A New Segmentation Method Based On Curvature Sparsity

Segmentation is one of the most important problems in Image Processing. Recently, Chan-Vese Model(CV) is widely used to study the segmentation problem. By improving this model for varieties of application, CV Model has been proved to be effective. However, most improvements shared one flaw, which over smoothing the corner features of polygonal contours. This some-times undesired property is caused by lacking terms describing the geometrical character of polygon in the energy functional of CV Model.Seeking to overcome the above imperfection, the author of [12] proposed adding a new so-called low curvature image simpliers (LCIS) term into the Eluer-Lagrange(EL) equations of Geodesic Active Contour Model(GAC), which enforces the solution of the partial differentia equation(PDE) into piecewise linear function as well as the contours. So the modified model has better performance on polygonal contours. Later in [28] the LCIS is induced into Level Set(LS) based CV Model, which combines the advantages of Level Set Method and LCIS and works very well for some cases.However [12] and [28] have one common difficulty on understanding that their models are both deduced from theories of Laplace-Beltrami Oper-ate, which is far too sophisticated and lack of intuition in Image Processing. Furthermore,[12] and [28] considered the modification of PDEs associated with CV model and GAC instead of energy functional form, which will even-tually face a solution of fourth-order none-linear PDE, which problem is hard and time-consumed.Inspired from Compressed Sensing(CS)[17] Theory, the author of this pa-per proposed a new energy functional modified from CV model by adding an additional term describing curvature sparsity, which can be explained sensi-ble for polygonal contours. Furthermore, from the work of [31] and [27], the proposed modified CV model can be calculated by Augmented Lagrangian Method efficiently, which evaded the numerical difficulties in solving a fourth-order none-linear PDE.