Research On Recovering Three-dimensional Surfaces Methods With Monocular Multi-images Based On SFS Method

With the development of computer technology, using computer to automaticallyobtain the three-dimensional information of images and targets has shown anincreasingly important position and role in all aspects of social life and production.For example, in urban construction, people can provide useful information for roadplanning by sensing zone elevation data. In the field of medical analysis, doctorsexamine the endoscopic images to assist the staff analysis of pathology and disease.Another application is the military area, three-dimensional height information alsoplays an important role in locking targets and scouting fighting maps. Therefore, it isa hot point to reconstruct object surface height information based ontwo-dimensional images.Now it is popular and important method by SFS to recover three-dimensionalobject surface. Shape from shading method which uses the corresponding pixel valueof each point in the grey image to recover surface information. However, due to theill-posed problem of SFS, the current algorithms cannot reconstruct threedimensional surface height values completely. So a variety of efficient algorithmsand precise imaging model, as well as the appropriate constraints are effective waysto improve the accuracy of recovering results. Most of the articles choose singleimage to recover object three-dimensional surface. But the reflectance map equationis a nonlinear partial differential equation about two random variables. Theuniqueness of gradient vectors cannot be determined with a single grey image andwe can only take restrictive conditions to solve the question which will increase thedifficulty of calculating. This paper focuses on the ill-posed problem and weproposed algorithms which establish the corresponding equations by two or moregrey images to erase the problem. The article main contents are as follows:(1) Under perspective projection with three images based on Lambertianmodel to reconstruct object surfaces is demonstrated in this article. Three images under different lighting source directions are captured by camera firstly. Followingthree reflectance map equations are established by Lambertian model. Then thegradient vectors of the3-D surface are calculated by solving the equations.According to the relationship between the gradient vector and the object surfaceheight, Eulor-Poision equations and discrete difference equations are used to obtainthree-dimensional shape reconstruction iterative equation.(2) A SFS algorithm based on the Phong model to recovery three-dimensionalsurface is proposed in this paper. Three images under different light source directionsare captured by camera firstly. Following three reflectance map equations which aredescribed by Phong model are established to calculate the gradient vectors of thethree-dimensional surface. The gray constraint and gradient component constraintconditions are used to construct target function, and the corresponding Eulor-Poisionequations are derived. Simultaneously, discrete difference is used to approximatedifferential operation and iterative three-dimensional height reconstruction algorithmis proposed by the discrete difference equation.(3) A linear perspective SFS method based on two images is further proposedto recovery three dimensional object surfaces. Firstly, two images under differentlight source directions are captured by a still camera. Then, the reflectance mapequations based on Lambertian model are established under perspective projection.And two nonlinear partial differential equations (PDEs) are further transformed intoone linear PDE. In order to obtain three-dimensional object surface height iterativeequation, the semi-Lagrangian algorithm is used to resolve the linear equation. Thenumerical interpolation method is adopted to estimate the non-integer values of pixelpoints in image.By researching this project, we know that three-dimensional object surface canbe reconstructed by multi-images based on shape from shading method. In this paper,Phong model and hybrid models transition from simple Lambertian model has beenachieved. From the ideal orthogonal projection switch to practical perspective projection has also been realized. Experimental results of three-dimensionalreconstruction show that the proposed method is effective and valuable, which isbenefit for future research work. These methods also provide researching direction.