Keypoint Detection and Local Feature Matching for Textured 3D Face Recognition

In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 high-contrast patches ℳ. We develop a theoretical model for the high-density 2-dimensional submanifold of ℳ showing that it has the topology of the Klein bottle. Using our topological software package PLEX we experimentally verify our theoretical conclusions. We use polynomial representation to give coordinatization to various subspaces of ℳ. We find the best-fitting embedding of the Klein bottle into the ambient space of ℳ. Our results are currently being used in developing a compression algorithm based on a Klein bottle dictionary.     

Topology on the set of R 0 semantics for R 0 algebras

This paper introduces the concepts of R ₀ valuation, R ₀ semantic, countable R ₀ category , R ₀ fuzzy topological category , etc. It is established in a natural way that the fuzzy topology δ and its cut topology on the set Ω _M consisting of all R ₀ valuations of an R ₀ algebra M, and some properties of fuzzy topology δ and its cut topology are investigated carefully. Moreover, the representation theorem for R ₀ algebras by means of fuzzy topology is given, that is to say the category is equivalent to the category . By studying the relation between valuations and filters, the Loomis–Sikorski theorem for R ₀ algebras is obtained. As an application, K-compactness of the R ₀ logic is discussed.     

Simple Easy Terms

We illustrate the use of intersection types as a semantic tool for proving easiness result on λ-terms. We single out the notion of simple easiness for λ-terms as a useful semantic property for building filter models with special purpose features. Relying on the notion of easy intersection type theory, given λ-terms M and E, with E simple easy, we successfully build a filter model which equates interpretation of M and E, hence proving that simple easiness implies easiness. We finally prove that a class of λ-terms generated by ω₂ω₂ are simple easy, so providing alternative proof of easiness for them.     

Topological model for 3D image representation: Definition and incremental extraction algorithm

In this paper, we define the three-dimensional topological map, a model which represents both the topological and geometrical information of a three-dimensional labeled image. Since this model describes the image’s topology in a minimal way, we can use it to define efficient image processing algorithms. The topological map is the last level of map hierarchy. Each level represents the region boundaries of the image and is defined from the previous level in the hierarchy, thus giving a simple constructive definition. This model is an extension of the similar model defined for 2D images. Progressive definition based on successive map levels allows us to extend this model to higher dimension. Moreover, with progressive definition, we can study each level separately. This simplifies the study of disconnection cases and the proofs of topological map properties. Finally, we provide an incremental extraction algorithm which extracts any map of the hierarchy in a single image scan. Moreover, we show that this algorithm is very efficient by giving the results of our experiments made on artificial images.     

HybridGAN: hybrid generative adversarial networks for MR image synthesis

In this paper, we propose HybridGAN – a new medical MR image synthesis methods via generative adversarial learning. Specifically, our synthesizer generates MRI data in a sequential manner: first in order to improve the robustness of image synthesis, an input full-size real MR image is divided into an array of sub-images. Then, to avoid overfitting limited MRI encodings, these sub-images and an unlimited amount of random latent noise vectors become the input of automatic encoder for learning the marginal image distributions of real images. Finally, pseudo patches with constrained noise vectors are put into RU-NET which is a component of our HybridGAN to generate a large number of synthetic MR images. In RU-NET, A SpliceLayer is then employed to fuse sub-images together in an interlaced manner into a full-size image. The experimental results show that HybridGAN can effectively synthesize a large variety of MR images and display a good visual quality. Compared to the state-of-the-art synthesis methods, our method achieves a significant improvement in terms of both visual and quantitative evaluation metrics.

     

Characterizing degrees of freedom for geometric design of developable composite Bézier surfaces

This paper studies geometric design of developable composite Bézier surfaces from two boundary curves. The number of degrees of freedom (DOF) is characterized for the surface design by deriving and counting the developability constraints imposed on the surface control points. With a first boundary curve freely chosen, (2m+3), (m+4), and five DOFs are available for a second boundary curve of a developable composite Bézier surface that is G⁰, G¹, and G², respectively, and consists of m consecutive patches, regardless of the surface degree. There remain five and (7-2m) DOFs for the surface with C¹ and C² continuity. Allowing the end control points to superimpose produces Degenerated triangular patches with four and three DOFs left, when the end ruling vanishes on one and both sides, respectively. Examples are illustrated to demonstrate various design methods for each continuity condition. The construction of a yacht hull with a patterned sheet of paper unrolled from 3D developable surfaces validates practicality of these methods in complex shape design. This work serves as a theoretical foundation for applications of developable composite Bézier surfaces in product design and manufacturing.     

