Giardina, C.R. and E.R. Dougherty. 1988. Morphological Methods in Image and Signal Processing. Prentice-Hall, Englewood Cliff, NJ.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....For each tool access direction a robust and efficient freeform shape machining strategy will be implemented. In this paper we describe such strategies using Minkowski operations. Researchers in the field of mathematical mor phology have studied the Minkowski addition and subtraction extensively [5, 13]. In this field the Minkowski addition and subtraction are used to define the dilation and erosion image processing operations, respectively. Although mathematical morphology has initially been applied to digital image processing, the Minkowski addition and subtraction are defined generally for ....

....has been implemented without using Minkowski operations (see, e.g. 12] In the next section we define Minkowski opera tions on numerical functions and in section 5 we describe the implementation of both algorithms using numerical functions on Z . numerical functions In gray scale morphology [5, 13] the definitions of Minkowski operations on sets are modified to real valued functions defined on finite subsets of R n, the Euclidean space of dimension n, and on Z n, the Euclidean grid of dimension n. These functions are called numerical functions. In the next section we use numerical ....

R.G. Giardina and R.D. Dougherty. Morphological Methods in Image and Signal Processing. Prentice Hall, 1988.

....the form and structure of objects present in a given image. It is a set theoretic and geometric approach to image processing which is very efficient in extracting image components that are useful in the representation and description of the object shapes, such as object boundaries, skeletons, etc. [1, 2]. In morphology, a quantitative measurement for the size distribution of objects in an image is given e mail: gajarampalli hotmail.com t Author for correspondence: Phone 91 361 690321 28, extn. 2058, e maih dghosh iitg hotmail.com by the pattern spectrum or pecstrum [3] This size ....

....a set A whose elements are the coordinates of the ob ject pixels. Therefore, A is a set in a 2D Euclidean space 2, i.e. A= ax, ay) where (ax, ay) are the coordinates of the object pixels. Let, B be another set in 2 given as B= bx, by) Then dilation and erosion of A w.r.t. B are defined as [1, 2] Dilation: A)B Erosion: bx,bv)eB (ax, ay) A (1) AB (bx,by)CB (ax, ay) A (2) The set B is called the structuring element (SE) Combinations of dilation and erosion give two other morphological operations as follows: Opening: O(A, B) AoB: AB) B (3) Closing: C(A, B) A B: A)B)B (4) The ....

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C. R. Giardina and E. R. Dougherty, Morphological Methods in Image and Signal Processing, PrenticeHall, Englewood Cliffs, New Jersey, 1998.

....the pixel level logical filters, mathematical morphol 16 ogy, and simulated annealing. Logical filtering is one of the most intuitive method of fusing the data from two pixels. The choice of the logical operators is dependent on the fusion applications [3] Mathematical morphological method [31] in image analysis transforms each pixels of an image through the use of a set of morphological operators. These operators are derived from the basis operations of set union, intersection, difference, and their conditional combinations. Lee employed binary morphology to fuse images from a pair of ....

C. R. Giardina and E. R. Dougherty, Morphological methods in image and signal processing, Prentice-Hall, Englewood Cliffs, New Jersey, 1988.

....in mesh size. 3. Octree Encoding: Here a new octree discretization of the domain Omega is generated. The goal is to (1) merge similar voxels into larger octants and (2) refine regions were the shape is changing. A convolution filter is applied to the voxel densities to accomplish these tasks [3, 16]. This step results in a new finite element mesh of size n (ffl) and a new set of element effective densities is achieved as follows. a) Assign densities r i for each voxel i so that r i = ae e whenever voxel i is contained in element e. b) Apply the convolution filter r i = 1 P N j=1 H ....

C. R. Giardina and E. R. Dougherty. Morphological Methods in Image and Signal Processing. Prentice Hall, 1988.

....Springer Verlag Berlin Heidelberg 2000 2 Sets of structuring elements 2. 1 Hit or Miss transformations The field of cellular logic image processing and mathematical morphology is extensively described in several works (Golay 1969 [2] Preston 1970 [3] Serra 1982 [4] 1988 [5] Giardina 1988 [6], Heijmans 1994 [7] Soille 1999 [8] and many others) A basic operation in mathematical morphology is the Hit or Miss transformation, and as a starting point for this section we will quote its definition by Serra (1982) The Hit or Miss transformation is a point by point transformation of a ....

