Image segmentation with depth information can be modeled as a minimization problem with Nitzberg-Mumford-Shiota functional, which can be transformed into a tractable variational level set formulation. However, such fo...
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Image segmentation with depth information can be modeled as a minimization problem with Nitzberg-Mumford-Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss-Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency.
Image vectorization is a process to convert a raster image into a scalable vector graphic format. The objective is to effectively remove pixelization effects while representing image boundaries by scalable parameteriz...
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Image vectorization is a process to convert a raster image into a scalable vector graphic format. The objective is to effectively remove pixelization effects while representing image boundaries by scalable parameterized curves. We propose a new image vectorization method which considers depth ordering among shapes and use curvature-based inpainting for convexifying shapes in the vectorization process. From a given color-quantized raster image, we first define each connected component of the same color as a shape layer and construct depth ordering among them using a newly proposed depth ordering energy. Global depth ordering among all shapes is described by a directed graph, and we propose an energy to remove cycles within the graph. After constructing a depth ordering of shapes, we convexify occluded regions by Euler's elastica curvature-based variational inpainting and leverage the stability of Modica-Mortola double-well potential energy to inpaint large regions. This is following human vision perception, where boundaries of shapes extend smoothly, and we assume that shapes are likely to be convex. Finally, we fit Be'\zier curves to the boundaries and store vectorization results as a scalable vector graphics file, allowing superposition of curvaturebased inpainted shapes following the depth ordering. This is a new way to vectorize images by decomposing an image into scalable shape layers with computed depth ordering. This approach makes editing shapes and images more natural and intuitive. We also consider grouping shape layers for semantic vectorization. We present various numerical results and comparisons against recent layer-based vectorization methods to validate the proposed model.
Given an image that depicts a scene with several objects in it, the goal of segmentation with depth is to automatically infer the shapes of the objects and the occlusion relations between them. Nitzberg, Mumford and S...
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Given an image that depicts a scene with several objects in it, the goal of segmentation with depth is to automatically infer the shapes of the objects and the occlusion relations between them. Nitzberg, Mumford and Shiota formulated a variational approach to this problem: in their model, the solution is obtained as the minimizer of an energy. We describe a new technique of minimizing their energy that avoids explicit detection/connection of T-junctions.
Given an image that depicts a scene with several objects in it, the goal of segmentation with depth is to automatically infer the shapes of the objects and the occlusion relations between them. Nitzberg, Mumford and S...
详细信息
Given an image that depicts a scene with several objects in it, the goal of segmentation with depth is to automatically infer the shapes of the objects and the occlusion relations between them. Nitzberg, Mumford and Shiota formulated a variational approach to this problem: in their model, the solution is obtained as the minimizer of an energy. We describe a new technique of minimizing their energy that avoids explicit detection/connection of T-junctions.
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