A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections

We present a novel technique for encoding and decoding constant weight binary vectors that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and then analyze its complexity. The complexity depends on the weight of the vector, rather than on the block length as in other algorithms. This approach is advantageous when the weight is smaller than the square root of the block length.      

AND/OR net representation for robotic task sequence planning

The paper describes a framework for task sequence planning for a generalized robotic work cell. The AND/OR net provides a compact, distributed, domain-specific representation of geometric configurations of parts and devices in the work cell. The approach maintains a correspondence from geometric state information to task and motion plans and on-line discrete-event control that is not available in traditional action-based planners. The feasibility criteria for each AND/OR net transition guide the geometric reasoning required in the planning of feasible sequences. The resulting search space for plans is often much smaller (due to explicit representation of geometric constraints) than the state space of an action-based task planner. For purposes of analysis, the AND/OR net is mapped into a Petri net and the resulting Petri net is shown to be bounded and have guaranteed properties of liveness, safeness, and reversibility. In this form, the AND/OR net may be viewed as a Petri net synthesis tool in which the resulting Petri net representation may be used for on-line scheduling and control of the system     

Face Recognition Using Dual-Tree Complex Wavelet Features

We propose a novel facial representation based on the dual-tree complex wavelet transform for face recognition. It is effective and efficient to represent the geometrical structures in facial image with low redundancy. Moreover, we experimentally verify that the proposed method is more powerful to extract facial features robust against the variations of shift and illumination than the discrete wavelet transform and Gabor wavelet transform.     

Hyperbolic Embedding of Internet Graph for Distance Estimation and Overlay Construction

Estimating distances in the Internet has been studied in the recent years due to its ability to improve the performance of many applications, e.g., in the peer-to-peer realm. One scalable approach to estimate distances between nodes is to embed the nodes in some d dimensional geometric space and to use the pair distances in this space as the estimate for the real distances. Several algorithms were suggested in the past to do this in low dimensional Euclidean spaces. It was noted in recent years that the Internet structure has a highly connected core and long stretched tendrils, and that most of the routing paths between nodes in the tendrils pass through the core. Therefore, we suggest in this work, to embed the Internet distance metric in a hyperbolic space where routes are bent toward the center. We found that if the curvature, that defines the extend of the bending, is selected in the adequate range, the accuracy of Internet distance embedding can be improved. We demonstrate the strength of our hyperbolic embedding with two applications: selecting the closest server and building an application level multicast tree. For the latter, we present a distributed algorithm for building geometric multicast trees that achieve good trade-offs between delay (stretch) and load (stress). We also present a new efficient centralized embedding algorithm that enables the accurate embedding of short distances, something that have never been done before.     

Topology preserving non-negative matrix factorization for face recognition.

In this paper, a novel topology preserving non-negative matrix factorization (TPNMF) method is proposed for face recognition. We derive the TPNMF model from original NMF algorithm by preserving local topology structure. The TPNMF is based on minimizing the constraint gradient distance in the high-dimensional space. Compared with L(2) distance, the gradient distance is able to reveal latent manifold structure of face patterns. By using TPNMF decomposition, the high-dimensional face space is transformed into a local topology preserving subspace for face recognition. In comparison with PCA, LDA, and original NMF, which search only the Euclidean structure of face space, the proposed TPNMF finds an embedding that preserves local topology information, such as edges and texture. Theoretical analysis and derivation given also validate the property of TPNMF. Experimental results on three different databases, containing more than 12,000 face images under varying in lighting, facial expression, and pose, show that the proposed TPNMF approach provides a better representation of face patterns and achieves higher recognition rates than NMF.     

Tree representation of digital picture embeddings

It is often the case that the same object is imaged in different ways, resulting in digital pictures of (some parts of) it at different resolutions. This leads to the combinatorial problem of “embedding” one of these pictures into the other in a way that corresponds to physical truth. In this paper we present a mathematical formulation of this intuitive concept of embedding. We also show, using a tree representation of digital pictures, how picture embedding relates to tree embedding, which has been a subject of much study in combinatorial computer science (mostly for reasons other than application to digital pictures).     