Polyhedral Representation and Adjacency Graph in n-dimensional Digital Images

In this paper we generalize the concept of digital topology to arbitrary dimension n, in the context of (2n, 3ⁿ−1)-adjacency. We define an n-digital image as an uplet ( ⁿ, , H), where H is a finite subset of ⁿ and represents the adjacency relation in the whole lattice in a specific way. We give a natural and simple construction of polyhedral representation of based on cubical-complex decomposition. We develop general properties which provide a link between connectivity in digital and Euclidean space. This enables us to use methods of continuous topology in studying properties related to the connectivity, adjacency graph, and borders connectivity in n-digital images.     

Gesture image segmentation with Otsu’s method based on noise adaptive angle threshold

By analyzing the essence and deficiency of the improved Otsu’s method, this paper proposes a noise adaptive angle threshold based Otsu’s method for gesture image segmentation. It first designs a two-dimensional histogram of gray value-neighborhood truncated gray mean to avoid the interference of extreme noise by discarding the extremes of the neighborhood. Then, the probability that the pixel is noise is calculated according to the actual situation, adaptive filtering is implemented to enhance the algorithm’s universal applicability. It finally converts the threshold space to an angle space from 0° to 90°, and the threshold search range is compressed to improve its efficiency. As the gesture is close to the background and the boundary is blurred, this paper combines the global and local Otsu’s method to segment the gesture images based on the angle space. On the one hand, it uses the global Otsu’s method to obtain the global threshold t₁. On the other hand, it uses the local Otsu’s method to obtain the local threshold t₂, and segments gesture images based on t₂. Experimental results show that the proposed method is effective and can accurately segment gesture images with different noises.

     

Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation

A novel adaptive and exemplar-based approach is proposed for image restoration (denoising) and representation. The method is based on a pointwise selection of similar image patches of fixed size in the variable neighborhood of each pixel. The main idea is to associate with each pixel the weighted sum of data points within an adaptive neighborhood. We use small image patches (e.g. 7×7 or 9×9 patches) to compute these weights since they are able to capture local geometric patterns and texels seen in images. In this paper, we mainly focus on the problem of adaptive neighborhood selection in a manner that balances the accuracy of approximation and the stochastic error, at each spatial position. The proposed pointwise estimator is then iterative and automatically adapts to the degree of underlying smoothness with minimal a priori assumptions on the function to be recovered. The method is applied to artificially corrupted real images and the performance is very close, and in some cases even surpasses, to that of the already published denoising methods. The proposed algorithm is demonstrated on real images corrupted by non-Gaussian noise and is used for applications in bio-imaging.     

Algorithmical determination of the topology of a real algebraic surface

We present an algorithm to compute the topology of a non-singular real algebraic surface S in RP³, that is the number of its connected components and a topological model for each of them. Our strategy consists in computing the Euler characteristic of each connected component by means of a Morse-type investigation of S or of a suitably constructed compact affine surface. This procedure can be used to determine the topological type of an arbitrary non-singular surface; in particular it extends an existing algorithm applicable only to surfaces disjoint from a line.     

Suburban atmospheric visibility sensing by an image degradation processor: model development and field test

This study describes some preliminary results of a new approach which seeks to develop a method by which uneven decay of atmosphere can be described by the fluctuation of a degradation parameter, k, extracted from online recorded images. The proposed processor is a combination of the empirical model for atmospheric non-homogeneity and an image degradation method. Estimation of the other parameter, C _ave, derived from k values was an attempt to quantify the blurred level of atmospheric visibility according to the full-scale image computation. The C _ave of code A–E images ranged from 0.437 to 0.831, and the related visual range observed by investigators was from 14.1 to 3.0 km, respectively. The standard deviation of C _ave reveals that non-homogeneous degradation of blurring atmosphere happens. Low visibility related with a small visual range and a degraded image is companied by a large C _ave and inherits high variation from heaving k values. Because of fluctuation and full-scale image representation, C _ave is more meaningful and sensitive for atmospheric decay measurement than the prevailing visibility equal to the distance at which the farthest target can be recognized. Finally, a field test was applied to confirm a good correlation between observed visual range and two parameters (k and C _ave).     

