The fact that objects in the world appear in different ways depending on the scale of observation has important implications if one aims at describing them. It shows that the notion of scale is of utmost importance when processing unknown measurement data by automatic methods. In their seminal works, Witkin (1983) and Koenderink (1984) proposed to approach this problem by representing image structures at different scales in a so-called scale-space representation. Traditional scale-space theory building on this work, however, does not address the problem of how to select local appropriate scales for further analysis. This article proposes a systematic methodology for dealing with this problem. A framework is proposed for generating hypotheses about interesting scale levels in image data, based on a general principle stating that local extrema over scales of different combinations of γ-normalized derivatives are likely candidates to correspond to interesting structures. Specifically, it is shown how this idea can be used as a major mechanism in algorithms for automatic scale selection, which

Many computer vision problems can be considered to consist of two main tasks: the extraction of image content descriptions and their subsequent matching. The appropriate choice of type and level of description is of course task dependent, yet it is generally accepted that the low-level or so called early vision layers in the Human Visual System are context independent. This paper concentrates on the use of low-level approaches for solving computer vision problems and discusses three inter-related aspects of this: saliency; scale selection and content description. In contrast to many previous approaches which separate these tasks, we argue that these three aspects are intrinsically related. Based on this observation, a multiscale algorithm for the selection of salient regions of an image is introduced and its application to matching type problems such as tracking, object recognition and image retrieval is demonstrated.

In computer vision and image processing, edge detection concerns the localization of significant variations of the grey level image and the identification of the physical phenomena that originated them. This information is very useful for applications in 3D reconstruction, motion, recognition, image enhancement and restoration, image registration, image compression, and so on. Usually, edge detection requires smoothing and differentiation of the image. Differentiation is an ill-conditioned problem and smoothing results in a loss of information. It is difficult to design a general edge detection algorithm which performs well in many contexts and captures the requirements of subsequent processing stages. Consequently, over the history of digital image processing a variety of edge detectors have been devised which differ in their mathematical and algorithmic properties. This paper is an account of the current state of our understanding of edge detection. We propose an overview of research...

. We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusion-transparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization. Keywords: topographic map, mathematical morphology, level set, junctions, contrast changes, digitization 1.

When observing a dynamic world, the size of image structures may vary over time.

We discuss the physical generation process of images as a combination of occlusions, transparencies and contrast changes. This description #ts to the phenomenological description of Gaetano Kanizsa, according to which visual perception tends to remain stable with respect to these basic operations by detecting several kinds of essential singularities which we call junctions. The most frequent junctions are T-junctions and X-junctions, generated respectively by occlusion and transparency. We deduce a mathematical and computational model for image analysis according to which the "atoms", that is, the starting elements of every image analysis process must be "pieces of level lines joining T-or X-junctions". A junction detection algorithm, parameter-free except for two #xed thresholds eliminating quantization e#ects in space and grey level, is proposed for the computation of the "atoms of perception" thus de#ned. We then propose the adequate modi#cation of morphological #ltering algorithms so that they smooth the "atoms" without altering the junctions. This permits to display easy-to-read topographic maps for images, where the subjacent #and mostly hidden to the human awareness# occlusion-transparency structure is put into evidence by the interplay of level lines. 1

This article presents a method for segmenting and classifying edges using minimum description length (MDL) approximation with automatically generated break points. A scheme is proposed where junction candidates are first detected in a multi-scale preprocessing step, which generates junction candidates with associated regions of interest. These junction features are matched to edges based on spatial coincidence. For each matched pair, a tentative break point is introduced at the edge point closest to the junction. Finally, these feature combinations serve as input for an MDL approximation method which tests the validity of the break point hypotheses and classifies the resulting edge segments as either "straight " or "curved". Experiments on real world image data demonstrate the viability of the approach.

A basic functionality of a vision system concerns the ability to compute deformation fields between di#erent images of the same physical structure. This article advocates the need for incorporating an explicit mechanism for scale selection in this context, in algorithms for computing descriptors such as optic flow and for performing stereo matching . A basic reason why such a mechanism is essential is the fact that in a coarse-to-fine propagation of disparity or flow information, it is not necessarily the case that the most accurate estimates are obtained at the finest scales. The existence of interfering structures at fine scales may make it impossible to accurately match the image data at fine scales. A systematic methodology for approaching this problem is proposed, by estimating the uncertainty in the computed flow estimate at each scale, and then selecting deformation estimates from the scales that minimize the (suitably normalized) uncertainty over scales . A specific implementat...

this article is to consider the domain of feature tracking and to complement previous works by addressing the scale problems arising in this context. In most previous works, the analysis is performed at a single predetermined scale, and this may can cause severe problems if the size of image structures change over time due to expansions or contractions. We will show how an explicit mechanism for automatic scale selection can be included in a feature tracker to handle tracking situations in which the size variations are large. Besides avoiding explicit setting of scale levels for feature detection, and thus overcoming some of the very fundamental limitations of processing image sequences at a single scale, it will be demonstrated how scale levels selected by a scale selection procedure are useful for adapting the window size for correlation and as a matching cue. It will also be illustrated how an appropriate choice of temporal scale can improve the performance. Fixed scale tracking Adaptive scale tracking Fig. 1. Illustration of the importance of automatic scale selection when tracking image structures over time. A fixed scale tracker fails early when the size variations are large (left), whereas all visible blobs are correctly tracked up to the last image when a mechanism for adaptive scale selection has been included (right). 2 The need for automatic scale selection in tracking

We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusion-transparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization. 1 Introduction What are the basic, computable elements from which the analysis of an...