This paper proposes a new color image edge detection method

which utilizes quaternion based representation of color images and is based on a locally defined convolution filter that directly operates on the quaternion domain. The filter

which is a convolving kernel as a function of the pixel under consideration

is applied only to a pre defined neighborhood of the current pixel. Based on the properties of vector dot product and vector cross product between color pixels in quaternion domain

the convolution results are used to determine if the current pixel lies inside a locally homogenous region. A pixel that does not lie inside a locally homogenous region is classified as an edge pixel. Experiments with both synthetic and real color images are presented

along with comparisons with some other existing methods

illustrating the advantages of the proposed method.