H. Freeman, "Boundary encoding and processing," in Picture Processing and Psychopictories. New York: Academic, 1970.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1. INTRODUCTION Region based image coding is an area that has seen tremendous interest in recent years. One of the tools required for a successful region based image encoding is an efficient image partition encoding method. The classical method for solving is problem is based on using chain codes [1, 2]. However as the number of regions in an image partition increases, the performance of the chain coder goes down rapidly. An interesting alternative approach to the partition encoding problem is based on using lossless compression methods on image bitmaps created by associating a single color with ....

H. Freeman, "Boundary encoding and processing," in Picture Processing and Psychopictorics, B. S. Lipkin and A. Rosenfeld, Eds., pp. 241--266. Academic Press, 1970.

....digital curve representation schemes consist of a quantization (or digitization) stage followed by chain encoding. Chain codes are the standard input format for numerous shape analysis and machine vision algorithms. Various 2 D curve representation schemes have been considered in the literature [13, 14, 16, 18, 23, 32, 40, 41, 42, 44, 51, 55]. A valuable comparison between the main techniques appears in [32] The details of the digital curve representation scheme can have great influence on the performance of subsequent algorithms. For example, Kulpa [35] resolved a controversy between two approaches to area measurement by showing ....

....different representation schemes. Consider the evolution of estimators for the original perimeter of a 2 D shape from Currently with RDC Communications Ltd. P.O. Box 34233, Jerusalem 91341, Israel y To whom correspondence should be addressed 1 its chain code, from the original work of Freeman [13, 14] to recent contributions [11, 33] It is apparent that careful analysis of the digitization schemes and their effects on the properties of digitized straight lines [6, 9, 10, 12, 13, 19, 20, 37, 39, 47, 56] that are a limiting case for fine sampling of smooth curves) has been the key to ....

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H. Freeman, "Boundary Encoding and Processing", in B.S. Lipkin and A. Rosenfeld (eds.), Picture Processing and Psychopictorics, pp. 241-266, Academic Press, New York, 1970.

....approach is used for the development of 3 D length estimators in the sequel. 6 3 Cube Quantization The properties and advantages of cube quantization over other 3 D digital curve representation schemes have been studied in [9] A brief summary is provided in this section. Square Quantization [5, 6, 13] is a scheme for digital representation of 2 D curves. The image plane is divided to square pixels and the curve is implicitly segmented according to its intersections with the square pixels. The digital representation is the sequence of points at the centers of these pixels, following the order ....

....order of the segments along the curve. For a curve in general position, the probability of corner crossing between pixels is zero and can be ignored, so diagonal links do not appear and a 4 chain is obtained. Other 2 D schemes can be used to get 8 chains. In Grid Intersection Quantization (GIQ) [5, 6] the curve is represented by selecting, at each intersection of the curve with a grid line, the closer grid point. The order of points follows the order of intersections along the curve. Cube Quantization (CQ) is an extension of Square Quantization to 3 D in which cubic voxels replace square ....

H. Freeman, "Boundary Encoding and Processing", in B.S. Lipkin and A. Rosenfeld (eds.), Picture Processing and Psychopictorics, pp. 241-266, Academic Press, New York, 1970. 32

....our methods. The two stage framework for polygon retrieval Considerable work has been carried out on shape matching problem. A literature survey is presented in Chapter 2. Traditional techniques use model driven approach in which the target shape is compared individually against each model shape [14, 15, 9]. This approach is inefficient because of its linear searching complexity. Other techniques use data driven approach in which features of shapes are extracted and mapped into a multidimensional index structure. Matching is conducted by performing searching in the index tree [23, 28, 29] The ....

....invariant numerical values from Chapter 1 Introduction 7 the distance between corresponding vertices of different polygons as the similarity measures between these polygons. Characteristics study and performance evaluation We have studied the characteristics of the Freeman Chain Code method [14, 15], the Moment method [25] the Rectangular Cover method [23] the Potential based method [9] the Normalized Coordinate System method [28, 29] the Hausdorff Distance method [20, 2] and the PCA method [44] We also compare the performance of the Normalized Coordinate System method and the ....

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H. Freeman. Boundary Encoding and Processing. In Picture Processing and Psychopictorics, pages 241--266.

....line segment. Rosenfeld [3] defined the straight line segment introducing the so called chord property. A digital arc is a digitization of a straight line segment if and only if it has the chord property. To describe a digital straight line on a lattice, Freeman s chain coding scheme can be used [2]. In a later paper three conditions are suggested which must be obeyed by a chain code to be a representation of the digital straight line. Analysis of the problem was continued in [4] where an algorithm is given with the output saying whether the analyzed chain code represent the straight line ....

....to define more data structures containing complete data representing the given non descending digital curve. As it is shown below, in our case the Non descending Digital Straight Line Segment with the initial point S[0; 0] and the endpoint E[h; v] may be represented by the v tuple T j T [1] T [2]; T [i] T [v] where T [i] is the integer value of x coordinate and i is the integer y coordinate of the i th transition point. Further we show that a proper digitization scheme may be derived yielding explicit formulas for 2 calculation of coordinates of transition points. The ....

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H. Freeman, "Boundary encoding and processing, " B.S.Lipkin and A. Rosenfeld, eds., Picture Processing and Psychopictorics, Academic Press, New York, 1970, pp. 241-266.

....a short segment at the end. In this article, the structure of these segments is investigated in detail. In particular, it is shown that this structure is related to the greatest common divisor of the end point coordinates. We would like to stress, that there is also a different point of view [14, 13] which gives a similar structural information. In particular, so called Freeman sequences can be used to analyse the structure of those segments. The main difference between our approach and Freeman sequences is that they are defined for infinite lines and as far as we know the greatest common ....

H. Freeman, "Boundary encoding and processing," B.S.Lipkin and A. Rosenfeld, eds., Picture Processing and Psychopictorics, Academic Press, New York, 1970, pp. 241-266. 7

....until they are superimposed, and then compute the area between them. The smaller the area is, the more similar are the curves. However, it is not possible to achieve the superimposition at this stage, given that expansion, rotation and translation are unknown yet. We have chosen the chain codes [6] for representing boundaries in order to obtain an approximate invariance under rotation, translation, and expansion. The comparison of the boundary shapes is based on the Mahalanobis distance between the frequencies of various types of boundary corners, represented by first differences of ....

H. Freeman. Boundary encoding and processing. In B. S. Lipjin and A. Rosenfield, editors, Picture Processing and Psychopictorics, pages 241--266, New York, 1970. Academic Press.

....is, extracting the edges from the implicit iconic representation and storing them in an explicit junction and edge representation. Several other procedures for edge extraction and localisation have been reported previously, including ones that require only one pass of the image as this one does [2, 3, 4, 5, 6, 7, 8, 9]. The rest of this paper is outlined as follows: Section 2 describes edges as boundaries between regions. Therefore, edge connectivity is related to the topology of regions. It is Figure 1: A simple image incorrectly divided into two regions by using 8 connectedness. shown that many of the ....

H. Freeman. Boundary encoding and processing. In B. S. Lipkin and A. Rosenfeld, editors, Picture Processing and Psychopictories. Academic Press, 1970.

.... (a subset of ZZ 2 ) or the union of black squares (a subset of IR 2 ) When digitlal straight line models were first studied by Freeman and Rosenfeld, the digitization models that were assumed were based on the intersection digitization, which is called square box quantization by Freeman [3]. We have the following inclusions Dig 1 (C) Dig v (C) Dig (C) for every v 2 [0; 1] see Figure 1) and Dig v (C) Digw (C) if w v for every v; w 2 [0; 1] c) b) a) Figure 1: a) The two squares represent a digitization of the ellipse in which the ratio of the area is equal to 1. b) The ....

H. Freeman. Boundary Encoding and Processing. In B. S. Lipkin and A. Rosenfeld (eds.): Picture Processing and Psychopictures, pp. 241-- 266, Academic Press, New York, 1970.

....with the average being slightly less than two. Structural methods encompass not only research in efficient line generation but also general investigations into the properties of straight lines drawn on a discrete lattice with applications in compaction, pattern recognition and image processing [6, 7, 8, 10, 11, 14, 15, 16]. For the purpose of efficiently generating lines, the most interesting finding of this research is the existence of nested periodic patterns in the output of best fit line generators. Brons was the first to develop an algorithm that generates a line by first determining these periodic patterns ....

....between 0 and 1) are considered here since other lines can be transformed to meet these conditions through simple x y translation and reflection about the x or y axis or the lines y = x or y = x . 2. 1 Chain Codes A simple notation for describing a line on a raster grid is Freeman s chain coding [11]. A chain code is a string whose symbols are digits between 0 and 7. Each symbol represents a one pixel move in the direction shown in Figure 2.1. 0 7 6 2 1 5 4 3 Figure 2.1. Chain code symbols and associated movements. Freeman also identified three properties of the chain code of a line drawn on ....

Freeman, H. Boundary encoding and processing . In Picture Processing and Pyshopictorics. B. S. Lipkin and A. Rosenfeld, Eds., Academic Press, New York 1970, 214-266.

....problem outlined before. But we will see that the solution of this problem points to ways to solve the general problem. We focus mainly on the calculation of estimators for the length of a digitized straight line segment. Prior to our study, various length measures had been published. Those of [11], 12] 19] were of the form L = an e bn o . Freeman [11] used the intuitive but inaccurate (a; b) 1; p 2) Groen and Verbeek [12] and Kulpa [19] calculated the coefficients by a statistical analysis over all digitized straight lines. Later, Koplowitz [16] computed the probability of odd ....

....of this problem points to ways to solve the general problem. We focus mainly on the calculation of estimators for the length of a digitized straight line segment. Prior to our study, various length measures had been published. Those of [11] 12] 19] were of the form L = an e bn o . Freeman [11] used the intuitive but inaccurate (a; b) 1; p 2) Groen and Verbeek [12] and Kulpa [19] calculated the coefficients by a statistical analysis over all digitized straight lines. Later, Koplowitz [16] computed the probability of odd and even codes for arbitrary digitization schemes and curving ....

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H. Freeman, Boundary Encoding and Processing, In: Picture Processing and Psychopictorics (B.S. Lipkin and A. Rosenfeld, eds.), Academic Press, New York, pp.241-266, 1970.

....citing an unpublished note of Duda A = 1 4 nfQ 1 g 1 2 nfQ 2 g 7 8 nfQ 3 g nfQ 4 g 3 4 nfQD g (3) and P = nfQ 2 g 1 p 2 [nfQ 1 g nfQ 3 g 2nfQD g] 4) Methods Based on Chain Codes Chain coding is a method to represent a binary object. The 8 connected Freeman chain coding [9] uses a 3 bit code 0 c 7 for each boundary point. The number c indicates the direction in which the next boundary point is located, as shown in Fig. 1(a) The 8 connected Freeman chain coding strategy is shown in Fig. 1(b) There are some variations of the Freeman chain coding, for example, the ....

....Fig. 1(c) The mid crack codes possess some special properties in measuring shape features [11, 12] Boundary chain codes can be determined using a contour following [8] which is a traversing process to identify the boundary of a binary object. The algorithm requires operations of O(N) Freeman [9] computed the area enclosed by the contour of the Freeman chain codes c 1 c 2 Delta Delta Delta c n A = n X i=1 c ix (y i Gamma1 c iy =2) 5) where n is the length of the chain, c ix and c iy are the x and y components of the ith chain element c i (c ix , c iy 2 f1; 0; Gamma1g ....

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H. Freeman. Boundary encoding and processing. In B. S. Lipkin and A. Rosenfeld, editors, Picture Processing and Psychopictorics, pages 241266. Academic Press, 1970.

No context found.

H. Freeman, "Boundary encoding and processing," in Picture Processing and Psychopictories. New York: Academic, 1970.

No context found.

H. Freeman. Boundary encoding and processing. In B.S. Lipkin and A. Rosenfeld, editors, Picture processing and Psychopictorics, pages 241--266. New York: Academic, 1970.

No context found.

Freeman, H., Boundary encoding and processing, in Picture Processing and Psychopictorics, B.S. Lipkin and A. Rosenfeld, Editors. 1970, Academic Press: New York. p. 241-266.

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