2D facial expression recognition via 3D reconstruction and feature fusion

In this paper, a novel feature extraction method is proposed for facial expression recognition by extracting the feature from facial depth and 3D mesh alongside texture. Accordingly, the 3D Facial Expression Generic Elastic Model (3D FE-GEM) method is used to reconstruct an expression-invariant 3D model from the human face. Then, the texture, depth and mesh are extracted from the reconstructed face model. Afterwards, the Local Binary Pattern (LBP), proposed 3D High-Low Local Binary Pattern (3DH-LLBP) and Local Normal Binary Patterns (LNBPs) are applied to texture, depth and mesh of the face, respectively, to extract the feature from 2D images. Finally, the final feature vectors are generated through feature fusion and are classified by the Support Vector Machine (SVM). Convincing results are acquired for facial expression recognition on the CK+, CK, JAFFE and Bosphorus image databases compared to several state-of-the-art methods.     

Geometry-based distributed scene representation with omnidirectional vision sensors

This paper addresses the problem of efficient representation of scenes captured by distributed omnidirectional vision sensors. We propose a novel geometric model to describe the correlation between different views of a 3-D scene. We first approximate the camera images by sparse expansions over a dictionary of geometric atoms. Since the most important visual features are likely to be equivalently dominant in images from multiple cameras, we model the correlation between corresponding features in different views by local geometric transforms. For the particular case of omnidirectional images, we define the multiview transforms between corresponding features based on shape and epipolar geometry constraints. We apply this geometric framework in the design of a distributed coding scheme with side information, which builds an efficient representation of the scene without communication between cameras. The Wyner-Ziv encoder partitions the dictionary into cosets of dissimilar atoms with respect to shape and position in the image. The joint decoder then determines pairwise correspondences between atoms in the reference image and atoms in the cosets of the Wyner-Ziv image in order to identify the most likely atoms to decode under epipolar geometry constraints. Experiments demonstrate that the proposed method leads to reliable estimation of the geometric transforms between views. In particular, the distributed coding scheme offers similar rate-distortion performance as joint encoding at low bit rate and outperforms methods based on independent decoding of the different images.     

Language-guided graph parsing attention network for human-object interaction recognition

This paper focuses on the task of human-object interaction (HOI) recognition, which aims to classify the interaction between human and objects. It is a challenging task partially due to the extremely imbalanced data among classes. To solve this problem, we propose a language-guided graph parsing attention network (LG-GPAN) that makes use of the word distribution in language to guide the classification in vision. We first associate each HOI class name with a word embedding vector in language and then all the vectors can construct a language space specified for HOI recognition. Simultaneously, the visual feature is extracted from the inputs via the proposed graph parsing attention network (GPAN) for better visual representation. The visual feature is then transformed into the linguistic one in language space. Finally, the output score is obtained via measuring the distance between the linguistic feature and the word embedding of classes in language space. Experimental results on the popular CAD-120 and V-COCO datasets validate our design choice and demonstrate its superior performance in comparison to the state-of-the-art.     

Watermarking 3D models using spectral mesh compression

We propose a robust and imperceptible spectral watermarking method for high rate embedding of a watermark into 3D polygonal meshes. Our approach consists of four main steps: (1) the mesh is partitioned into smaller sub-meshes, and then the watermark embedding and extraction algorithms are applied to each sub-mesh, (2) the mesh Laplacian spectral compression is applied to the sub-meshes, (3) the watermark data is distributed over the spectral coefficients of the compressed sub-meshes, (4) the modified spectral coefficients with some other basis functions are used to obtain uncompressed watermarked 3D mesh. The main attractive features of this approach are simplicity, flexibility in data embedding capacity, and fast implementation. Extensive experimental results show the improved performance of the proposed method, and also its robustness against the most common attacks including the geometric transformations, adaptive random noise, mesh smoothing, mesh cropping, and combinations of these attacks.     

Facial micro-expression recognition based on accordion spatio-temporal representation and random forests

Micro-expressions are very brief involuntary facial expressions which appear on the face of humans when they unconsciously conceal an emotion. Creating a solution allowing an automatic recognition of the facial micro-expressions from video sequences has garnered increasing attention from experts across such different disciplines as computer science, security, and psychology. This paper offered a solution to facial micro-expressions recognition, based on accordion spatio-temporal representation and Random Forests. The proposed feature space, called “Uniform Local Binary Patterns on an Accordion 2D representation of sub-regions presented by a Pyramid of levels (LBPAccP^u2)”, exploits the effectiveness of uniform LBP patterns applied on an accordion representation of sub-regions at different sizes. Random Forests were used to select the most discriminating features and reduce the classification ambiguity of similar micro-expressions through a new proximity measure. The main objective of our paper was to demonstrate that the use of few features could be more efficient to produce a strong micro-expression recognition classifier that outperforms the approaches that rely on high dimensional features space. The experimental results across six micro-expression datasets show the effectiveness of the proposed solution with an accuracy rate that can reach 81.38% on CasmeII dataset. Compared to some famous competitive state-of-the-art approaches, the proposed solution proved its performance thanks to its accuracy rate as well as the number of features it uses.     

