C.E. Kim and A. Rosenfeld, Digital straight lines and convexity of digital regions, IEEE T. on PAMI 4 (1982), 149--153.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....one shortest path or geodesic linking u to v while remaining in S. 3. A set of points S within a grid is convex if it is equivalent to points falling within the intersection of all half planes containing S. These definitions and further discussions about digital convexity issues can be found in [17, 8, 10, 11, 12, 7]. In [16] a set is said to be weakly or strongly convex depending on whether it satisfies the first or the second definition. Since the intersection of any family of convex sets is also a convex set, there exists a smallest convex set containing any given set. The smallest convex set containing ....

C. Kim and A. Rosenfeld. Digital straight lines and convexity of digital regions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2):149--153, March 1982.

.... the Cantor set and its 2 D generalization, the Sierpinski carpet, have both an infinite number of convex concavities (i.e. the degree of the root is infinite but the height of the tree equals 1) In the discrete case, there are problems with the definition of convexity in terms of line segments [15]. This is because there may be more than one connected digital line segments linking two points [21] Hence, several definitions have been proposed for determining whether a discrete set is convex or not: 1. The set of vertices of a graph 6 is convex, if for all u, v C , every vertex on all ....

C. Kim and A. Rosenreid. Digital straight lines and convexity of digital regions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(2):149-153, March 1982.

....corner points are obtained by the incremental splitting polygonal approximation method [4] Since we only want the contact points between the different elliptical objects, it becomes necessary to verify if the detected corner points belong to a convex neighbourhood or not. It has been shown in [5] that an arc segment is convex if every point of a line segment, defined by any two points of that arc, lies inside the region of support. Let x be the ith corner point detected by the splitting method. Given the noisy neighbourhood of x i , it is considered to be a contact point if and only if ....

Chul Kim and A.Rosenfeld, "Digital straight lines and convexity of digital regions", IEEE Trans. On Pattern Analysis and Machine Vision, 4, 1991.

....methods and (ii) curvature based methods. In this work we apply the incremental splitting introduced in [3] which is computationally very efficient. This algorithm identifies extreme points in non convex, as well as in convex contour regions. By applying the convexity criterion introduced [4] it is seen that point P i , obtained with the incremental splitting method, lies on a non convex region if and only if ,P i Pm D and Pm lies outside the object (Pm middle point of line segment defined by the contour points z position to the right and to the left to P i ; D user defined ....

C. Kim and A. Rosenfeld. Digital straight lines and convexity of digital regions. IEEE Trans. Pattern Analysis and Machine Vision, 17, (1991).

....curvature based methods. In this work we apply the incremental splitting algorithm (Esplid and Jonassen, 1991) which is computationally very efficient. This algorithm identifies extreme points in non convex, as well as in convex contour regions. By applying the convexity criterion introduced in (Kim and Rosenfeld, 1991) it is seen that point P i , obtained with the incremental splitting method, lies on a nonconvex region if and only if ,P i Pm D and Pm lies outside the object (Pm middle point of line segment defined by the contour points z position to the right and to the left to P i ; D user defined ....

Kim, C. and Rosenfeld, A. (1991). Digital straight lines and convexity of digital regions. IEEE Trans. On Pattern Analysis and Machine Vision.17.

....is computationally ecient. After the calculation of all corner points, the contact points between the elliptical shapes (corner points which delimit convex regions) are identi. ed with the application of the following criterion: Convexity Criterion: elementary arcs are convex. Kim and Rosenfeld [11] have shown that an arc segment is convex if every point of a line segment, de. ned by any two points of that arc segment, lie inside the region of support. Let P i = x i ; y i ) be the ith corner point obtained by the incremental splitting method in contour Cont k;j . Point P i is considered to ....

Chul Kim; A. Rosenfeld. Digital straight lines and convexity of digital regions. IEEE Trans. on Pattern Analysis and Machine Vision, 4, 1991.

....identification. 7. 1 Geometric Problems There are a number of problems in discrete geometry and image processing in which one is interested in studying discrete approximations of an underlying continuous object and or extracting properties of an object from its discrete approximations (e.g. see [7, 9, 14, 17]) In the case where some estimate is made based on a digitized version of an object, a natural condition to impose is that the estimates converge as the digitization level gets finer and finer [9] The classification paradigm can be used to address the existence of decision rules with various ....

C.E. Kim and A. Rosenfeld, "Digital straight lines and convexity of digital regions," IEEE Trans. PAMI, Vol. 4, pp. 149-153, 1982.

....not a set A of digital points is a digital line, that is, the image of a line segment, defined as the set of closest pixels to the intersections of a given line segment with the coordinate lines parallel to the sides of the image and having fixed integer coordinates. We use the criteria given in [30]. Specifically, A is a digital line if and only if the following two conditions are satisfied: a) A is a digital arc (i.e. each pixel from A has exactly two neighbors except for the endpoints which have one neighbor each) b) A is a convex digital region. The first condition can be easily ....

....per processor in a MHB of size p n Theta p n is a digital line can be determined in O(log n) time. The problem of detecting digital lines can be extended to higher dimensions using the digitization scheme and recognition algorithm from [52] The method in [52] generalizes the planar case [30] and uses the criteria that a set of points in higher dimensional grid is a digital line if and only if some projections of the set of points on two dimensional grids are digital lines in plane. The solution is obtained from the planar case and the above criteria, and its complexity is O(k log ....

C.E. Kim and A. Rosenfeld, Digital straight lines and convexity of digital regions, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4, (1982), 149--153.

....be sorted by x and y coordinates. Note that the mapping of the set to either x or y coordinate is one to one on a given interval (the condition is necessary but not sufficient for a digital line; a set that maps one to one on x coordinate can be even disconnected) We use the criteria given in [13]. A is a digital line if and only if the following two conditions are met: a) A is a digital arc (i.e. each pixel from A has exactly two neighbors except two endpoints which have one neighbor each) b) A is a convex digital region. It is easy to confirm that both criteria, and therefore the ....

....n Theta p n can be determined in O(n 1=6 ) time. Furthermore, this is time optimal on this architecture. The problem of detecting digital lines can be extended to higher dimensions using the digitization scheme and recognition algorithm from [22] The method in [22] generalizes the planar case [13] and uses the criteria that a set of points in higher dimensional grid is a digital line if and only if some projections of the set of points on two dimensional grids are digital lines in plane. The solution is obtained from the planar case and the above criteria, and its complexity is O( k n ....

C.E. Kim and A. Rosenfeld, Digital straight lines and convexity of digital regions, IEEE Transactions on PAMI, 4, 149--153, 1982.

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C.E. Kim and A. Rosenfeld, Digital straight lines and convexity of digital regions, IEEE T. on PAMI 4 (1982), 149--153.

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C. E. Kim and A. Rosenfeld. Digital Straight Lines and Convexity of Digital Regions. IEEE Trans. PAMI 4, 149--153, 1982.

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