Generalization of form in visual pattern classification.

Human observers were trained to criterion in classifying compound Gabor signals with sym- metry relationships, and were then tested with each of 18 blob-only versions of the learning set. General- ization to dark-only and light-only blob versions of the learning signals, as well as to dark-and-light blob versions was found to be excellent, thus implying virtually perfect generalization of the ability to classify mirror-image signals. The hypothesis that the learning signals are internally represented in terms of a 'blob code' with explicit labelling of contrast polarities was tested by predicting observed generalization behaviour in terms of various types of signal representations (pixelwise, Laplacian pyramid, curvature pyramid, ON/OFF, local maxima of Laplacian and curvature operators) and a minimum-distance rule. Most representations could explain generalization for dark-only and light-only blob patterns but not for the high-thresholded versions thereof. This led to the proposal of a structure-oriented blob-code. Whether such a code could be used in conjunction with simple classifiers or should be transformed into a propo- sitional scheme of representation operated upon by a rule-based classification process remains an open question

Approximation learning methods of Harmonic Mappings in relation to Hardy Spaces

A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper upper-high complex plane. If considering this in the Hardy space, the optimization operator of this problem will be highly simplified and an efficient algorithm is possible. This is mainly realized by the help of reproducing properties of the functions in the Hardy space of upper-high complex plane, and the detail algorithm is proposed. Moreover, harmonic mappings, which is a significant geometric transformation, are commonly used in many applications such as image processing, since it describes the energy minimization mappings between individual manifolds. Particularly, when we focus on the planer mappings between two Euclid planer regions, the harmonic mappings are exist and unique, which is guaranteed solidly by the existence of harmonic function. This property is attractive and simulation results are shown in this paper to ensure the capability of applications such as planer shape distortion and surface registration.Comment: 2016 3rd International Conference on Informative and Cybernetics for Computational Social Systems (ICCSS

Optimization for automated assembly of puzzles

The puzzle assembly problem has many application areas such as restoration and reconstruction of archeological findings, repairing of broken objects, solving jigsaw type puzzles, molecular docking problem, etc. The puzzle pieces usually include not only geometrical shape information but also visual information such as texture, color, and continuity of lines. This paper presents a new approach to the puzzle assembly problem that is based on using textural features and geometrical constraints. The texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. Feature values are derived from these original and predicted images of pieces. An affinity measure of corresponding pieces is defined and alignment of the puzzle pieces is formulated as an optimization problem where the optimum assembly of the pieces is achieved by maximizing the total affinity measure. An fft based image registration technique is used to speed up the alignment of the pieces. Experimental results are presented on real and artificial data sets

Visual identification by signature tracking

We propose a new camera-based biometric: visual signature identification. We discuss the importance of the parameterization of the signatures in order to achieve good classification results, independently of variations in the position of the camera with respect to the writing surface. We show that affine arc-length parameterization performs better than conventional time and Euclidean arc-length ones. We find that the system verification performance is better than 4 percent error on skilled forgeries and 1 percent error on random forgeries, and that its recognition performance is better than 1 percent error rate, comparable to the best camera-based biometrics

Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction

International audienceThis paper addresses the gray-level image representation ability of the Fourier-Mellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical di±culty of the FMT lies in the accuracy and e±ciency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and ¯nite-extent sets of Fourier- Mellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities. Experimental results on real gray-level images show that it is possible to recover an image to within a speci¯ed degree of accuracy and to classify objects reliably even when a large set of descriptors is used. Finally, an example will be given, illustrating both theoretical and numerical results in the context of content-based image retrieval

Beyond developable: computational design and fabrication with auxetic materials

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications