The Local Structure of Space-Variant Images

Local image structure is widely used in theories of both machine and biological vision. The form of the differential operators describing this structure for space-invariant images has been well documented (e.g. Koenderink, 1984). Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant domain has received little attention. In this report we derive the form of the most common differential operators and surface characteristics in the space-variant domain and show examples of their use. The operators include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrate the use of these results by deriving the space-variant form of corner detection and image enhancement algorithms. The latter is shown to have interesting properties in the complex log domain, implicitly encoding a variable grid-size integration of the underlying PDE, allowing rapid enhancement of large scale peripheral features while preserving high spatial frequencies in the fovea.Office of Naval Research (N00014-95-I-0409

A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection

We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian distribution. The highly flexible variational structure of the corresponding regulariser encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. For the numerical solution of the corresponding image restoration model, we use an iterative algorithm based on the Alternating Direction Method of Multipliers (ADMM). A suitable preliminary variable splitting together with a novel result in multivariate non-convex proximal calculus yield a very efficient minimisation algorithm. Several numerical results showing significant quality-improvement of the proposed model with respect to some related state-of-the-art competitors are reported, in particular in terms of texture and detail preservation

Real-Time Anisotropic Diffusion using Space-Variant Vision

Many computer and robot vision applications require multi-scale image analysis. Classically, this has been accomplished through the use of a linear scale-space, which is constructed by convolution of visual input with Gaussian kernels of varying size (scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian is the Green's function of such a system (Koenderink, 1984). Recently, much work has been focused on the use of a variable conductance function resulting in anisotropic diffusion described by a nonlinear partial differential equation (PDF). The use of anisotropic diffusion with a conductance coefficient which is a decreasing function of the gradient magnitude has been shown to enhance edges, while decreasing some types of noise (Perona and Malik, 1987). Unfortunately, the solution of the anisotropic diffusion equation requires the numerical integration of a nonlinear PDF which is a costly process when carried out on a fixed mesh such as a typical image. In this paper we show that the complex log transformation, variants of which are universally used in mammalian retino-cortical systems, allows the nonlinear diffusion equation to be integrated at exponentially enhanced rates due to the non-uniform mesh spacing inherent in the log domain. The enhanced integration rates, coupled with the intrinsic compression of the complex log transformation, yields a seed increase of between two and three orders of magnitude, providing a means of performing real-time image enhancement using anisotropic diffusion.Office of Naval Research (N00014-95-I-0409

A survey on rotation optimization in structure from motion

We consider the problem of robust rotation optimization in Structure from Motion applications. A number of different approaches have been recently proposed, with solutions that are at times incompatible, and at times complementary. The goal of this paper is to survey and compare these ideas in a unified manner, and to benchmark their robustness against the presence of outliers. In all, we have tested more than forty variants of a these methods (including novel ones), and we find the best performing combination.NSFDGE-0966142 (IGERT), NSF-IIS-1317788, NSF-IIP-1439681 (I/UCRC), NSF-IIS-1426840, ARL MAST-CTA W911NF-08-2-0004, ARL RCTA W911NF-10-2-0016, ONR N000141310778

Distributed Deblurring of Large Images of Wide Field-Of-View

Image deblurring is an economic way to reduce certain degradations (blur and noise) in acquired images. Thus, it has become essential tool in high resolution imaging in many applications, e.g., astronomy, microscopy or computational photography. In applications such as astronomy and satellite imaging, the size of acquired images can be extremely large (up to gigapixels) covering wide field-of-view suffering from shift-variant blur. Most of the existing image deblurring techniques are designed and implemented to work efficiently on centralized computing system having multiple processors and a shared memory. Thus, the largest image that can be handle is limited by the size of the physical memory available on the system. In this paper, we propose a distributed nonblind image deblurring algorithm in which several connected processing nodes (with reasonable computational resources) process simultaneously different portions of a large image while maintaining certain coherency among them to finally obtain a single crisp image. Unlike the existing centralized techniques, image deblurring in distributed fashion raises several issues. To tackle these issues, we consider certain approximations that trade-offs between the quality of deblurred image and the computational resources required to achieve it. The experimental results show that our algorithm produces the similar quality of images as the existing centralized techniques while allowing distribution, and thus being cost effective for extremely large images.Comment: 16 pages, 10 figures, submitted to IEEE Trans. on Image Processin

Fast Detection of Curved Edges at Low SNR

Detecting edges is a fundamental problem in computer vision with many applications, some involving very noisy images. While most edge detection methods are fast, they perform well only on relatively clean images. Indeed, edges in such images can be reliably detected using only local filters. Detecting faint edges under high levels of noise cannot be done locally at the individual pixel level, and requires more sophisticated global processing. Unfortunately, existing methods that achieve this goal are quite slow. In this paper we develop a novel multiscale method to detect curved edges in noisy images. While our algorithm searches for edges over a huge set of candidate curves, it does so in a practical runtime, nearly linear in the total number of image pixels. As we demonstrate experimentally, our algorithm is orders of magnitude faster than previous methods designed to deal with high noise levels. Nevertheless, it obtains comparable, if not better, edge detection quality on a variety of challenging noisy images.Comment: 9 pages, 11 figure

The prismatic Sigma 3 (10-10) twin bounday in alpha-Al2O3 investigated by density functional theory and transmission electron microscopy

The microscopic structure of a prismatic $\Sigma 3$ $(10\bar{1}0)$ twin boundary in \aal2o3 is characterized theoretically by ab-initio local-density-functional theory, and experimentally by spatial-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope (STEM), measuring energy-loss near-edge structures (ELNES) of the oxygen $K$-ionization edge. Theoretically, two distinct microscopic variants for this twin interface with low interface energies are derived and analysed. Experimentally, it is demonstrated that the spatial and energetical resolutions of present high-performance STEM instruments are insufficient to discriminate the subtle differences of the two proposed interface variants. It is predicted that for the currently developed next generation of analytical electron microscopes the prismatic twin interface will provide a promising benchmark case to demonstrate the achievement of ELNES with spatial resolution of individual atom columns

Progressive growing of self-organized hierarchical representations for exploration

Designing agent that can autonomously discover and learn a diversity of structures and skills in unknown changing environments is key for lifelong machine learning. A central challenge is how to learn incrementally representations in order to progressively build a map of the discovered structures and re-use it to further explore. To address this challenge, we identify and target several key functionalities. First, we aim to build lasting representations and avoid catastrophic forgetting throughout the exploration process. Secondly we aim to learn a diversity of representations allowing to discover a "diversity of diversity" of structures (and associated skills) in complex high-dimensional environments. Thirdly, we target representations that can structure the agent discoveries in a coarse-to-fine manner. Finally, we target the reuse of such representations to drive exploration toward an "interesting" type of diversity, for instance leveraging human guidance. Current approaches in state representation learning rely generally on monolithic architectures which do not enable all these functionalities. Therefore, we present a novel technique to progressively construct a Hierarchy of Observation Latent Models for Exploration Stratification, called HOLMES. This technique couples the use of a dynamic modular model architecture for representation learning with intrinsically-motivated goal exploration processes (IMGEPs). The paper shows results in the domain of automated discovery of diverse self-organized patterns, considering as testbed the experimental framework from Reinke et al. (2019)