Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

Connectivity Compression for Irregular Quadrilateral Meshes

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and VRML models, however, are represented as quadrilateral meshes or mixed triangle/quadrilateral meshes, and these models may also require compression. We present an algorithm for encoding the connectivity of such quadrilateral meshes, and we demonstrate that by preserving and exploiting the original quad structure, our approach achieves encodings 30 - 80% smaller than an approach based on randomly splitting quads into triangles. We present both a code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per vertex for meshes without valence-two vertices) and entropy-coding results for typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the regularity of the mesh. Our method may be implemented by a rule for a particular splitting of quads into triangles and by using the compression and decompression algorithms introduced in [Rossignac99] and [Rossignac&Szymczak99]. We also present extensions to the algorithm to compress meshes with holes and handles and meshes containing triangles and other polygons as well as quads

Novel Color Image Compression Algorithm Based-On Quadtree

This paper presents a novel algorithm having two image processing systems that have the ability to compress the colour image. The proposed systems divides the colour image into RGB components, each component is selected to be divided. The division processes of the component into blocks are based on quad tree method. For each selection, the other two components are divided using the same blocks coordinates of the selected divided component. In the first system, every block has three minimum values and three difference values. While the other system, every block has three minimum values and one average difference. From experiments, it is found that the division according to the G component is the best giving good visual quality of the compressed images with appropriate compression ratios. It is also noticed, the performance of the second system is better than the first one. The obtained compression ratios ofthe second system are between 1.3379 and 5.0495 at threshold value 0.1, and between 2.3476 and 8.9713 at threshold value 0.2

Underwater radio frequency image sensor using progressive image compression and region of interest

The increasing demand for underwater robotic intervention systems around the world in several application domains requires more versatile and inexpensive systems. By using a wireless communication system, supervised semi-autonomous robots have freedom of movement; however, the limited and varying bandwidth of underwater radio frequency (RF) channels is a major obstacle for the operator to get camera feedback and supervise the intervention. This paper proposes the use of progressive (embedded) image compression and region of interest (ROI) for the design of an underwater image sensor to be installed in an autonomous underwater vehicle, specially when there are constraints on the available bandwidth, allowing a more agile data exchange between the vehicle and a human operator supervising the underwater intervention. The operator can dynamically decide the size, quality, frame rate, or resolution of the received images so that the available bandwidth is utilized to its fullest potential and with the required minimum latency. The paper focuses first on the description of the system, which uses a camera, an embedded Linux system, and an RF emitter installed in an OpenROV housing cylinder. The RF receiver is connected to a computer on the user side, which controls the camera monitoring parameters, including the compression inputs, such as region of interest (ROI), size of the image, and frame rate. The paper focuses on the compression subsystem and does not attempt to improve the communications physical media for better underwater RF links. Instead, it proposes a unified system that uses well-integrated modules (compression and transmission) to provide the scientific community with a higher-level protocol for image compression and transmission in sub-sea robotic interventions

An Efficient Boosted Classifier Tree-Based Feature Point Tracking System for Facial Expression Analysis

The study of facial movement and expression has been a prominent area of research since the early work of Charles Darwin. The Facial Action Coding System (FACS), developed by Paul Ekman, introduced the first universal method of coding and measuring facial movement. Human-Computer Interaction seeks to make human interaction with computer systems more effective, easier, safer, and more seamless. Facial expression recognition can be broken down into three distinctive subsections: Facial Feature Localization, Facial Action Recognition, and Facial Expression Classification. The first and most important stage in any facial expression analysis system is the localization of key facial features. Localization must be accurate and efficient to ensure reliable tracking and leave time for computation and comparisons to learned facial models while maintaining real-time performance. Two possible methods for localizing facial features are discussed in this dissertation. The Active Appearance Model is a statistical model describing an object\u27s parameters through the use of both shape and texture models, resulting in appearance. Statistical model-based training for object recognition takes multiple instances of the object class of interest, or positive samples, and multiple negative samples, i.e., images that do not contain objects of interest. Viola and Jones present a highly robust real-time face detection system, and a statistically boosted attentional detection cascade composed of many weak feature detectors. A basic algorithm for the elimination of unnecessary sub-frames while using Viola-Jones face detection is presented to further reduce image search time. A real-time emotion detection system is presented which is capable of identifying seven affective states (agreeing, concentrating, disagreeing, interested, thinking, unsure, and angry) from a near-infrared video stream. The Active Appearance Model is used to place 23 landmark points around key areas of the eyes, brows, and mouth. A prioritized binary decision tree then detects, based on the actions of these key points, if one of the seven emotional states occurs as frames pass. The completed system runs accurately and achieves a real-time frame rate of approximately 36 frames per second. A novel facial feature localization technique utilizing a nested cascade classifier tree is proposed. A coarse-to-fine search is performed in which the regions of interest are defined by the response of Haar-like features comprising the cascade classifiers. The individual responses of the Haar-like features are also used to activate finer-level searches. A specially cropped training set derived from the Cohn-Kanade AU-Coded database is also developed and tested. Extensions of this research include further testing to verify the novel facial feature localization technique presented for a full 26-point face model, and implementation of a real-time intensity sensitive automated Facial Action Coding System

Proximal Methods for Hierarchical Sparse Coding

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and we propose in this paper efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the L1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally organize in a prespecified arborescent structure, leading to a better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models