The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Research on a modifeied RANSAC and its applications to ellipse detection from a static image and motion detection from active stereo video sequences

制度:新 ; 報告番号:甲3091号 ; 学位の種類:博士(国際情報通信学) ; 授与年月日:2010/2/24 ; 早大学位記番号:新535

A minimalistic approach to appearance-based visual SLAM

This paper presents a vision-based approach to SLAM in indoor / outdoor environments with minimalistic sensing and computational requirements. The approach is based on a graph representation of robot poses, using a relaxation algorithm to obtain a globally consistent map. Each link corresponds to a relative measurement of the spatial relation between the two nodes it connects. The links describe the likelihood distribution of the relative pose as a Gaussian distribution. To estimate the covariance matrix for links obtained from an omni-directional vision sensor, a novel method is introduced based on the relative similarity of neighbouring images. This new method does not require determining distances to image features using multiple view geometry, for example. Combined indoor and outdoor experiments demonstrate that the approach can handle qualitatively different environments (without modification of the parameters), that it can cope with violations of the “flat floor assumption” to some degree, and that it scales well with increasing size of the environment, producing topologically correct and geometrically accurate maps at low computational cost. Further experiments demonstrate that the approach is also suitable for combining multiple overlapping maps, e.g. for solving the multi-robot SLAM problem with unknown initial poses

Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

Vanishing point detection for visual surveillance systems in railway platform environments

© 2018 Elsevier B.V. Visual surveillance is of paramount importance in public spaces and especially in train and metro platforms which are particularly susceptible to many types of crime from petty theft to terrorist activity. Image resolution of visual surveillance systems is limited by a trade-off between several requirements such as sensor and lens cost, transmission bandwidth and storage space. When image quality cannot be improved using high-resolution sensors, high-end lenses or IR illumination, the visual surveillance system may need to increase the resolving power of the images by software to provide accurate outputs such as, in our case, vanishing points (VPs). Despite having numerous applications in camera calibration, 3D reconstruction and threat detection, a general method for VP detection has remained elusive. Rather than attempting the infeasible task of VP detection in general scenes, this paper presents a novel method that is fine-tuned to work for railway station environments and is shown to outperform the state-of-the-art for that particular case. In this paper, we propose a three-stage approach to accurately detect the main lines and vanishing points in low-resolution images acquired by visual surveillance systems in indoor and outdoor railway platform environments. First, several frames are used to increase the resolving power through a multi-frame image enhancer. Second, an adaptive edge detection is performed and a novel line clustering algorithm is then applied to determine the parameters of the lines that converge at VPs; this is based on statistics of the detected lines and heuristics about the type of scene. Finally, vanishing points are computed via a voting system to optimize detection in an attempt to omit spurious lines. The proposed approach is very robust since it is not affected by ever-changing illumination and weather conditions of the scene, and it is immune to vibrations. Accurate and reliable vanishing point detection provides very valuable information, which can be used to aid camera calibration, automatic scene understanding, scene segmentation, semantic classification or augmented reality in platform environments

The Multiscale Morphology Filter: Identifying and Extracting Spatial Patterns in the Galaxy Distribution

We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures.}Comment: Replacement with higher resolution figures. 28 pages, 17 figures. For Full Resolution Version see: http://www.astro.rug.nl/~weygaert/tim1publication/miguelmmf.pd