Backward diffusion processes appear naturally in image enhancement and deblurring applications. However, the inverse problem of backward diffusion is known to be ill-posed and straightforward numerical algorithms are unstable. So far, existing stabilisation strategies in the literature require sophisticated numerics to solve the underlying initial value problem. Therefore, it is desirable to establish a backward diffusion model which implements a smart stabilisation approach that can be used in combination with a simple numerical scheme. We derive a class of space-discrete one-dimensional backward diffusion as gradient descent of energies where we gain stability by imposing range constraints. Interestingly, these energies are even convex. Furthermore, we establish a comprehensive theory for the time-continuous evolution and we show that stability carries over to a simple explicit time discretisation of our model. Finally, we confirm the stability and usefulness of our technique in experiments in which we enhance the contrast of digital greyscale and colour images.
As mentioned in sec:app:grey:global , applying the global model -- with @math -- is identical to histogram equalisation (a common formulation can e.g. be found in @cite_30 ). Furthermore, there exist other closely related histogram specification techniques -- such as @cite_24 @cite_33 @cite_17 -- which can have the same steady state. If we compare our evolution with the histogram modification flow introduced by Sapiro and Caselles @cite_24 , we see that their flow can also be translated into a combination of repulsion among grey-values and a barrier function. However, in @cite_24 the repulsive force is constant, and the barrier function quadratic. Thus, they cannot be derived from the same kind of interaction between the @math and their reflected counterparts as in our paper.
@cite_30 @cite_33 @cite_24 @cite_17
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This paper presents a simple and robust method, namely discriminative histograms of local dominant orientation (D-HLDO), for biometric image feature extraction. In D-HLDO, the local dominant orientation map and the corresponding relative energy map are obtained by applying the singular value decomposition (SVD) to the collected gradient vectors over a local patch. The dominant orientation map and the relative energy map are then used to construct the concatenated histogram features. Local mean based nearest neighbor discriminant analysis (LM-NNDA) is finally employed to reduce the redundancy information and get the low-dimensional and discriminative features. The proposed method is applied to face, finger-knuckle-print and Palm biometrics and is examined using the AR, CMU PIE and FRGCv2.0 face image databases, the PolyU Palmprint database, and the PolyU Finger-Knuckle-Print database. Experimental results demonstrate the effectiveness of the proposed D-HLDO method. This paper presents a novel approach to face recognition, named Multi-resolution Histograms of Local Variation Patterns (MHLVP), in which face images are represented as the concatenation of the local spatial histogram of local variation patterns computed from the multi-resolution Gabor features. For a face image with abundant texture and shape information, aGabor feature map(GFM) is computed by convolving the image with each of the forty multi-scale and multi-orientation Gabor filters. Each GFM is then divided into small non-overlapping regions to enhance its shape information, and then Local Binary Pattern (LBP) histograms are extracted for each region and concatenated into a feature histogram to enhance the texture information in the specific GFM. Further more, all of the feature histograms extracted from the forty GFMs are further concatenated into a single feature histogram as the final representation of the given face image. Eventually, the identification is achieved by histogram intersection operation. Our experimental results on FERET face databases show that the proposed method performs terrifically better than the performance of some classical results including the best results in FERET'97. In this paper, we present a color consistency technique in order to make images in the same collection share the same color style and to avoid gamut problems. Some previous methods define simple global parameter-based models and use optimizing algorithms to obtain the unknown parameters, which usually cause gamut problems in bright and dark regions. Our method is based on the range-preserving histogram specification and can enforce images to share the same color style, without resulting in gamut problems. We divide the input images into two sets having respectively high visual quality and low visual quality. The high visual quality images are used to make color balance. And then the low visual quality images are color transferred using the previous corrected high quality images. Our experiments indicate that such histogram-based color correction method is better than the compared algorithm. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations.