3D Reconstruction From Multiple Cameras Based On Variational Level Set Method

There are many real world applications of 3D reconstruction,such as medical image analysis,film special effects,military field,navigation of mobile robot,intelligent transportation,object identification and so on,which has important application values.Thus,the research of 3D reconstruction is essential in practice.Because of considering of the same scene object under different angle of view of geometric constraint information,3D reconstruction from multiple camera can eliminate ambiguous in the matching process and more accurately reconstruction results can be gained.Firstly,the method of multi-camera calibration was described in this paper.Then analyze the model of multiview 3D reconstruction.In view of the energy function based on the improved variational level set method is non-convex,the original energy function was transformed into a convex function by using continuous convex relaxation scheme in this paper.The main innovation of this paper can be grouped into the following two points:1.The property of signed distance function was proved in this paper by using the same vector has an unique length in an Eucliden space under different standard orthogonal basis.The level set method is the basis theory of variational level set method,which can overcome the problem brought by the change of surface topology.In order to keep the numerical stability,level set function? usually was initialized by signed distance function because it meets the property of |??|=1.The property of signed distance function was proved in this paper by using the same vector has an unique length in an Eucliden space under different standard orthogonal basis.The evolution of level set function can't preserve the property of signed distance function,an example was given to prove it.2.The solution of the minimal value of non convex function is transformed into the minimal value of convex function.In view of the existing energy function is non-convex,locally optimal solution may be gained by using the gradient descent.In this paper,the original energy function was converted into another function with an introducing a middle variable as the independent variable.The solution of the minimal value of non convex function is transformed into the solution of the minimal value of convex function that proposed in this paper.We proved the minimum solution of the convex function is also a minimum of the original function.We can avoid the use of level set function by an introducing the intermediate variable,and no need to initialize the level set function of signed distance function,which can effectively reduce the complexity of calculation.Compared to compute the gradient descent of original energy function directly,convex optimization method is proposed in this paper will not only be independent of the selection of initial values,but also can obtain global optimal solution.An experiment was given to prove that the method is of better robustness.