Giardina, C.R. (1988) Morphological methods in image and signal processing. Prentice Hall, Englewood Cliffs-NJ. ISBN 0-13601295-7

....the junction. Morphological operators Morphological operators can be employed to highlight various image characteristics such as peaks, lines and boundaries. Only three morphological techniques are described here, and the reader is referred to texts such as Dougherty [17] Giardina and Dougherty [28] or Serra [79] for a more thorough treatment of this extensive topic. Morphological dilation, A Phi B involves expanding the set, A, or function) using some structuring element, B. Morphological erosion, A Psi B, contracts the set. For dilation of binary images the reflection of the ....

C. R. Giardina and E. R. Dougherty. Morphological Methods in Image and Signal Processing. Prentice Hall, 1988.

....Furthermore, anisotropic diffusion is a computational expensive method. 3.5 Proposed morphological operations 3.5. 1 Preliminaries Morphological operations are very effective for edge detection of binary images, where white pixels denote uniform regions and black pixels denote region boundaries[8, 9]. Usually, the following detectors are used: # ) 0 21436573 8:9: A, B 0 C143D573 8 E (7) where denotes the binary image, denotes the edge image, denotes the erosion (dilation) operator, 3D573 denotes the erosion (dilation) F GHF kernel used, and ( ....

....the four pixels in the output image are set (at a time) to white. Set theoretical formulation: An advantage of the proposed operations is that they can be formally defined based on set theoretical intersection, union, and translation in analogy to the formal definitions of the standard operation[8]. The standard erosion and dilation satisfy the following two properties[8] 1) the erosion of an image by the union of kernels is equivalent to erosion by each kernel independently Erosion Original image Proposed detection Standard detection (a) Erosion by a P Q P cross kernel Standard ....

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C. Giardina and E. Dougherty, Morphological Methods in Image and Signal Processing. New Jersey: Prentice Hall, 1988.

....imaging plane around the center of projection. Requiring in addition invariance under angular homogeneous luminance transformations then the class of theories is more conned. Our second aim is to point out that our dynamic scale space paradigm can be applied and supplement mathematical morphology [23, 37, 14, 16, 17]. Morphological ltering by means of size density estimators [41, 42] statistical and Bayesian morphological scale spaces [13, 51] and mathematical morphological scale spaces based on watershed methods [48, 29, 6, 7, 25] and based on parabolic dilations [44, 45] are described, substantiated as well ....

....morphology. Furthermore, we show in section 3.2 that our dynamic scale space paradigm can substantiate and generalise existing mathematical morphological scale space theories. In the sequel we not dene existing notions in mathematical morphology that can be found in several standard textbooks [23, 37, 14, 16, 17] and referenced articles. We merely indicate how to apply the dynamic scale space paradigm in mathematical morphology to obtain new results. 3.1. Applications of Dynamic Scale Space Paradigm In [51] statistical morphological operations such as statistical dilations, erosions, openings and ....

C. R. Giardina and E. R. Dougherty, editors. Morphological Methods in Image and Signal Processing. Prentice-Hall, Inc., 1988.

....for data filtering is discussed. The general scheme involves two main strategies S and H responsible for generating a set of approximation functions and their proper applications to transformed data. One of the possible ideas to build such strategies can be taken from mathematical morphology [3]. In Section 4 we recall fundamentals of mathematical morphology trying to present its general scheme. This scheme is taken in Section 5 as a starting point to develop an abstract version of morphology called analytical morphology. The different versions of morphological operations, e.g. ....

....Sampling problem: How to choose A 0 in STEP 1 The random choice of A 0 (proposed in STEP 1) may be not sufficient. Some methods for the proper choice of A 0 can be developed basing on properties of reducts [18] 15] 16] One can apply also some analogies from mathematical morphology [14] [3] which have been used in building the so called analytical morphology (see Section 4.4) Here we would like only to add, by analogy with the mathematical morphology operations of erosion and dilation, that one can randomly choose a subset A 00 of A Gamma A 0 as a new subset of A after ....

