This paper builds upon the current methods to increase their capability and automation for 3D surface construction from noisy and potentially sparse point clouds. It presents an analysis of an artificial neural network surface regression and mapping method, describing caveats, improvements and justification for the different approach.
An approach was suggested by @cite_8 using an image processing inspiration for surface de-noising. It removes noise by applying a Weiner filter which approximates the components of the surface as a statistical distribution. There are two problems with this algorithm in our context. First, it needs to be decided this algorithm should be applied, unnecessary smoothing might remove features that describe the underlying geometry, although there is some attempt to apply a surface based anisotropic diffusion to preserve edges. In addition, the formula used requires the user to both know and supply the noise denoted by the variance @math @cite_8 . It may not be possible to determine the noise of the data as it is an unstructured point cloud.
@cite_8
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A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more natural than step images which anisotropic diffusion (second order PDEs) uses to approximate an observed image. So the proposed PDEs are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion, while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion. Although both approaches seem to be comparable in removing speckles in the observed images, speckles are more visible in images processed by the proposed PDEs, because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges. Speckles can be easily removed by simple algorithms such as the one presented in this paper. A highly studied problem in image processing and the field of electrical engineering in general is the recovery of a true signal from its noisy version. Images can be corrupted by noise during their acquisition or transmission stages. As noisy images are visually very poor in quality, and complicate further processing stages of computer vision systems, it is imperative to develop algorithms which effectively remove noise in images. In practice, it is a difficult task to effectively remove the noise while simultaneously retaining the edge structures within the image. Accordingly, many de-noising algorithms have been considered attempt to intelligent smooth the image while still preserving its details. Recently, a non-local means (NLM) de-noising algorithm was introduced, which exploited the redundant nature of images to achieve image de-noising. The algorithm was shown to outperform current de-noising standards, including Gaussian filtering, anisotropic diffusion, total variation minimization, and multi-scale transform coefficient thresholding. However, the NLM algorithm was developed in the spatial domain, and therefore, does not leverage the benefit that multi-scale transforms provide a framework in which signals can be better distinguished by noise. Accordingly, in this paper, a multi-scale NLM (MS-NLM) algorithm is proposed, which combines the advantage of the NLM algorithm and multi-scale image processing techniques. Experimental results via computer simulations illustrate that the MS-NLM algorithm outperforms the NLM, both visually and quantitatively. Fourth-order nonlinear diffusion filters used for image noise removal are mainly isotropic filters. It means that the spatially varying diffusivity determined by a diffusion function is applied on the image regardless of the orientation of its local features. However, the optimal choice of parameters in the numerical solver of these filters for having a minimal distortion of the image features results in forming speckle noise on the denoised image and a very slow convergence rate especially when the noise level is moderately high. In this paper, a new fourth-order nonlinear diffusion filter is introduced, which has an anisotropic behavior on the image features. In the proposed filter, it is shown that a suitable choice for a set of diffusivity functions to unevenly control the strength of the diffusion on the directions of the level set and gradient leads to a good edge preservation capability compared to the other diffusion or regularization filters. The comparison of the results obtained by the proposed filter with those of the other second and fourth-order filters shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively. Theoretical Foundations of Anisotropic Diffusion in Image Processing. A frequent problem in low-level vision consists of eliminating noise and small-scale details from an image while still preserving or even enhancing the edge structure. Nonlinear anisotropic diffusion filtering may be one possibility to achieve these goals. The objective of the present paper is to review the author’s results on a scale-space interpretation of a class of diffusion filters which comprises also several nonlinear anisotropic models. It is demonstrated that these models—which use an adapted diffusion tensor instead of a scalar diffusivity—offer advantages over isotropic filters. Most of the restoration and scale-space properties carry over from the continuous to the discrete case. Applications are presented ranging from preprocessing of medical images and postprocessing of fluctuating numerical data to visualizing quality relevant features for the grading of wood surfaces and fabrics.