This paper introduces a new class of fractional-order anisotropic diffusion equations for noise removal. These equations are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function, so the proposed equations can be seen as generalizations of second-order and fourth-order anisotropic diffusion equations. We use the discrete Fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain. It is one important aspect of the algorithm that it considers the input image as a periodic image. To overcome this problem, we use a folded algorithm by extending the image symmetrically about its borders. Finally, we list various numerical results on denoising real images. Experiments show that the proposed fractional-order anisotropic diffusion equations yield good visual effects and better signal-to-noise ratio.

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The introduction of RGB-Depth (RGB-D) sensors into the visually impaired people (VIP)-assisting area has stirred great interest of many researchers. However, the detection range of RGB-D sensors is limited by narrow depth field angle and sparse depth map in the distance, which hampers broader and longer traversability awareness. This paper proposes an effective approach to expand the detection of traversable area based on a RGB-D sensor, the Intel RealSense R200, which is compatible with both indoor and outdoor environments. The depth image of RealSense is enhanced with IR image large-scale matching and RGB image-guided filtering. Traversable area is obtained with RANdom SAmple Consensus (RANSAC) segmentation and surface normal vector estimation, preliminarily. A seeded growing region algorithm, combining the depth image and RGB image, enlarges the preliminary traversable area greatly. This is critical not only for avoiding close obstacles, but also for allowing superior path planning on navigation. The proposed approach has been tested on a score of indoor and outdoor scenarios. Moreover, the approach has been integrated into an assistance system, which consists of a wearable prototype and an audio interface. Furthermore, the presented approach has been proved to be useful and reliable by a field test with eight visually impaired volunteers.

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The use of RGB-Depth (RGB-D) sensors for assisting visually impaired people (VIP) has been widely reported as they offer portability, function-diversity and cost-effectiveness. However, polarization cues to assist traversability awareness without precautions against stepping into water areas are weak. In this paper, a polarized RGB-Depth (pRGB-D) framework is proposed to detect traversable area and water hazards simultaneously with polarization-color-depth-attitude information to enhance safety during navigation. The approach has been tested on a pRGB-D dataset, which is built for tuning parameters and evaluating the performance. Moreover, the approach has been integrated into a wearable prototype which generates a stereo sound feedback to guide visually impaired people (VIP) follow the prioritized direction to avoid obstacles and water hazards. Furthermore, a preliminary study with ten blindfolded participants suggests its effectivity and reliability.