Showing papers by "Azriel Rosenfeld published in 1982"
TL;DR: Several techniques are presented for measuring 'cornerity' values in gray-level images, without prior segmentation, so that corners can be detected by thresholding these values.
659 citations
Book•
11 Aug 1982
TL;DR: The rapid rate at which the field of digital picture processing has grown in the past five years had necessitated extensive revisions and the introduction of topics not found in the original edition as discussed by the authors.
Abstract: The rapid rate at which the field of digital picture processing has grown in the past five years had necessitated extensive revisions and the introduction of topics not found in the original edition.
Table of Contents
Introduction. Mathematical Preliminaries. Visual Perception. Digitization. Compression. Enhancement. Restoration. Reconstruction. Index.
264 citations
TL;DR: It is shown that a digital region is convex if and only if every pair of points in the region is connected by a digital straight line segment contained in the area if it has the median-point property.
Abstract: It is shown that a digital region is convex if and only if every pair of points in the region is connected by a digital straight line segment contained in the region. The midpoint property is shown to be a necessary but not a sufficient condition for the convexity of digital regions. However, it is shown that a digital region is convex if and only if it has the median-point property.
119 citations
01 Sep 1982
TL;DR: This paper investigates several variations on the basic linking process with regard to such factors as initialization, criteria for linking, and iteration scheme used and extends the approach to links based on more than one feature of a pixel, e.g., on color components or local property values.
Abstract: A recently developed method of image smoothing and segmentation makes use of a "pyramid" of images at successively lower resolutions. It establishes links between pixels at successive levels of the pyramid; the subtrees of the pyramid defined by these links yield a segmentation of the image into regions over which the smoothing takes place. This paper investigates several variations on the basic linking process with regard to such factors as initialization, criteria for linking, and iteration scheme used. It also studies generalizations in which the links are weighted rather than forced, and in which interactions among the pixels at a given level are also allowed. Finally, it extends the approach to links based on more than one feature of a pixel, e.g., on color components or local property values.
71 citations
TL;DR: A simple class of piecewise constant approximations to an image is constructed as follows: start with the entire image, subdivide it into quadrants if its gray level standard deviation is high, and repeat the process for each quadrant so that each of them can be approximated by a constant value, namely, its mean.
Abstract: A simple class of piecewise constant approximations to an image is constructed as follows: start with the entire image, subdivide it into quadrants if its gray level standard deviation is high, and repeat the process for each quadrant. This yields a decomposition of the image into blocks, each having low standard deviation, so that each of them can be approximated by a constant value, namely, its mean. The histogram of this approximated image tends to have sharper peaks than that of the original image since the block averaging reduces the variability of the gray levels within homogeneous regions. A possible way of further improving the histogram is based on the fact that small blocks tend to occur near region borders; thus, suppressing these blocks should tend to deepen the valleys on the histogram, making threshold selection (to separate regions of different types) easier. Conversely, the histogram of the small blocks only represents a population of pixels near region borders, and if there are only two types of regions (e.g., objects and background), the mean of this histogram should be a useful threshold for separating them; but in practice, this method is not very reliable since background fluctuations also give rise to border pixels.
65 citations
TL;DR: It is proved that a digital solid is convex if and only if it has the chordal triangle property, which is only necessary, but not sufficient, conditions for a digitalSolid to be convex.
Abstract: A definition of convexity of digital solids is introduced. Then it is proved that a digital solid is convex if and only if it has the chordal triangle property. Other geometric properties which characterize convex digital regions are shown to be only necessary, but not sufficient, conditions for a digital solid to be convex. An efficient algorithm that determines whether or not a digital solid is convex is presented.
43 citations
TL;DR: A hybrid “split-and link” approach that combines features of both the split-and-merge and the overlapped “pyramid” approaches to segmentation is proposed.
40 citations
TL;DR: The assumption of orientability is shown not to be necessary in the case of 6-connectedness and, unexpectedly, it is shown that the property oforientability is not symmetric with respect to the two types of connectedness.
Abstract: This is a continuation of a series of papers on the digital geometry of three-dimensional images. In an earlier paper by Morgenthaler and Rosenfeld, a three-dimensional analog of the two-dimensional Jordan curve theorem was established. This was accomplished by defining simple surface points under the symmetric consideration of 6-connectedness and 26-connectedness and by characterizing a simple closed surface as a connected collection of “orientable” simple surface points. The necessity of the assumption of orientability, a condition of often prohibitive computational cost to establish, was the major unresolved issue of that paper. In this paper, the assumption is shown not to be necessary in the case of 6-connectedness and, unexpectedly, it is shown that the property of orientability is not symmetric with respect to the two types of connectedness.
40 citations
01 Jul 1982
TL;DR: The purpose of this investigation was to construct a geographic information system based on the quadtree hierarchical data structure, and to gather statistics to allow the evaluation of the usefulness of this approach in geographical information system organization.
