This paper mainly focuses on the structure tensor based image modeling approaches

including partial differential equations (PDE) and variational functionals.A type of corner shock filter is designated based on measures of corner strength and the theory of level-set evolution to enhance the corner structures.The filtering behavior of structure tensor based anisotropic PDE's is subsequently analyzed based on the edge shock filter and our proposed corner shock filter.The analysis comes to the conclusion that

Weickert's anisotropic PDE corresponds to a kind of smoothing-enhancing

and corner-preserving filtering mechanism

while Tschumperlè's trace-based PDE is the reduced version of Weickert's PDE

corresponding to a kind of smoothing filtering scheme but not corner-preserving.With the above conclusion

conditions of corner- preservation are intuitively proposed for structure tensor based variational functionals.Finally

a kind of unified regularization PDE framework is proposed for different image applications.The filtering behavior on homogeneous regions

edge

and corner structures can be described by our unified framework more intuitively and efficiently.Experimental results on image magnification demonstrate the efficiency of the unified PDE framework.