Improved Eigenfeature Regularization for Face Identification

In this work, we propose to divide each class (a person) into subclasses using spatial partition trees which helps in better capturing the intra-personal variances arising from the appearances of the same individual. We perform a comprehensive analysis on within-class and within-subclass eigenspectrums of face images and propose a novel method of eigenspectrum modeling which extracts discriminative features of faces from both within-subclass and total or between-subclass scatter matrices. Effective low-dimensional face discriminative features are extracted for face recognition (FR) after performing discriminant evaluation in the entire eigenspace. Experimental results on popular face databases (AR, FERET) and the challenging unconstrained YouTube Face database show the superiority of our proposed approach on all three databases.Comment: 6 pages, 4 figures, ICIP 201

Appearance Based Robot and Human Activity Recognition System

In this work, we present an appearance based human activity recognition system. It uses background modeling to segment the foreground object and extracts useful discriminative features for representing activities performed by humans and robots. Subspace based method like principal component analysis is used to extract low dimensional features from large voluminous activity images. These low dimensional features are then used to classify an activity. An apparatus is designed using a webcam, which watches a robot replicating a human fall under indoor environment. In this apparatus, a robot performs various activities (like walking, bending, moving arms) replicating humans, which also includes a sudden fall. Experimental results on robot performing various activities and standard human activity recognition databases show the efficacy of our proposed method.Comment: 6 pages, 4 figure

Regions of variability for a class of analytic and locally univalent functions defined by subordination

In this article we consider a family $\mathcal{C}(A, B)$ of analytic and locally univalent functions on the open unit disc \ID=\{z :|z|<1\} in the complex plane that properly contains the well-known Janowski class of convex univalent functions. In this article, we determine the exact set of variability of $\log(f'(z_0))$ with fixed z_0 \in \ID and $f"(0)$ whenever $f$ varies over the class $\mathcal{C}(A, B)$.Comment: 9 pages, To appear in Proc. Indian Acad. Sci. Math. Sc

Sufficient conditions for univalence and study of a class of meromorphic univalent functions

In this article we consider the class $\mathcal{A}(p)$ which consists of functions that are meromorphic in the unit disc \ID having a simple pole at $z=p\in (0,1)$ with the normalization $f(0)=0=f'(0)-1$. First we prove some sufficient conditions for univalence of such functions in \ID. One of these conditions enable us to consider the class $\mathcal{V}_{p}(\lambda)$ that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that $\mathcal{U}_{p}(\lambda)\subsetneq \mathcal{V}_{p}(\lambda)$, where $\mathcal{U}_{p}(\lambda)$ was introduced and studied in \cite{BF-1}. Finally, we discuss some coefficient problems for $\mathcal{V}_{p}(\lambda)$ and end the article with a coefficient conjecture.Comment: 7 pages, Submitte

On the Taylor coefficients of a subclass of meromorphic univalent functions

Let $\mathcal{V}_p(\lambda)$ be the collection of all functions $f$ defined in the unit disc \ID having a simple pole at $z=p$ where $0<p<1$ and analytic in \ID\setminus\{p\} with $f(0)=0=f'(0)-1$ and satisfying the differential inequality $|(z/f(z))^2 f'(z)-1|< \lambda$ for z\in \ID, $0<\lambda\leq 1$. Each $f\in\mathcal{V}_p(\lambda)$ has the following Taylor expansion: $$f(z)=z+\sum_{n=2}^{\infty}a_n(f) z^n, \quad |z|<p.$$ In \cite{BF-3}, we conjectured that |a_n(f)|\leq \frac{1-(\lambda p^2)^n}{p^{n-1}(1-\lambda p^2)}\quad \mbox{for}\quad n\geq3. In the present article, we first obtain a representation formula for functions in the class $\mathcal{V}_p(\lambda)$. Using this representation, we prove the aforementioned conjecture for $n=3,4,5$ whenever $p$ belongs to certain subintervals of $(0,1)$. Also we determine non sharp bounds for $|a_n(f)|,\,n\geq 3$ and for $|a_{n+1}(f)-a_n(f)/p|,\,n\geq 2$.Comment: 8 page

Bohr phenomenon for operator valued functions

In this article we establish Bohr inequalities for operator valued functions, which can be viewed as the analogues of a couple of interesting results from scalar valued settings. Some results of this paper are motivated by the classical flavor of Bohr inequality, while the others are based on a generalized concept of the Bohr radius problem.Comment: 14 pages, Submitted to a journa

Coefficient Inequalities for Concave and Meromorphically Starlike Univalent Functions

Let \ID denote the open unit disk and f:\,\ID\TO\BAR\IC be meromorphic and univalent in \ID with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion $$f(z)=\sum_{n=-1}^{\infty}a_n(z-p)^n,\quad |z-p|<1-p,$$ such that $f$ maps \ID onto a domain whose complement with respect to \BAR{\IC} is a convex set (starlike set with respect to a point w_0\in \IC, w_0\neq 0 resp.). We call these functions as concave (meromorphically starlike resp.) univalent functions and denote this class by $Co(p)$ $(\Sigma^s(p, w_0)$ resp.). We prove some coefficient estimates for functions in the classes where the sharpness of these estimates is also achieved

Spontaneous vs. Posed smiles - can we tell the difference?

Smile is an irrefutable expression that shows the physical state of the mind in both true and deceptive ways. Generally, it shows happy state of the mind, however, `smiles' can be deceptive, for example people can give a smile when they feel happy and sometimes they might also give a smile (in a different way) when they feel pity for others. This work aims to distinguish spontaneous (felt) smile expressions from posed (deliberate) smiles by extracting and analyzing both global (macro) motion of the face and subtle (micro) changes in the facial expression features through both tracking a series of facial fiducial markers as well as using dense optical flow. Specifically the eyes and lips features are captured and used for analysis. It aims to automatically classify all smiles into either `spontaneous' or `posed' categories, by using support vector machines (SVM). Experimental results on large database show promising results as compared to other relevant methods.Comment: 10 pages, 5 figures, 6 tables, International Conference on Computer Vision and Image Processing (CVIP 2016

Bohr phenomenon for locally univalent functions and logarithmic power series

In this article we prove Bohr inequalities for sense-preserving $K$-quasiconformal harmonic mappings defined in $\mathbb{D}$ and obtain the corresponding results for sense-preserving harmonic mappings by letting $K\to\infty$. One of the results includes the sharpened version of a theorem by Kayumov $\textit{et. al.}$ ($\textit{Math. Nachr.}$, 291 (2018), no. 11--12, 1757--1768). In addition Bohr inequalities have been established for uniformly locally univalent holomorphic functions, and for $\log(f(z)/z)$ where $f$ is univalent or inverse of a univalent function.Comment: 13 pages, Submitted to a journa

Loewner chain and quasiconformal extension of some classes of univalent functions

In this article, we obtain quasiconformal extensions of some classes of conformal maps defined either on the unit disc or on the exterior of it onto the extended complex plane. Some of these extensions have been obtained by constructing suitable Loewner chains and others have been obtained by applying a well-known result.Comment: 14 page