Methods of solving reduced lead systems for inverse electrocardiography

In the context of inverse electrocardiography, we examine the problem of using measurements from sets of electrocardiographic leads that are smaller than the number of nodes in the associated geometric models of the torso. We compared several methods to estimate the solution from such reduced-lead measurements sets both with and without knowledge of prior statistics of the measurements. We present here simulation results that indicate that deleting rows of the forward matrix corresponding to the unmeasured leads performs best in the absence of prior statistics, and that Bayesian (or least-squares) estimation performs best in the presence of prior statistics.     

Spatial color image processing using Clifford algebras: application to color active contour

In the literature, the color information of the pixels of an image has been represented by different structures. Recently, algebraic entities such as quaternions or Clifford algebras have been used to perform image processing for example. This paper presents the embedding of color information into the vectorial parts of a multivector. This multivector is an element of the geometric or Clifford algebra constructed from a three-dimensional vector space. This formalism presents the advantage of algebraically separating colors which are handled entities from the geometric operations done to them. We propose to introduce several contributions for color image processing by using this Clifford algebra. First, as colors are represented by 1-vectors, we point out that a color pixel given in the RGB color space can be expressed algebraically by its hue saturation and value using the geometry. Then, we illustrate how this formalism can be used to define color alterations with algebraic operations. We generalize linear filtering algorithms already defined with quaternions and define a new color edge detector. Finally, the application of the new color gradient is illustrated by a new color formulation of snakes. Thus, we propose in this paper the definition and exploitation of a formalism in which we geometrically handle colors with algebraic entities and expressions.     

Image coding with geometric wavelets.

This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.     

应用于人脸识别的监督局部邻域保持嵌入算法

提出了一种应用于人脸识别的监督线性维数约简 算法。首先引入图像距离度量方法以确定人脸数据 之间的相似程度,之后将训练样本的类标先验信息融入到邻域保持嵌入(NPE,neighborhood preserving embedding)算法的目标函 数中,使得降维后的嵌入空间的投影数据呈多流形分布,不仅最优保持了样本空间的局部几 何结构,同时各类样本 投影的类内散度最小化,类间散度最大化,增大了各类数据分布之间的间隔,提高了嵌入空 间的辨别能力。在Extended Yale B和CMU PIE两个开放人脸数据库上进行了识别实验,结果表明,本文算法取得了很好 的识别效果。     

基于图像归一化的抗几何攻击水印技术

在数字图像水印中,确保水印和图像的同步问题是水印图像有效抵抗几何攻击的关键.本文利用几何不变矩,对水印抗几何攻击进行了探讨,提出了一种基于几何不变矩的抗几何攻击的水印算法.通过对原始图像和攻击后的图像的归一化处理,使水印和图像在嵌入与提取过程保证同步.实验证明该方法对常见的几何攻击有很好的鲁棒性,嵌入的水印容量较大且水印图像的质量也较高.     

基于核稀疏编码的阵发性房颤检测

阵发性房颤(PAF)是一种具有偶发性的心律失常,其较高的漏检率导致心脏相关疾病的增加。该文提出了一种基于核稀疏编码的自动检测方法,可以仅根据较短RR间期数据识别PAF发作。该方法采用特殊几何结构来分析数据高维特性,通过计算协方差矩阵作为特征描述子,找到蕴含在数据中的黎曼流形结构;然后基于Log-Euclid框架,利用核方法将流形空间映射到高维可再生核希尔伯特空间,以获取更准确的稀疏表示来快速识别PAF。经麻省理工学院-贝斯以色列医院房颤数据库验证,获得98.71%的敏感性、98.43%的特异度和98.57%的总准确率。因此,该研究对检测短暂发作的PAF有实质性的改善,在临床监测和治疗方面显示出良好的潜力。     

人脸显性特征的融合构造方法及识别

 目前的人脸识别研究中,面部几何特征没有得到很好的利用.本文阐述了几何特征对于人脸识别的重要性,在此基础上提出了一种提取面部几何特征的新方法;通过融合几何信息和纹理信息构造出一种面部显性特征,并给出了相应的人脸识别方法.这种新的人脸识别方法相对于基于统计学习的子空间方法具有一定的优势,同时也可作为后者的有益补充.实验表明,本文提出的人脸表示特征及识别方法对人脸表情变化和环境光照变化均有一定的鲁棒性.