Abstract: : The purposes of this investigation were twofold: (1) to construct a geographic information system based on the quadtree hierarchical data structure, and (2) to gather statistics to allow the evaluation of the usefulness of this approach in geographic information system organization. To accomplish the above objectives, in Phase I of the project was built that contained three maps supplied under the terms of the contract. These maps described the floodplain, elevation contours, and land use classes of a region in California. In Phase II, a quadtree-based Geographic Information System was partially implemented, allowing manipulation of images which store area, point, and line data. Phase III primarily dealt with enhancements and alterations to this information system package, an evaluation of some of the design decisions, and the collection of empirical results to indicate the utility of the software and to justify the indicated design decisions. Phase IV primarily dealt with developing new structures for storing linear feature data. The attribute attachment package was extended to point and linear feature data. Existing area map algorithms were improved to yield significant efficiency speedups by reducing node accesses. The efficiency of the linear quadtree was compared to that of the pixel array for computation of several important geographic functions. The particular tasks reported on in this document are: (a) Memory management improvements; (b) Database enhancements; (c) Attribute attachment; (d) New linear feature representation; (e) Quadtree/array comparisons.
40 citations
29 citations
TL;DR: The GRADMAT as discussed by the authors is a generalization of the medial axis transformation, in which a score is computed for each point P of a grayscale picture based on the gradient magnitudes at pairs of points that have P as their midpoint.
Abstract: Blum's medial axis transformation (MAT) for binary pictures yields medial axis points that lie midway between opposite borders of a region or along angle bisectors. This note discusses a generalization of the MAT in which a score is computed for each point P of a grayscale picture based on the gradient magnitudes at pairs of points that have P as their midpoint. These scores are high at points that lie midway between pairs of antiparallel edges or along angle bisectors, so that they define a MAT-like ``skeleton,'' which we may call the GRADMAT. However, this skeleton is rather sensitive to the presence of noise edges or to irregularities in the region edges, and it also is subject to artifacts created by pairs of edges belonging to different objects.
TL;DR: A number of methods are presented for finding clusters in collinear collections of line segments using merging methods and splitting methods that make use of an evaluation function.
TL;DR: An image can be segmented by classifying its pixels using local properties as features, and two intuitively useful properties are the gray level of the pixel and the ``busyness,'' or gray level fluctuation, measured in its neighborhood.
Abstract: An image can be segmented by classifying its pixels using local properties as features. Two intuitively useful properties are the gray level of the pixel and the ``busyness,'' or gray level fluctuation, measured in its neighborhood. Busyness values tend to be highly vari-able in busy regions; but great improvements in classification accuracy can be obtained by smoothing these values prior to classifying. An alternative possibility is to classify probabilistically and use relaxation to adjust the probabilities.
TL;DR: Figures of merit are defined for possible linking of pairs of edge segments that continue one another or are anti-parallel to each other based on both the geometrical configuration of the segments and the gray levels associated with them.
01 Jan 1982
TL;DR: One segmentation technique, 'superspike', outperformed all the others, detecting 88% of the targets and yielding only 1.6 false alarms per true target.
Abstract: : Several segmentation techniques were applied to a set of 51 FLIR (forward-Looking Infrared) images of four different types, and the results were compared to hand segmentations. There were substantial differences in performance, indicating that the choice of proper technique is very important. The segmentation techniques used were 'superslice,' 'pyramid spot detection', two versions of 'relaxation', pyramid linking', and 'superspike', One technique, 'superspike', outperformed all the others, detecting 88% of the targets and yielding only 1.6 false alarms per true target.
TL;DR: Results indicate that cultural features such as roads and buildings can be extracted and that a significant reduction in the complexity of the image description can be obtained.
Abstract: A method of pairing antiparallel straight lines is presented and discussed. The pairing is based on the distance between the lines, the amount by which they overlap, and on whether or not other lines are interposed. Examples are shown of applying the method to high resolution aerial photographs. Results indicate that cultural features such as roads and buildings can be extracted and that a significant reduction in the complexity of the image description can be obtained.
TL;DR: A bibliography of nearly 1000 references related to the computer processing of pictorial information, arranged by subject matter is presented.
01 Jan 1982
TL;DR: This chapter discusses picture and scene segmentation techniques, and the perceptual processes involved in segmentation of a scene by the human visual system, such as the Gestalt laws of organization, are not yet well understood.
Abstract: Publisher Summary
In image compression or enhancement, the desired output is a picture— an approximation to, or an improved version of, the input picture. Another major branch of picture-processing program deals with image analysis or scene analysis. This chapter discusses picture and scene segmentation techniques. Some segmentation operations can be applied directly to any picture; others can only be applied to a picture that has already been partially segmented as they depend on the geometry of the parts that have already been extracted from the picture. For example, a chromosome picture can be (crudely) segmented by thresholding its gray level. Once this has been done, further segmentation into individual chromosomes can be attempted, based on connectedness, size, and shape criteria. There is no single standard approach to segmentation. The perceptual processes involved in segmentation of a scene by the human visual system, such as the Gestalt laws of organization, are not yet well understood.