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Giardina, C.R., Dougherty, E.R.: Morphological Methods in Image and Signal Processing, Prentice Hall, Englewood Cliffs, 1988.

....allows one to perform operations that basically depend on the shape size of the features to remove (or fill in) portions of the foreground. There have been many papers one the mathematical properties of morphology as well as its practical applications, e.g. Haralick et al. 1987, Vogt 1989, Giardina and Dougherty 1988 ] One of the difficulties of binary morphology is that it depends only on the shape size of features, not on the actual signal values used to obtain them. A generalization, gray scale morphology, is signal dependent, but requires significantly more computational effort. We propose that ....

C.R. Giardina and E.R. Dougherty. Morphological methods in image and signal processing. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1988.

....Volume 102, Number 4, July August 1997 Journal of Research of the National Institute of Standards and Technology We will introduce definitions and properties of morphological operators as we need them. Motivation for the former and proofs of the latter may be found in the morphology literature [22 26]. However, since it may be unfamiliar, we introduce some of the notation and basic ideas here. In most treatments of SPM imaging, the image, specimen, and tip surfaces are described in terms of single valued functions which give the height of the corresponding object at the given lateral ....

C. R. Giardina and E. R. Dougherty, Morphological Methods in Image and Signal Processing, (Prentice Hall, 1988).

....angles are equal. This approach has some advantages in our representation of the profile face. Position of the centroid is: 1 , 2 1 2 1 n y y y y n x x x x n c n c = 3. Mathematical morphology The science of digital morphology is relatively recent [11], 12] 2] since it is only recently that digital computers have made it practical. On the other hand, the mathematics behind it is simply set theory, which is a well studied area. The idea underlying digital morphology is that images consist of a set picture elements (pixels) that collect into ....

C.R. Giardina and E.R. Dougherty, "Morphological Methods in Image and Signal Processing", Englewood Cliffs, NJ: Prentice-Hall, 1988.

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Giardina, C.R. and E.R. Dougherty. 1988. Morphological Methods in Image and Signal Processing. Prentice-Hall, Englewood Cliff, NJ.

.... The increasing constraint has played a key role in image operator theory, and morphological erosion representation of increasing operators pre dates the general representation of arbitrary translation invariant operators, rst in terms of the operator kernel [43] and then in terms of its basis [24,41,42]. Owing to their prevalence and early morphological representation, automatic design of increasing operators came rst [7,10,11] Binary increasing lters, and stack lters, which are essentially binary because a single Boolean function operates on threshold sets, have been especially studied ....

C. Giardina, E.R. Dougherty, Morphological Methods in Image and Signal Processing, Prentice-Hall, Englewood Cli!s, NJ, 1988.

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Giardina, C.R., and Dougherty, E.R. (1988). "Morphological Methods in Image and Signal Processing." Prentice-Hall, Englewood Cliffs, New Jersey.

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C. Giardina and E. Dougherty, Morphological Methods in Image and Signal Processing, Prentice Hall, New Jersey, 1988.

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Giardina, C. R. and Dougherty, E. R., Morphological Methods in Image and Signal Processing. Englewood Cliffs, NJ, Prentice-Hall, 1988.

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C. R. Giardina and E. R. Dougherty, Morphological Methods in Image and Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1988.

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Giardina, C.R. and E.R. Dougherty, Morphological Methods in Image and Signal Processing. 1988, Englewood Cliffs, New Jersey: Prentice--Hall. 321. 109

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Giardina, C. R., and Dougherty, E. R. Morphological Methods in Image and Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1988.

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C.R. Giardina and E.R. Dougherty. Morphological methods in image and signal pro- cessing. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1988.

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Dougherty, E. and Giardina, C., Morphological Methods In Image And Signal Processing, Prentice-Hall, Englewood Cliffs, 1988.

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C.R.Giardina, E.R.Dougherty. Morphological Methods in Image and Signal Processing. Prentice Hall, 1988

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C. Giardina and E. Dougherty, Morphological Methods in Image and Signal Processing, Prentice Hall, New Jersey, 1988.

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C. R. Giardina, and E. R. Dougherty, Morphological Methods in Image and Signal Processing, Prentice-Hall, Englewood Cli#s, N.J., 1988.

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