EDGE DETECTION USING MINMAX MEASURES SOUNDARARAJAN EZEKIEL Matthew Lang Department of Computer...
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Transcript of EDGE DETECTION USING MINMAX MEASURES SOUNDARARAJAN EZEKIEL Matthew Lang Department of Computer...
EDGE DETECTION USING EDGE DETECTION USING MINMAX MEASURESMINMAX MEASURES
SOUNDARARAJAN EZEKIELMatthew Lang
Department of Computer ScienceIndiana University of Pennsylvania
Indiana, PA USA [email protected]
INTRODUCTIONINTRODUCTION In this paper, we present a minmax measure-
based algorithm for edge detection for images. Edge detection is a tool that has been widely used
in image processing and computer vision for a variety of reasons.
In an image, edges are areas where there is a strong change in contrast.
Typically, edges represent the boundaries of objects within an image, and therefore, determining the locations of these boundaries is important in further machine analysis of image
content.
In most cases, edge detection requires smoothing and differentiation of the image. Smoothing results in the loss of image information, and differentiation is an ill-conditioned problem.
In this paper, we calculate the local fractal dimension to estimate the roughness of that region.
To calculate the local fractal dimension, we use the minmax measure. We then form an image, called the slope image, from the fractal
dimension. We then apply simple threshold techniques on the slope image to
extract edge information. The results suggest that this method is more effective than traditional
methods and that is has the capability to be applied to a broad range of image categories.
MINMAX MEASURE MINMAX MEASURE we describe the basics of the minmax approach to
image edge detection. The essential difference between this approach
and classical methods (Canny edge detector, mathematical morphology etc.,) lies in the way they handle irregularity.
Our study of edge detection analysis starts with the following definitions due to Vehel, Canus, and Vojak.
MethodologyMethodology We know that the Hausdorff dimension cannot be
computed.
Minmax Mask: Minmax Mask: We define a special square mask of size 9 by 9 for the
purpose of calculating local fractal dimension. This mask can be expanded to various sizes. Figure 1 shows the mask who’s elements are the distance values from the center (* denotes a power of ½). This mask has an advantage during computation due to the fact that distances are fixed and do not need to be computed for every pixel. 32* 25* 20* 17* 4 17* 20* 25* 32*
25* 18* 13* 10* 3 10* 13* 18* 25*
20* 13* 8* 3* 2 3* 8* 13* 20*
17* 10* 3* 2* 1 2* 3* 10* 17*
4 3 2 1 0 1 2 3 4
17* 10* 3* 2* 1 2* 3* 10* 17*
20* 13* 8* 3* 2 3* 8* 13* 20*
25* 18* 13* 10* 3 10* 13* 18* 25*
32* 25* 20* 17* 4 17* 20* 25* 25*
Algorithm:- Minmax Algorithm:- Minmax The minmax algorithm for calculating local fractal
dimension is as follows:Step 1: Start with the image that has to be
analyzed with the edge detection algorithm. If the image is a color image, convert it to grayscale or analyze the red, green, and blue images individually.
Step 2: Choose the mask size and resize the original image by padding the boundaries so that the mask can be applied to the boundary pixels.
Step 3: Center the mask on a pixel and extract those pixels that lie at a distance d, for every d in the mask. Compute the maximum value and minimum value for those pixels extracted. Compute the slope by plotting log (max) vs. log (d). Repeat the same process for minimum values. The local fractal dimension can be calculated from the following expression: fractal dimension (fd) = topological dimension (T) + 1 – slope.
Step 4: Form the slope image(s) by computing the slope values for every pixel in the image [11]. Figure 2 shows the slope images for max and min of Lena (512 by 512) and Figure 3 shows the original image.
Step 5: Extract the edge features from the slope image(s) by applying a threshold value.
Slope image for Max Slope image for Min
EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS We illustrate our proposed maxmin method for edge detection by
applying it to a set of images. We apply our maxmin method and create a slope image, and then we
extract the edge information by applying a threshold value.
The resulting mages are the edge features of the original image.
Lena Original Rice Original
Max Edges Min Edges
Max slopeMin Slope
Max EdgesMin Edges
Max Edge
Max Edge