... origin. Define N :
X ’ 2
X
is defined by
The image algebra formulation of the opening of the image a by the structuring element B is given by
The image algebra equivalent of the closing of a by ... evaluation of Án will require a total of
O(nlog
2
n) integer operations. The amount of integer arithmetic involved in computing Án is of the same order
of magnitude a...
... computer vision algorithms in succinct
algebraic form. For instance, in certain interpolation schemes it becomes necessary to switch from points with
real-valued coordinates (floating point coordinates) ... Transforms
8 .9. References
Chapter 9 Pattern Matching and Shape Detection
9. 1. Introduction
9. 2. Pattern Matching Using Correlation
9. 3. Pattern Matching in the Frequen...
... second coordinate of
.
Image restrictions in terms of subsets of the value set
is an extremely useful concept in computer vision as
many image processing tasks are restricted to image domains over ... sup(X) (for finite point set X)
infimum inf(X) (for finite point set X)
choice function choice(X) X (randomly chosen element)
cardinality card(X) = the cardinality of...
... c
(2,1)(2,3)
, the two underlined elements of A are combined with the two underlined
elements of B as illustrated:
In particular,
If
In the following list of pertinent recursive image- template products ... neighborhoods.
Another advantage of using neighborhoods instead of templates can be seen by considering the simple
example of image smoothing by local averaging. Suppose...
... Florida CIS Department, Gainesville, 198 9.
46 J. Wilson, “An introduction to image algebra Ada,” in Image Algebra and Morphological Image
Processing II, vol. 1568 of Proceedings of SPIE, (San ... Department of Computer Science, Queen’s University of Belfast, Northern Ireland, 199 0.
51 J. Wilson, “Supporting image algebra in the C++ language,” in Image Algebr...
... set of points
in A2 whose 8-neighborhoods intersect A. That is, the image b is defined by
(d) The image b is an interior 4-boundary image if B is 4-connected, B 4 A, and B is the set of points
in ... as
images. One may want to map each point (y
1
, y
2
) in Y to the point (2y
1
, 2y
2
). In such a case, the domain of the
crack edge image does not cover a rectangular subs...
... below.
and Image Processing, vol. 49, pp. 297 -331, Mar. 199 0.
17 A. Rosenfeld, “A nonlinear edge detection technique,” Proceedings of the IEEE, Letters, vol. 58,
May 197 0.
18 J. M. Prager, “Extracting ... processing,” Computer
Graphics and Image Processing, vol. 4, no. 2, pp. 104-1 19, 197 5.
22 A. Kaced, “The K-forms: A new technique and its applications in digital image proce...
... B, is the set of all points obtained by adding the points of B to the points in the underlying point
set of the black pixels. An erosion can be obtained by dilating the complement of the black ... transformation that combines two sets by using vector addition of set elements.
In particular, a dilation of the set of black pixels in a binary image by another set (usually c...
... transform of the original image is shown in Figure 8.7.3, and the column-by-column
Haar transform of the original image is shown in Figure 8.7.4.
Figure 8.7.3 Row-by-row Haar transform of the input image.
Figure ... Column-by-column Haar transform of the input image.
Computing the column-by-column Haar transform of the image in Figure 8.7.3, or computing the row-by-r...