Fast algorithm for dilation and erosion using arbitrary flat structuring element: Improvement of urbach and Wilkinson´s algorithm to GPU computing

Mathematical morphology is widely used in image processing. Since all morphological operations are based on evaluating values contained in a local neighborhood, calculations on large neighborhood are particularly computationally intensive. Fast implementations for morphological operations do exist but are mostly only adapted to structuring elements of a limited size and/or a specific shape. Therefore, difficulties appear when an arbitrary or complex shape like a circle of a large size is needed. Since dilation and erosion can be used for the representation of all morphological operations, an efficient implementation of those operators is fundamental. Thus, this paper presents a new efficient algorithm for these basic operators of mathematical morphology. It enables the use of any shape of flat structuring element for grayscale images up to 3 dimensions. Also, we have defined this method as an iterative algorithm so it can be used on any parallel architecture and in particular, for GPU (Graphic Processor Unit) computing.