Jean-Michel Jolion

Robust clustering with applications in computer vision

A clustering algorithm based on the minimum volume ellipsoid (MVE) robust estimator is proposed. The MVE estimator identifies the least volume region containing h percent of the data points. The clustering algorithm iteratively partitions the space into clusters without prior information about their number. At each iteration, the MVE estimator is applied several times with values of h decreasing from 0.5. A cluster is hypothesized for each ellipsoid. The shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the Kolmogorov-Smirnov test. The best fitting cluster is then removed from the space, and a new iteration starts. Constrained random sampling keeps the computation low. The clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm: multithresholding of gray level images, analysis of the Hough space, and range image segmentation. >

A fast parallel algorithm for blind estimation of noise variance

A blind noise variance algorithm that recovers the variance of noise in two steps is proposed. The sample variances are computed for square cells tessellating the noise image. Several tessellations are applied with the size of the cells increasing fourfold for consecutive tessellations. The four smallest sample variance values are retained for each tessellation and combined through an outlier analysis into one estimate. The different tessellations thus yield a variance estimate sequence. The value of the noise variance is determined from this variance estimate sequence. The blind noise variance algorithm is applied to 500 noisy 256*256 images. In 98% of the cases, the relative estimation error was less than 0.2 with an average error of 0.06. Application of the algorithm to differently sized images is also discussed. >

An O(log n) pyramid hough transform

Abstract This paper describes a divide-and-conquer Hough transform technique for detecting a given number of straight edges or lines in an image. This technique is designed for implementation on a pyramid of processors, and requires only O(log n) computational steps for an image of size n × n.

Cluster detection in background noise

Abstract If a feature space contains a set of clusters and background noise, it may be difficult to extract the clusters correctly. In particular, when we use a partitioning scheme such as k-means clustering, where k is the correct number of clusters, the background noise points are forced to join the clusters, thus biasing their statistics. This paper describes a preprocessing technique that gives each data point a weight related to the density of data points in its vicinity. Points belonging to clusters thus get relatively high weights, while background noise points get relatively low weights. k-means clustering of the resulting weighted points converges faster and yields more accurate clusters.

Border delineation in image pyramids by concurrent tree growing

Abstract A new method for delineation of compact objects in image pyramids is presented. The borders of the objects are detected in a low resolution representation of the input, a higher level of the pyramids of the pixels on the two sides of an edge are the roots for two classes (object and background). The two classes are employed in two independent top-down tree growing processes. The information is passed downward by adjusting confidence measures. The employment of multiple roots defined on the smoothed representation of the input contributes to the robustness of the method at very low signal-to-noise ratios.

Local operations on labelled dot patterns

Abstract When a local operation is performed on the pixels in an array, the new value of the pixel is a function of the old values of the pixel and its neighbors. This paper introduces the more general concept of local operations on labelled dot patterns, where the new label of a dot is a function of the old labels of the dot and a set of its neighbors (e.g., its Voronoi neighbors). Such operations may change the positions of the dots, in addition to changing their ‘values’. We illustrate these ideas by giving examples of operations that perform local feature detection (e.g., isolated dot detection, cluster edge detection, dotted curve detection) and ‘enhancement’ (e.g., ‘smoothing’ the dot spacing or ‘sharpening’ the edges of diffuse clusters), as well as ‘morphological’ operations. Local operations on labelled graphs are also briefly discussed.

Hierarchical Frameworks for Early Vision

The serial processing mode was the first mode used in computer vision, as in many other domains. It is due to Von Neumann, although he was even more interested in parallel computing. In this context, a computer basically consists of a memory (whose capacity can now be as high as several gigabytes) containing the data to be processed and the codes for the instructions to be applied to the data; a processor which reads an instruction in the memory and executes the basic computation it describes.

Integration and Extensions

In Chapter 3, we presented a set of modules whose purpose is to extract information about global structures in images. The next step toward a computer vision system is integration. This leads us to the need for a methodology.

Pyramid Based Visual Modules

As outlined in Chapter 1, this Chapter will deal almost entirely with a particular class of techniques that seem to play a key role in the early stages of the visual process—namely, techniques for segmenting the image into distinctive parts. Indeed, when we look at a scene, we do not perceive an array of brightnesses; usually, we see a collection of regions separated by more or less well-defined edges. In computer vision, processes that decompose a scene into parts are called segmentation techniques.

Coarse-fine bimodality analysis of circular histograms

Abstract The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fischer distance between the resulting two subpopulations P 1 and P 2 . If P is a mixture of two (approximately) Gaussian subpopulations, then P 1 and P 2 are good approximations to the original Gaussians, if their Fisher distance if great enough. For a histogram having n bins this method of bimodality analysis requires n − 1 Fisher distance computations, since the range can be divided into two intervals in n − 1 ways. The method can also be applied to ‘circular’ histograms, e.g. of populations of slope or hue values; but for such histograms it is much more computationaly costly, since a circular histogram having n bins can be divided into two intervals (arcs) in n ( n − 1)/2 ways. The cost can be reduced by performing bimodality analysis on a ‘reduced-resolution’ histogram having n / k bins; finding the subdivision of this histogram that maximizes the Fisher distance; and then finding a maximum Fisher distance subdivision of the full-resolution histogram in the neighborhood of this subdivision. This reduces the required number of Fisher distance computations to n ( n − 1)/2 K 2 + O( k ). For histograms representing mixtures of two Gaussians, this method was found to work well for n / k as small as 8.