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Edge Detector with Local Statistics

IP.com Disclosure Number: IPCOM000108081D
Original Publication Date: 1992-Apr-01
Included in the Prior Art Database: 2005-Mar-22
Document File: 3 page(s) / 123K

Publishing Venue

IBM

Related People

Yoshida, R: AUTHOR

Abstract

Disclosed is an algorithm for textural boundary detection in a digital image where every voxel has its own respective density. This algorithm can also detect boundaries with no clear step edges even though the statistical characteristics of two spaces on both sides of the boundary have different values. A local statistic is a function of the statistical characteristics in each space of a complete image and is used to observe and evaluate the transition of the characteristics in each space. The concept of the present algorithm is based on the fact that every space in the image has its own local statistics, such as the mean and the homogeneity of the variance of densities of voxels in the space.

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Edge Detector with Local Statistics

       Disclosed is an algorithm for textural boundary detection
in a digital image where every voxel has its own respective density.
This algorithm can also detect boundaries with no clear step edges
even though the statistical characteristics of two spaces on both
sides of the boundary have different values.  A local statistic is a
function of the statistical characteristics in each space of a
complete image and is used to observe and evaluate the transition of
the characteristics in each space.  The concept of the present
algorithm is based on the fact that every space in the image has its
own local statistics, such as the mean and the homogeneity of the
variance of densities of voxels in the space.  Thus, the evaluated
space, which is a part of a complete image, is moved across the
complete image, and the space in which the local statistic begins to
vary (for example, the space in which the mean value of densities
changes to another value) is regarded as a textural boundary.  The
algorithm uses the local statistic based on the second- order joint
probability distribution to express the characteristic (1,2) and
transforms a set of densities of voxels in the space into a local
statistic at the center of the space by referring to the
characteristic values of the surrounding space.  It can be used not
only with three-dimensional images, but also with two-dimensional
(2D) ones.  (When the image is 2D, pixels are considered instead of
voxels.)  In the result, a high value indicates similar values of
characteristics in the surrounding space, while a low value implies a
gradual variation of textural characteristics in the space, namely, a
textural boundary.

      Suppose that a density appearing in a complete image I to be
analyzed has L levels.  Suppose also that the image I contains a
smaller space with volume V, and let Wx, Wy, and Wz be the widths
(>3) of V in the x, y, and z directions, respectively.  Let D = {0,
1, 2, ... ,L-1} be the set of L, and let f(xk, yk, zk) e
D be the density of the voxel located at (xk, yk, zk).
1.  Consider the small space V (Wx x Wy x Wz), which is a part
of a complete image I.  The space V has many pairs of neighboring
voxels separated by a distance d in a certain direction.  Figure 1
shows a small region R (Wx x Wy) in two dimensions that is a part
of the image I, and a pair of pixels in R that is separated by
a distance d in a certain direction.  Consider the region R (Wx x Wy)
instead of the volume V when the image is 2D.  In Figure 1, one pixel
o...