Facial Expression Classification Using Rotation Slepian-based Moment Invariants

Rotation moment invariants have been of great interest in image processing and pattern recognition. This paper presents a novel kind of rotation moment invariants based on the Slepian functions, which were originally introduced in the method of separation of variables for Helmholtz equations. They were first proposed for time series by Slepian and his coworkers in the 1960s. Recent studies have shown that these functions have an good performance in local approximation compared to other approximation basis. Motivated by the good approximation performance, we construct the Slepian-based moments and derive the rotation invariant. We not only theoretically prove the invariance, but also discuss the experiments on real data. The proposed rotation invariants are robust to noise and yield decent performance in facial expression classification.Comment: 13 pages, 4 figure

Content Based Image Retrieval Using Exact Legendre Moments and Support Vector Machine

Content Based Image Retrieval (CBIR) systems based on shape using invariant image moments, viz., Moment Invariants (MI) and Zernike Moments (ZM) are available in the literature. MI and ZM are good at representing the shape features of an image. However, non-orthogonality of MI and poor reconstruction of ZM restrict their application in CBIR. Therefore, an efficient and orthogonal moment based CBIR system is needed. Legendre Moments (LM) are orthogonal, computationally faster, and can represent image shape features compactly. CBIR system using Exact Legendre Moments (ELM) for gray scale images is proposed in this work. Superiority of the proposed CBIR system is observed over other moment based methods, viz., MI and ZM in terms of retrieval efficiency and retrieval time. Further, the classification efficiency is improved by employing Support Vector Machine (SVM) classifier. Improved retrieval results are obtained over existing CBIR algorithm based on Stacked Euler Vector (SERVE) combined with Modified Moment Invariants (MMI).Comment: 11 Pages, IJM

Shape-Color Differential Moment Invariants under Affine Transformations

We propose the general construction formula of shape-color primitives by using partial differentials of each color channel in this paper. By using all kinds of shape-color primitives, shape-color differential moment invariants can be constructed very easily, which are invariant to the shape affine and color affine transforms. 50 instances of SCDMIs are obtained finally. In experiments, several commonly used color descriptors and SCDMIs are used in image classification and retrieval of color images, respectively. By comparing the experimental results, we find that SCDMIs get better results.Comment: 13 pages, 4 figure

Rotation invariants of two dimensional curves based on iterated integrals

We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to order six. We present an application to online (stroke-trajectory based) character recognition. This seems to be the first time in the literature that the use of iterated integrals of a curve is proposed for (invariant) feature extraction in machine learning applications

Image Projective Invariants

In this paper, we propose relative projective differential invariants (RPDIs) which are invariant to general projective transformations. By using RPDIs and the structural frame of integral invariant, projective weighted moment invariants (PIs) can be constructed very easily. It is first proved that a kind of projective invariants exists in terms of weighted integration of images, with relative differential invariants as the weight functions. Then, some simple instances of PIs are given. In order to ensure the stability and discriminability of PIs, we discuss how to calculate partial derivatives of discrete images more accurately. Since the number of pixels in discrete images before and after the geometric transformation may be different, we design the method to normalize the number of pixels. These ways enhance the performance of PIs. Finally, we carry out some experiments based on synthetic and real image datasets. We choose commonly used moment invariants for comparison. The results indicate that PIs have better performance than other moment invariants in image retrieval and classification. With PIs, one can compare the similarity between images under the projective transformation without knowing the parameters of the transformation, which provides a good tool to shape analysis in image processing, computer vision and pattern recognition

Edge direction matrixes-based local binar patterns descriptor for shape pattern recognition

Shapes and texture image recognition usage is an essential branch of pattern recognition. It is made up of techniques that aim at extracting information from images via human knowledge and works. Local Binary Pattern (LBP) ensures encoding global and local information and scaling invariance by introducing a look-up table to reflect the uniformity structure of an object. However, edge direction matrixes (EDMS) only apply global invariant descriptor which employs first and secondary order relationships. The main idea behind this methodology is the need of improved recognition capabilities, a goal achieved by the combinative use of these descriptors. This collaboration aims to make use of the major advantages each one presents, by simultaneously complementing each other, in order to elevate their weak points. By using multiple classifier approaches such as random forest and multi-layer perceptron neural network, the proposed combinative descriptor are compared with the state of the art combinative methods based on Gray-Level Co-occurrence matrix (GLCM with EDMS), LBP and moment invariant on four benchmark dataset MPEG-7 CE-Shape-1, KTH-TIPS image, Enghlishfnt and Arabic calligraphy . The experiments have shown the superiority of the introduced descriptor over the GLCM with EDMS, LBP and moment invariants and other well-known descriptor such as Scale Invariant Feature Transform from the literature

Using 3D Hahn Moments as A Computational Representation of ATS Drugs Molecular Structure

The campaign against drug abuse is fought by all countries, most notably on ATS drugs. The technical limitations of the current test kits to detect new brand of ATS drugs present a challenge to law enforcement authorities and forensic laboratories. Meanwhile, new molecular imaging devices which allowed mankind to characterize the physical 3D molecular structure have been recently introduced, and it can be used to remedy the limitations of existing drug test kits. Thus, a new type of 3D molecular structure representation technique should be developed to cater the 3D molecular structure acquired physically using these molecular imaging devices. One of the applications of image processing methods to represent a 3D image is 3D moments, and this study formulates a new 3D moments technique, namely 3D Hahn moments, to represent the 3D molecular structure of ATS drugs. The performance of the proposed technique was analysed using drug chemical structures obtained from UNODC for the ATS drugs, while non-ATS drugs are obtained randomly from ChemSpider database. The evaluation shows the technique is qualified to be further explored in the future works to be fully compatible with ATS drug identification domain

Rigid-Motion Scattering for Texture Classification

A rigid-motion scattering computes adaptive invariants along translations and rotations, with a deep convolutional network. Convolutions are calculated on the rigid-motion group, with wavelets defined on the translation and rotation variables. It preserves joint rotation and translation information, while providing global invariants at any desired scale. Texture classification is studied, through the characterization of stationary processes from a single realization. State-of-the-art results are obtained on multiple texture data bases, with important rotation and scaling variabilities.Comment: 19 pages, submitted to International Journal of Computer Visio

Shape Distributions of Nonlinear Dynamical Systems for Video-based Inference

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligenc

Naturally Combined Shape-Color Moment Invariants under Affine Transformations

We proposed a kind of naturally combined shape-color affine moment invariants (SCAMI), which consider both shape and color affine transformations simultaneously in one single system. In the real scene, color and shape deformations always exist in images simultaneously. Simple shape invariants or color invariants can not be qualified for this situation. The conventional method is just to make a simple linear combination of the two factors. Meanwhile, the manual selection of weights is a complex issue. Our construction method is based on the multiple integration framework. The integral kernel is assigned as the continued product of the shape and color invariant cores. It is the first time to directly derive an invariant to dual affine transformations of shape and color. The manual selection of weights is no longer necessary, and both the shape and color transformations are extended to affine transformation group. With the various of invariant cores, a set of lower-order invariants are constructed and the completeness and independence are discussed detailedly. A set of SCAMIs, which called SCAMI24, are recommended, and the effectiveness and robustness have been evaluated on both synthetic and real datasets