| Mathematical morphology is an efficient digital image processing tool,which has been applied and developed in image edge detection,image feature recognition,image segmentation and image filtering.The main idea of mathematical morphology is the structuring element which is used as target object to extract and analyze the corresponding geometric shape for image recognition and simplification.However,as demand for color image processing grows,the traditional color-morphology ignores the correlation of channels and the local correlation of pixels,which leads to generating noise,destroying image topology and limiting processing effect by the size of structuring element in morphology operation.Thus,a formal concept structuring element algorithm and a matrix partial ordering are proposed based on matrix relation and operations,which is the foundation of the new mathematical morphology model.The new model is used to address the problems which exist in traditional color-morphology model.Firstly,the pixel window with each pixel as the center is extracted from the image.Then the background matrix is constructed to describe each pixel window,which is based on matrix relation.The object relation matrix is obtained by matrix operations on the background matrix.And the formal concept structuring element is extracted according to the value of elements in the object relation matrix to regard as the structuring element.The effectiveness of the formal concept structuring element algorithm in suppressing noise is proved by comparing in both subjective and objective dimensions.Next,the matrix partial ordering is proposed based on the matrix norm to ensure the local correlation of pixels.The correctness and validity of the matrix partial ordering are proved through theoretical proof and pixel ordering way.Subsequently,a new mathematical morphology model is proposed based on the formal concept structuring element algorithm and the matrix partial ordering.Then the definitions of the morphological operators,including dilation,erosion,opening and closing,are given based on the model.The processing effect is shown in detail by the experimental results.Experiments have indicated that the new model has the advantages of preserving the image topology and being more tolerant to the window size of the structuring element by comparing with the traditional model.Finally,the new model is applied to color image edge extraction,so dilated edge extraction operator and eroded edge extraction operator based on matrix partial ordering are proposed.And the resulting images have shown the extraction effect of the edge extraction operators.Experimental results indicate that the edge extraction operators are better than the traditional operators in extracting the edge of the image,which proves the effectiveness and value of the new model from the perspective of practical application. |