TL;DR: This note points out that texture analysis techniques are applicable, in principle, to three-dimensional data arrays and to arrays of range (or terrain elevation) data.
TL;DR: Besides reducing thick responses to thin, the application of non-maximum suppression to digital gradient magnitudes also improves the form of the edge response histogram, making the choice of thresholds easier.
01 Jan 1982
TL;DR: This chapter discusses various representation schemes and their application to geometric property measurement in segmentation, which decomposes a picture into subsets or regions.
Abstract: Publisher Summary
Segmentation decomposes a picture into subsets or regions. The geometrical properties of these subsets—connectedness, size, shape—are often important in picture description. There are many methods of measuring such properties; the preferred method usually depends on how the subsets are represented. This chapter discusses various representation schemes and their application to geometric property measurement. Each row of a picture consists of a sequence of maximal runs of points such that the points in each run all have the same value. Thus, the row is completely determined by specifying the lengths and values of these runs. The run length coding is sometimes used for picture compression. The set of centers and radii (and values) of the maximal blocks is called the medial axis (or symmetric axis) transformation. It also explains that the maximal connected regions of constant value are analogous to runs; however, they are not good primitive elements for representation purposes as they themselves cannot be specified compactly; a block, on the other hand, is defined by specifying its center and radius.
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TL;DR: An analgous method of piecewise approximating a waveform or a closed curve by linking nodes in a one-dimensional “pyramid” of reduced-resolution versions of the curve is developed.
TL;DR: Hueckel-type edge operators find the best-fitting step function to a given image neighborhood to derive some basic properties of such operators for various classes of neighborhoods.
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TL;DR: This chapter discusses the mapping of a three-dimensional scene into a two-dimensional picture from the standpoint of the coordinate transformations that are involved — translation, rotation, scale change, and reflection.
Abstract: Publisher Summary
There are many situations in which two pictures are matched with one another or a piece of the pictures are matched. The registration of two pictures taken from different positions requires an understanding of imaging geometry, that is, of how three-dimensional scenes are mapped into two-dimensional pictures. In some cases, two pictures of a scene can be registered by applying an overall perspective transformation. More commonly, a simple transformation cannot be used rather a transformation should be defined piecewise, based on comparing the positions of corresponding landmarks in the two pictures. The position comparisons can also be used to determine the three-dimensional positions of points in the pictures. This chapter discusses the mapping of a three-dimensional scene into a two-dimensional picture from the standpoint of the coordinate transformations that are involved. This chapter discusses the transformations that map one Cartesian coordinate system into another — translation, rotation, scale change, and reflection.
01 Jan 1982
TL;DR: This chapter presents the geometric properties of picture subsets, including the local properties and property complexity, the template properties—such as moments—the properties of projections and transforms, and the statistical and textural properties.
Abstract: Publisher Summary
Picture descriptions generally specify the properties of parts of the picture and relationships among these parts. Thus, such descriptions are often represented by relational structures, such as graphs, in which the nodes correspond to the parts; each node is labeled with its associated property values and the arcs correspond to relations between parts, labeled with the associated relation values if the relations are quantitative. In the special case where the description does not refer to the parts of the picture, it consists simply of a list of property values, defined for the picture as a whole. This chapter presents the geometric properties of picture subsets. Such properties depend only on the set of points in the given subset and not on the gray levels of these points. The chapter discusses the properties of pictures and picture subsets that depend on gray level. The chapter also discuss some general classes of picture properties—in particular, linear and transformation-invariant properties—and explains some specific types of properties, including the local properties and property complexity, the template properties—such as moments—the properties of projections and transforms, and the statistical and textural properties.
04 Oct 1982
TL;DR: A class of cellular computers is described, and general examples are given illustrating how such a computer could initially configure itself to represent a given decomposition of an image into regions, and dynamically reconfigure itself, in parallel, as regions merge or split.
Abstract: It is well known that cellular computers can be used very effectively for parallel image processing at the pixel level, by assigning a processor to each level or block of pixels, and passing information as necessary between processors whose blocks are adjacent This paper discusses the use of cellular computers for parallel processing of images at the region level, assigning a processor to each region and passing information between processors whose regions are related The basic difference between the pixel and region levels is that the regions (eg, obtained by segmenting the given image) and relationships differ from image to image, and even for a given image, they do not remain fixed during processing Thus, one cannot use the standard type of cellular parallelism, in which the set of processors and interprocessor connections remain fixed, for processing at the region level Reconfigurable cellular computers, in which the set of processors that each processor can communicate with can change during a computation, are more appropriate A class of such computers is described, and general examples are given illustrating how such a computer could initially configure itself to represent a given decomposition of an image into regions, and dynamically reconfigure itself, in parallel, as regions merge or split
TL;DR: Two methods of waveform approximation were compared, one based on maximal homogeneous neighborhoods, the other on recursive subdivision of nonuniform subintervals, and the compactness/error tradeoff was found to favor the former method.