492 research outputs found
Anisotropic diffusion of surface normals for feature preserving surface reconstruction
technical reportFor 3D surface reconstruction problems with noisy and incomplete range data measured from complex scenes with arbitrary topologies, a low-level representation, such as level set surfaces, is used. Such surface reconstruction is typically accomplished by minimizing a weighted sum of data-model discrepancy and model smoothness terms. This paper introduces a new nonlinear model smoothness term for surface reconstruction based on variations of the surface normals. A direct solution requires solving a fourth-order partial differential equation (PDE), which is very difficult with conventional numerical techniques. Our solution is based on processing the normals separately from the surface, which allows us to separate the problem into two second-order PDEs. The proposed method can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion
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A fourth-order PDE denoising model with an adaptive relaxation method
In this paper, an adaptive relaxation method and a discontinuity treatment of edges are proposed to improve the digital image denoising process by using the fourth-order partial differential equation (known as the YK model) first proposed by You and Kaveh. Since the YK model would generate some speckles into the denoised image, a relaxation method is incorporated into the model to reduce the formation of isolated speckles. An additional improvement is employed to handle the discontinuity on the edges of the image. In order to stop the iteration automatically, a control of the iteration is integrated into the denoising process. Numerical results demonstrate that such modifications not only make the denoised image look more natural, but also achieve a higher value of PSNR
Feature preserving variational smoothing of terrain data
Journal ArticleIn this paper, we present a novel two-step, variational and feature preserving smoothing method for terrain data. The first step computes the field of 3D normal vectors from the height map and smoothes them by minimizing a robust penalty function of curvature. This penalty function favors piecewise planar surfaces; therefore, it is better suited for processing terrain data then previous methods which operate on intensity images. We formulate the total curvature of a height map as a function of its normals. Then, the gradient descent minimization is implemented with a second-order partial differential equation (PDE) on the field of normals. For the second step, we define another penalty function that measures the mismatch between the the 3D normals of a height map model and the field of smoothed normals from the first step. Then, starting with the original height map as the initialization, we fit a non-parametric terrain model to the smoothed normals minimizing this penalty function. This gradient descent minimization is also implemented with a second-order PDE. We demonstrate the effectiveness of our approach with a ridge/gully detection application
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Automatically extracting cellular structures from images generated via electron microscopy
In this paper, we consider mathematical techniques for locating cellular structures in digital images generated via electron microscopy. We approach this problem in two steps: a pre-processing denoising stage and a segmentation stage. For image denoising, we will limit our discussion to Partial Differential Equation (PDE) based methods, primarily focusing on diffusion and total variation methods. Segmentation will also b
Kernel Based Telegraph-Diffusion Equation for Image Noise Removal
The second-order partial differential equations have good performances on noise smoothing and edge preservation. However, for low signal-to-noise ratio (SNR) images, the discrimination between edges and noise is a challenging problem. In this paper, the authors propose a kernel based telegraph-diffusion equation (KTDE) for noise removal. In this method, a kernelized gradient operator is introduced in the second-order telegraph-diffusion equation (TDE), which leads to more effective noise removal capability. Experiment results show that this method outperforms several anisotropic diffusion methods and the TDE method for noise removal and edge preservation
An Edge-Adapting Laplacian Kernel For Nonlinear Diffusion Filters
In this paper, first, a new Laplacian kernel is developed to integrate into it the anisotropic behavior to control the process of forward diffusion in horizontal and vertical directions. It is shown that, although the new kernel reduces the process of edge distortion, it nonetheless produces artifacts in the processed image. After examining the source of this problem, an analytical scheme is devised to obtain a spatially varying kernel that adapts itself to the diffusivity function. The proposed spatially varying Laplacian kernel is then used in various nonlinear diffusion filters starting from the classical Perona-Malik filter to the more recent ones. The effectiveness of the new kernel in terms of quantitative and qualitative measures is demonstrated by applying it to noisy images
A volume filtering and rendering system for an improved visual balance of feature preservation and noise suppression in medical imaging
Preserving or enhancing salient features whilst effectively suppressing noise-derived artifacts and extraneous detail have been two consistent yet competing objectives in volumetric medical image processing. Illustrative techniques (and methods inspired by them) can help to enhance and, if desired, isolate the depiction of specific regions of interest whilst retaining overall context. However, highlighting or enhancing specific features can have the undesirable side-effect of highlighting noise. Second-derivative based methods can be employed effectively in both the rendering and volume filtering stages of a visualisation pipeline to enhance the depiction of feature detail whilst minimising noise-based artifacts. We develop a new 3D anisotropic-diffusion PDE for an improved balance of feature-retention and noise reduction; furthermore, we present a feature-enhancing visualisation pipeline that can be applied to multiple modalities and has been shown to be particularly effective in the context of 3D ultrasound
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