Distance transformations in digital images
01 Jun 1986-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing (Academic Press Professional, Inc.)-Vol. 34, Iss: 3, pp 344-371
TL;DR: Six different distance transformations, both old and new, are used for a few different applications, which show both that the choice of distance transformation is important, and that any of the six transformations may be the right choice.
Abstract: A distance transformation converts a binary digital image, consisting of feature and non-feature pixels, into an image where all non-feature pixels have a value corresponding to the distance to the nearest feature pixel. Computing these distances is in principle a global operation. However, global operations are prohibitively costly. Therefore algorithms that consider only small neighborhoods, but still give a reasonable approximation of the Euclidean distance, are necessary. In the first part of this paper optimal distance transformations are developed. Local neighborhoods of sizes up to 7×7 pixels are used. First real-valued distance transformations are considered, and then the best integer approximations of them are computed. A new distance transformation is presented, that is easily computed and has a maximal error of about 2%. In the second part of the paper six different distance transformations, both old and new, are used for a few different applications. These applications show both that the choice of distance transformation is important, and that any of the six transformations may be the right choice.
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TL;DR: A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced, based on an immersion process analogy, which is reported to be faster than any other watershed algorithm.
Abstract: A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided. >
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TL;DR: 40 selected thresholding methods from various categories are compared in the context of nondestructive testing applications as well as for document images, and the thresholding algorithms that perform uniformly better over nonde- structive testing and document image applications are identified.
Abstract: We conduct an exhaustive survey of image thresholding methods, categorize them, express their formulas under a uniform notation, and finally carry their performance comparison. The thresholding methods are categorized according to the information they are exploiting, such as histogram shape, measurement space clustering, entropy, object attributes, spatial correlation, and local gray-level surface. 40 selected thresholding methods from various categories are compared in the context of nondestructive testing applications as well as for document images. The comparison is based on the combined performance measures. We identify the thresholding algorithms that perform uniformly better over nonde- structive testing and document image applications. © 2004 SPIE and IS&T. (DOI: 10.1117/1.1631316)
4,543 citations
Cites background from "Distance transformations in digital..."
...The distance function can be taken as Chamfer distance [107]....
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TL;DR: Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented and it is shown that the method extends naturally to the problem of comparing a portion of a model against an image.
Abstract: The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented. The focus is primarily on the case in which the model is only allowed to translate with respect to the image. The techniques are extended to rigid motion. The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. It is shown that the method extends naturally to the problem of comparing a portion of a model against an image. >
4,194 citations
Book•
30 Sep 2010
TL;DR: Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images and takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene.
Abstract: Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.
4,146 citations
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References
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Book•
01 Jan 1976
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.
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.
4,231 citations
TL;DR: It is shown that skeletons can be produced by simple procedures and since these are based on Euclidean distances it is assumed that they are superior to skeletons based on d4−, d8−, and even octagonal metrics.
1,777 citations
TL;DR: The relative merits of performing local operations on ~ digitized picture in parallel or sequentially are discussed and some applications of the connected component and distance functions are presented.
Abstract: The relative merits of performing local operations on ~ digitized picture in parallel or sequentially are discussed. Sequential local operations are described which l~bel the connected components of a given subset of the picture and compute u \"distance\" from every picture element to the subset. In terms of the \"distance\" function, ~ \"skeleton\" subset is defined which, in a certain sense, minimally determines the original subset. Some applications of the connected component and distance functions are also presented.
1,707 citations
"Distance transformations in digital..." refers background in this paper
...Values that have been suggested for a and b are: a = 1, b = infinity, and a = 1, b = 1 in [2]; a = 1, b = C ~ - i n [ 5 ] ; a = 2 , b = 3 i n [ 6 ] ; a n d a = 3 , b = 4 i n [ 1 ] ....
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...) In early papers about distance transforms, [2, 3], almost no attempt was made to optimize the local distances used in the DT....
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...Sequential DTs was first published in 1966 [2], and parallel ones in 1968 [3]....
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Proceedings Article•
22 Aug 1977TL;DR: The matching of image and map features is performed rapidly by a new technique, called "chamfer matching", that compares the shapes of two collections of shape fragments, at a cost proportional to linear dimension, rather than area.
Abstract: Parametric correspondence is a technique for matching images to a three dimensional symbolic reference map. An analytic camera model is used to predict the location and appearance of landmarks in the image, generating a projection for an assumed viewpoint. Correspondence is achieved by adjusting the parameters of the camera model until the appearances of the landmarks optimally match a symbolic description extracted from the image.
The matching of image and map features is performed rapidly by a new technique, called "chamfer matching", that compares the shapes of two collections of shape fragments, at a cost proportional to linear dimension, rather than area. These two techniques permit the matching of spatially extensive features on the basis of shape, which reduces the risk of ambiguous matches and the dependence on viewing conditions inherent in conventional image based correlation matching.
896 citations
"Distance transformations in digital..." refers background in this paper
...This DT, which is also found in [7], is described by the mask in Fig....
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...It is, among other places, found in [7]....
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01 Sep 1984-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: The purpose of this paper is to generalize these distance transformation families to higher dimensions and to compare the computed distances with the Euclidean distance.
Abstract: In many applications of digital picture processing, distances from certain feature elements to the nonfeature elements must be computed. In two dimensions at least four different families of distance transformations have been suggested, the most popular one being the city block/chessboard distance family. The purpose of this paper is twofold: To generalize these transformations to higher dimensions and to compare the computed distances with the Euclidean distance. All of the four distance transformation families are presented in three dimensions, and the two fastest ones are presented in four and arbitrary dimensions. The comparison with Euclidean distance is given as upper limits for the difference between the Euclidean distance and the computed distances.
870 citations