Internal And External Skeleton Transform Based On SV Mathematical Morphology Method

As a tool for skeleton extraction,skeleton transform is widely used in image coding,image decomposition and image reconstruction.Most of the studies on skeleton transform use the morphological transform of fixed structuring element,and the construction component is limited to the internal skeleton.Xu J established the internal and external skeleton transform using the mathematical morphology method of fixed structuring element,and applied the internal and external skeleton transform to the problem of image decomposition and reconstruction,and generalized the skeleton transform theory with a single inner skeleton as the component.In this paper,based on the study of Xu J's internal and external skeleton transform using the mathematical morphology method based on fixed structuring element,The spatially-variant mathematical morphology method is applied to the study of skeleton problems,the internal and external skeletons are extracted by using spatially-variant structural mapping,and internal and external skeletons based on spatially-variant structuring element are studied in detail.the internal and external skeleton transform based on spatially-variant structuring element is further studied.The spatially-variant internal and external skeleton transform formulas of images are established respectively,and the combined skeleton transform formulas are established using the internal and external skeletons as decomposition components.Finally,by changing the order of the open and closed transform,the number of spatially-variant structuring element that in the open and closed transform are expanded and combining with the established theoretical method of the joint skeleton transform formula,the three extensions of the joint skeleton transform formula are derived.The paper has given the corresponding calculation and proof process for all the Lemma and the establishment of the skeleton transform formula,the conclusions reached by the study extend and enrich the existing literature related theories and method.