Research On Some Algorithms Of Image Vectorization

Image Vectorization,i.e.converting raster images into vector graphics,is a fundamental problem of image representation in digital image processing.With the development of digital media technology,vector graphics have been widely applied in various fields.The choice of proper geometrical primitives for easiness of representation and editing,as well as for faithfulness of reconstruction of original images,has always been the kernel and crux of the problem.Therefore,finding an effective solution to the above problem becomes one of the basic tasks of image vectorization,which also conforms to the trends of digital image processing,and thus has great immediate significance.This dissertation mainly focuses on some algorithms on Image Vectorization,and a novel vectorial representation of images is also proposed.The contents of this dissertation are summarized as below:· We present an image meshing method via alternating optimization.The model of the original problem involves both geometry and topology information,which might be hard to solve directly.Our method separates both aspects,and solve them in an alternating and iterating manner.In each loop,it guarantees the decline of the energy function,and thus makes the original problem much easier to solve.In the stage of geometry optimization,a vertex moving scheme is proposed,in which,only one vertex is concerned and moved within its one-ring neighboring region at each time.The complicated non-convex problem with large number of variables is thus converted into a simpler one including only a few variables.In addition,when a vertex is moved,the positions of its one-ring neighbors might no longer be optimal,which can be mostly avoided by our vertex moving scheme.Although our method cannot guarantee a global optimal solution theoretically,a local optimal position can be achieved in each iteration.Given a proper initial value,our algorithm can converge within a few iterations for most test images,and reconstruct better results,compared with traditional methods.· We present another image meshing method via hierarchical optimization,which is an improvement of the above one.In the stage of problem modeling,the dictionary learning model is brought in our objective function to elegantly combine both topology and geometry aspects via linear composition.In this way,the model becomes conciser and also facilitates the process of later solution.In the stage of solution to the problem,a hierarchical framework is proposed to improve the initial value.In this framework,several levels are established from coarser to finer,and the input image is filtered in each level to form a series with gradual smoothness while keeping their local features.The output of a coarser level is employed as the input of its finer descendant.In this way,the difficulty of the original problem is diluted into sub-problems in separated levels,and thus makes it smoother.In the stage of geometry optimization,the color space and image space are combined,associated with the dictionary learning model,so as to reduce the non-linear problem to a linear one.Experiments show that this algorithm generates better results than the above one.· We propose a novel variational image representation via planar patch set.In tradi-tional methods,the color value of each vertex is usually determined as the one at its corresponding pixel,which can harcdly guarantee the local optimality.To ameliorate this problem,a new representation is proposed.In this representation,an image is represented by a set of planar patches with proper boundaries,and the color values of them are determined by global optimization,which improves the quality of reconstruc-tion.Two stages,namely plane optimization and boundary extraction,are involved in our algorithm.In the former one,a Lloyd scheme is employed to iteratively solve the problem.In each iteration,a Principal Component Analysis method is used to obtain the parameters of planes.In the latter one,after the curved boundaries of patches are extracted,a curved-edge polygon mesh is constructed to represent the topological connectivity in between these planar patches,and a half-curved-edge structure,similar to the half-edge structure,is also established to record--this data structure.Experi-ments show that this representation generates better results than other image meshing algorithms.