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Natural images exhibit geometric structures that are informative of the properties of the underlying scene. Modern image processing algorithms respect such characteristics by employing regularizers that capture the statistics of natural images. For instance, total variation (TV) respects the highly kurtotic distribution of the pointwise gradient by allowing for large magnitude outlayers. However, the gradient magnitude alone does not capture the directionality and scale of local structures in natural images. The structure tensor provides a more meaningful description of gradient information as it describes both the size and orientation of the image gradients in a neighborhood of each point. Based on this observation, we propose a variational model for image reconstruction that employs a regularization functional adapted to the local geometry of image by means of its structure tensor. Our method alternates two minimization steps: 1) robust estimation of the structure tensor as a semidefinite program and 2) reconstruction of the image with an adaptive regularizer defined from this tensor. This two-step procedure allows us to extend anisotropic diffusion into the convex setting and develop robust, efficient, and easy-to-code algorithms for image denoising, deblurring, and compressed sensing. Our method extends naturally to nonlocal regularization, where it exploits the local self-similarity of natural images to improve nonlocal TV and diffusion operators. Our experiments show a consistent accuracy improvement over classic regularization. [ABSTRACT FROM AUTHOR]

We describe a method for 3D object scanning by aligning depth scans that were taken from around an object with a Time-of-Flight (ToF) camera. These ToF cameras can measure depth scans at video rate. Due to comparably simple technology, they bear potential for economical production in big volumes. Our easy-to-use, cost-effective scanning solution, which is based on such a sensor, could make 3D scanning technology more accessible to everyday users. The algorithmic challenge we face is that the sensor's level of random noise is substantial and there is a nontrivial systematic bias. In this paper, we show the surprising result that 3D scans of reasonable quality can also be obtained with a sensor of such low data quality. Established filtering and scan alignment techniques from the literature fail to achieve this goal. In contrast, our algorithm is based on a new combination of a 3D superresolution method with a probabilistic scan alignment approach that explicitly takes into account the sensor's noise characteristics. [ABSTRACT FROM PUBLISHER]

The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill-conditioned operator. In such a situation, the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties. Such a priori information—commonly referred to as simply priors—is essential for image restoration, rendering it stable and robust to noise. Moreover, using the priors makes the recovered images exhibit some plausible features of their original counterpart. Particularly, if the original image is known to be a piecewise smooth function, one of the standard priors used in this case is defined by the Rudin-Osher-Fatemi model, which results in total variation (TV) based image restoration. The current arsenal of algorithms for TV-based image restoration is vast. In this present paper, a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage (aka iterated thresholding). In the proposed method, the TV-based image restoration is performed through a recursive application of two simple procedures, viz. linear filtering and soft thresholding. Therefore, the method can be identified as belonging to the group of first-order algorithms which are efficient in dealing with images of relatively large sizes. Another valuable feature of the proposed method consists in its working directly with the TV functional, rather then with its smoothed versions. Moreover, the method provides a single solution for both isotropic and anisotropic definitions of the TV functional, thereby establishing a useful connection between the two formulae. Finally, a number of standard examples of image deblurring are demonstrated, in which the proposed method can provide restoration results of superior quality as compared to the case of sparse-wavelet deconvolution. [ABSTRACT FROM PUBLISHER]