The only stable normal forms of affine systems under feedback are linear

We consider the problem of existence of structurally stable normal forms of affine control systems with m inputs and n-dimensional state space, equipped with C^∞-Whitney topology and acted on by the static state feedback group. It is proved that structurally stable normal forms exist only if m = n or m =1 and n = 2, and are linear. There are no stable normal forms in any other range of dimensions (m, n).     

Active Contours Under Topology Control—Genus Preserving Level Sets

We present a novel framework to exert topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automated topological changes. In some applications, where some a priori knowledge of the target topology is available, topological changes may not be desirable. This is typically the case in biomedical image segmentation, where the topology of the target shape is prescribed by anatomical knowledge. However, topologically constrained evolutions often generate topological barriers that lead to large geometric inconsistencies. We introduce a topologically controlled level set framework that greatly alleviates this problem. Unlike existing work, our method allows connected components to merge, split or vanish under some specific conditions that ensure that the genus of the initial active contour (i.e. its number of handles) is preserved. We demonstrate the strength of our method on a wide range of numerical experiments and illustrate its performance on the segmentation of cortical surfaces and blood vessels. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Lower Bounds for Merging Networks

A lower bound theorem is established for the number of comparators in a merging network. Let M(m, n) be the least number of comparators required in the (m, n)-merging networks, and let C(m, n) be the number of comparators in Batcher's (m, n)-merging network, respectively. We prove for n≥1 that M(4, n)=C(4, n) for n≡0, 1, 3 mod 4, M(4, n)≥C(4, n)−1 for n≡2 mod 4, and M(5, n)=C(5, n) for n≡0, 1, 5 mod 8. Furthermore Batcher's (6, 8k+6)-, (7, 8k+7)-, and (8, 8k+8)-merging networks are optimal for k≥0. Our lower bound for (m, n)-merging networks, m≤n, has the same terms as C(m, n) has as far as n is concerned. Thus Batcher's (m, n)-merging network is optimal up to a constant number of comparators, where the constant depends only on m. An open problem posed by Yao and Yao (Lower bounds on merging networks, J. Assoc. Comput. Mach.23, 566–571) is solved: lim_n→∞M(m, n)/n=log m/2+m/2^{log m}.     

Monoid-labeled transition systems

Given a -complete (semi)lattice , we consider -labeled transition systems as coalgebras of a functor ⁽⁻⁾, associating with a set X the set ^X of all -fuzzy subsets. We describe simulations and bisimulations of -coalgebras to show that L⁽⁻⁾ weakly preserves nonempty kernel pairs iff it weakly preserves nonempty pullbacks iff L is join infinitely distributive (JID).Exchanging for a commutative monoid , we consider the functor ⁽⁻⁾_ω which associates with a set X all finite multisets containing elements of X with multiplicities m M. The corresponding functor weakly preserves nonempty pullbacks along injectives iff 0 is the only invertible element of , and it preserves nonempty kernel pairs iff is refinable, in the sense that two sum representations of the same value, r₁ + … + r_m = c₁ + … + c_n, have a common refinement matrix (m_{(i, j)}) whose k-th row sums to r_k and whose l-th column sums to c_l for any 1≤ k ≤ m and 1 ≤ l ≤ n.     

An improved vessel extraction scheme from retinal fundus images

Vessel extraction from retinal fundus images is essential for the diagnosis of different opthalmologic diseases like glaucoma, diabetic retinopathy and hypertension. It is a challenging task due to presence of several noises embedded with thin vessels. In this article, we have proposed an improved vessel extraction scheme from retinal fundus images. First, mathematical morphological operation is performed on each planes of the RGB image to remove the vessels for obtaining noise in the image. Next, the original RGB and vessel removed RGB image are transformed into negative gray scale image. These negative gray scale images are subtracted and finally binarized (BW₁) by leveling the image. It still contains some granular noise which is removed based on the area of connected component. Further, previously detected vessels are replaced in the gray-scale image with mean value of the gray-scale image and then the gray-scale image is enhanced to obtain the thin vessels. Next, the enhanced image is binarized and thin vessels are obtained (BW₂). Finally, the thin vessel image (BW₂) is merged with the previously obtained binary image (BW₁) and finally we obtain the vessel extracted image. To analyze the performance of our proposed method we have experimented on publicly available DRIVE dataset. We have observed that our algorithm have provides satisfactory performance with the sensitivity, specificity and accuracy of 0.7260, 0.9802 and 0.9563 respectively which is better than the most of the recent works.