demonstrate the effectiveness of the technique. >

Reduced-difference pyramid: a data structure for progressive image transmission

Pyramid data structures have found an important role in progressive image transmission. In these data structures, the image is hierarchically represented, with each level corresponding to a reduced-resolution approximation. To achieve progressive image transmission, the pyramid is transmitted starting from the top level. However, in the usual pyramid data structures, extra significant bits may be required to accurately record the node values, the number of data to be transmitted may be expanded, and the node values may be highly correlated. In this paper, we introduce a reduced-difference pyramid data structure in which the number of nodes, corresponding to a set of decorrelated difference values, is exactly equal to the number of pixels. Experimental results demonstrate that the reduced-difference pyramid results in lossless progressive image transmission with some degree of compression. By use of an appropriate interpolation method, reasonable quality approximations are achieved at a bit rate less than 0.1 bit/pixel and excellent quality approximations at a bit rate of about 1.3 bits/pixel.

Progressive image transmission using vector quantization on images in pyramid form

A progressive image transmission scheme in which vector quantization is applied to images represented by pyramids is proposed. A mean pyramid representation of an image is first built up by forming a sequence of reduced-size images by averaging over blocks of 2*2 pixels. A difference pyramid is then built up by taking the differences between successive levels in the mean pyramid. Progressive transmission is achieved by sending all the nodes in the difference pyramid starting from the top level and ending at the bottom level. The kth approximate image can be formed by adding the information of level k to the previously reproduced (k-1)st approximation. To gain efficiency, vector quantization is applied to the difference pyramid of the image on a level-by-level basis. If the errors due to quantization at level k are properly delivered and included in the next level, k+1, then it is demonstrated that the original image can be reconstructed. An entropy coder is used to encode the final residual error image losslessly, thus ensuring perfect reproduction of the original image. The experiments demonstrate that it is possible to achieve simultaneously lossless and progressive transmission with compression. At the intermediate level, the use of vector quantization results in a coding gain over that obtained using only a Huffman coder. Excellent reproduction is achieved at a bit rate of only 0.06 bits/pixel. >