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Vector Edge Detectors

color vectors ranked images

Definition: Scalar (monochrome) edge detection may not be sufficient for certain applications since no edges will be detected in gray value images when neighhoring ohjects have different hues but equal intensities; in these cases vector edge detectors must be applied.

Psychological research on the characteristics of the human visual system reveals that color plays a significant role in the perception of edges or boundaries between two surfaces. Scalar (monochrome) edge detection may not be sufficient for certain applications since no edges will be detected in gray value images when neighboring objects have different hues but equal intensities. Objects with such boundaries are treated as one big object in the scene. Since the capability to distinguishing between different objects is crucial for applications such as object recognition, image segmentation, image coding, and robot vision, the additional boundary information provided by color is of paramount importance.

It is well-known that the color image is represented as the two-dimensional array of three component vectors. Thus, the color edge can be defined as a significant discountinuity in the vector field representing the color images function. Following the major performance issues in color edge detection such as the ability to extract edges accurately, robustness to noise, and the computational efficiency, most popular color edge detectors are those based on vector order statistics.

Edge detectors based on order statistics operate by detecting local minimum and maximum in the color image function and combining them in an appropriate way in order to produce the corresponding edge map. Since there is no unique way to define ranks for multichannel (vector) signals, such as color images and cDNA microarray images, the reduced ordering scheme is commonly used to achieve the ranked sequence x (1) , x (2) ,x ( N ) of the color vectors x 1 , x 2 ,x N , inside the processing window. Based on these two extreme vector order-statistics x (1) (lowest ranked vector) and x ( N ) (uppermost ranked vector), the vector range detector detects edges through the comparison of the threshold and the Euclidean distance value between x (1) and x ( N ) . The output of such an operator used in a uniform area, where all vectors inside the processing window are characterized by a similar magnitude and/or the direction, is small. However, in high-frequency regions, where x ( N ) is usually located at the one side of an edge, whereas x (1) is included in the set of vectors occupying spatial positions on other side of the edge, the response of the vector range detector is a large value.

Due to the utilization of the distance between the lowest and upper-most ranked vector, the vector range operator is rather sensitive to noise. More robust color edge detectors are obtained using linear combinations of the lowest ranked vector samples. This is mainly due to the fact that: i) the lowest ranks are associated with the most similar vectors in the population of the color vectors, and ii) upper ranks usually correspond to the outlying samples. The minimum over the magnitudes of these linear combinations defines the edge detector’s output. Different coefficients in the linear combinations result in a multitude of edge detectors which vary significantly in terms of performance and/or complexity.

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