Blur Invariants for Image Recognition

Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified theory of blur invariants. Unlike all previous attempts, the new theory does not require any prior knowledge of the blur type. The invariants are constructed in the Fourier domain by means of orthogonal projection operators and moment expansion is used for efficient and stable computation. It is shown that all blur invariants published earlier are just particular cases of this approach. Experimental comparison to concurrent approaches shows the advantages of the proposed theory.Comment: 15 page

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms

Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.Comment: 16 pages, 10 figure

Kinematic Diffraction from a Mathematical Viewpoint

Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Simultaneously, their relevance has grown in practice as well. In this context, the phenomenon of homometry shows various unexpected new facets. This is particularly so for systems with stochastic components. After the introduction to the mathematical tools, we briefly discuss pure point spectra, based on the Poisson summation formula for lattice Dirac combs. This provides an elegant approach to the diffraction formulas of infinite crystals and quasicrystals. We continue by considering classic deterministic examples with singular or absolutely continuous diffraction spectra. In particular, we recall an isospectral family of structures with continuously varying entropy. We close with a summary of more recent results on the diffraction of dynamical systems of algebraic or stochastic origin.Comment: 30 pages, invited revie

A comparative study of conventional visual servoing schemes in microsystem applications

This paper presents an experimental comparison of conventional (calibrated and uncalibrated) image based visual servoing methods in various microsystem applications. Both visual servoing techniques were tested on a microassembly workstation, and their regulation and tracking performances are evaluated. Calibrated visual servoing demands the optical system calibration for the image Jacobian estimation and if a precise optical system calibration is done, it ensures a better accuracy, precision and settling time compared with the uncalibrated approach. On the other hand, in the uncalibrated approach, optical system calibration is not required and since the Jacobian is estimated dynamically, it is more flexible

Feature Extraction for image super-resolution using finite rate of innovation principles

To understand a real-world scene from several multiview pictures, it is necessary to find the disparities existing between each pair of images so that they are correctly related to one another. This process, called image registration, requires the extraction of some specific information about the scene. This is achieved by taking features out of the acquired images. Thus, the quality of the registration depends largely on the accuracy of the extracted features. Feature extraction can be formulated as a sampling problem for which perfect re- construction of the desired features is wanted. The recent sampling theory for signals with finite rate of innovation (FRI) and the B-spline theory offer an appropriate new frame- work for the extraction of features in real images. This thesis first focuses on extending the sampling theory for FRI signals to a multichannel case and then presents exact sampling results for two different types of image features used for registration: moments and edges. In the first part, it is shown that the geometric moments of an observed scene can be retrieved exactly from sampled images and used as global features for registration. The second part describes how edges can also be retrieved perfectly from sampled images for registration purposes. The proposed feature extraction schemes therefore allow in theory the exact registration of images. Indeed, various simulations show that the proposed extraction/registration methods overcome traditional ones, especially at low-resolution. These characteristics make such feature extraction techniques very appropriate for applications like image super-resolution for which a very precise registration is needed. The quality of the super-resolved images obtained using the proposed feature extraction meth- ods is improved by comparison with other approaches. Finally, the notion of polyphase components is used to adapt the image acquisition model to the characteristics of real digital cameras in order to run super-resolution experiments on real images

3D reconstruction, classification and mechanical characterization of microstructures

Modeling and classifying 3D microstructures are important steps in precise micro-manipulation. This thesis explores some of the visual reconstruction and classification algorithms for 3D microstructures used in micromanipulation. Mechanical characterization of microstructures has also been considered. In particular, visual reconstruction algorithm (shape from focus - SFF) uses 2D image sequence of a microscopic object captured at different focusing levels to create a 3D range image. Then, the visual classification algorithm takes the range image as an input and applies a curvature-based segmentation method, HK segmentation, which is based on differential geometry. The object is segmented into surface patches according to the curvature of its surface. It is shown that the visual reconstruction algorithm works successfully for synthetic and real image data. The range images are used to classify the surfaces of the micro objects according to their curvatures in the HK segmentation algorithm. Also, a mechanical property characterization technique for cell and embryo is presented. A zebrafish embryo chorion is mechanically characterized using cell boundary deformation. Elastic modulus and developmental stage of the embryo are obtained successfully using visual information. In addition to these, calibrated image based visual servoing algorithm is experimentally evaluated for various tasks in micro domain. Experimental results on optical system calibration and image-based visual servoing in micropositioning and trajectory following tasks are presented

Feature Extraction for Image Super-resolution using Finite Rate of Innovation Principles

To understand a real-world scene from several multiview pictures, it is necessary to find the disparities existing between each pair of images so that they are correctly related to one another., This process. called image registration, reguires the extraction of some specific information about the scene. This is achieved by taking features out of the acquired imaqes. Thus, the quality of the, registration depends largely on the accuracy of the extracted features. Feature extraction can be formulated as a sampling problem for which perfect reconstruction of the, desired features is wanted. The recent sampling theory for signals with finite rate of innovation (FR/), and the B-spline theory offer an appropriate new framework for the extraction of features in real, images. This thesis first focuses on extending the sampling theory for FRI signals to a multichannel, case and then presents exact sampling results for two different types of image features used for, registration: moments and edges. In the first part, it is shown that the geometric moments of an observed scene can be retrieved exactly from sampled images and used as global features for registration. The second part describes how edges can also be retrieved perfectly from sampled images for registration purposes. The proposed feature extraction schemes therefore allow in theory the exact registration of images. Indeed, various simulations show that the proposed extraction/registration methods overcome traditional ones, especially at low-resolution. These characteristics make such feature extraction techniques very appropriate for applications like image super-resolution for which a very precise registration is needed. The quality of the superresolved images obtained using the proposed feature extraction methods is improved by comparison with other approaches. Finally, the notion of polyphase components is used to adapt the imaqe acquisition model to the characteristics of real digital cameras in order to run super-resolution experiments on real images