The Method And Applications Of Morphological Transforms Based On Binary Morphology

This thesis systematically establishes the method based on umbra transform and surface operator from the theory of binary morphology. In the application aspects, the method to filter out the salt -pepper noise and to detect the edge of image, are mainly introduced. Specific researches are as follows:The main properties of binary morphological transforms are proofed in detailed. The method of grayscale transforms based on the theory of binary morphology is established by introducing umbra transform. A signal can be turned into a set by umbra transform. Surface operator which is from set to signal is inverse operation of umbra. So grayscale morphology can be connected with binary morphology by umbra transform. From the definition of grayscale morphological transforms based on umbra transform, main properties of grayscale morphological transforms are proofed in detailed. It can be found that the grayscale morphological transforms have the similar properties with the binary morphological transforms. For example, grayscale morphological transforms are all satisfied with three properties (duality, translation invariance and increasing monotonicity), and some other properties.Based on the properties of morphological open and close, main properties of morphological filters of OC and CO are listed and proved in detailed. The algorithm using two structure elements to remove salt -pepper noise is proposed and it can satisfactorily remove the salt -pepper noise (expectation is 0 and variance is from 0 to 0.2).The basic morphological operators of edge detection are introduced by the property of expansion of morphological erosion and the property of anti-expansion of morphological erosion. The algorithm using eight elements to detect the edge of image is proposed. The algorithm which can be used in detecting edge of image disturbed by salt -pepper noise is also proposed.