COLOR EDGE DETECTION IN RGB USING JOINTLY EUCLIDEAN DISTANCE AND VECTOR ANGLE
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Abstract
Typically, the edge detection problem in color images has
been addressed using the Euclidean Distance or similar
metrics. Recently, the Vector Angle metric was introduced
to use the hue and saturation components in a color image
in order to capture more accurate edge data. However,
both the Euclidean Distance and Vector Angle metrics
have some limitations. Two methods which combine both
metrics are introduced. They try to leverage the
advantages of each metric to better detect edges in
complex color images.


Introduction
The purpose of a general image understanding system is
to recognize objects in a complex scene or document.
Typically, one of the first steps in such a system is edge
detection. Edge detection algorithms usually detect sharp
transitions within an image. These transitions are
characteristic of object edges. Once edges of an object are
detected other processing such as region segmentation,
text finding, and object recognition can take place.
Researchers have concentrated in the past few decades on
devising algorithms for grayscale image understanding.


Edge Detection Methods
In this paper, we will concentrate on vector-based
approaches for edge detection. For this purpose, we have
adapted the Difference Vector and Vector Gradient edge
detectors to both the Euclidean distance and vector angle
metrics.


4.1. Intensity-Based Combination
A simple method of combining both metrics would
involve using the intensity plane of the image. One way of
calculating intensity involves taking a simple average of
the RGB components. The use of intensity as a trade-off
variable is a logical choice given that the vector angle
metric breaks down for low values of intensity (see
Section 2.3). Therefore, vector angle could be used when
both pixels being compared have high intensity and
Euclidean distance would be used when one of the two
pixels would have low intensity.