Ishtiaq Rasool Khan

Taylor series based finite difference approximations of higher-degree derivatives

A new type of Taylor series based finite difference approximations of higher-degree derivatives of a function are presented in closed forms, with their coefficients given by explicit formulas for arbitrary orders. Characteristics and accuracies of presented approximations and already presented central difference higher-degree approximations are investigated by performing example numerical differentiations. It is shown that the presented approximations are more accurate than the central difference approximations, especially for odd degrees. However, for even degrees, central difference approximations become attractive, as the coefficients of the presented approximations of even degrees do not correspond to equispaced input samples.

Mathematical proof of closed form expressions for finite difference approximations based on Taylor series

Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients, However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.

Finite-Impulse-Response Digital Differentiators for Midband Frequencies Based on Maximal Linearity Constraints

Maximally linear digital differentiators (DDs) are known for high accuracy in narrow frequency bands centered at the frequency for which they are designed. In this paper, designs of DDs of odd and even lengths having maximal linearity at the middle of the frequency band are presented. Applying the maximal linearity constraints to the magnitude response of a differentiator gives a system of linear equations, which can be solved for the impulse response coefficients of the differentiator. It is observed that the coefficient matrices of these equations are Vandermonde matrices, and this helps in finding the solution of the equations in closed form. Design examples are presented to show the accuracy of the presented designs, and it is observed that even-length designs are more accurate in a significantly wider frequency band as compared with odd-length designs

Two layer scheme for encoding of high dynamic range images

With advent of high dynamic range (HDR) imaging techniques, it has been possible to capture natural scenes in larger details. HDR images are tone-mapped to lower dynamic range (LDR) versions for displaying on paper or a screen. Details lost during tone-mapping are important for certain existing and future applications, and need to be preserved. However, the size of HDR images is very large and that gives rise to need of effective encoding techniques. In this paper, we present an encoding scheme for HDR images, which significantly reduces their storage requirements, with a negligible loss of information. We model an HDR image as a piecewise linear function of its tone-mapped version. The tone-mapped image and the error in modeling are stored as LDR images, and these two along with the created model, approximate the HDR image. Comparison with the existing state of the art technique is given to show the effectiveness of our proposed scheme.

A mixed reality system for virtual glasses try-on

In this paper we present an augmented reality system for automatic try-on of 3D virtual eyeglasses. The user can select from various virtual models of eyeglasses for trying-on and the system will automatically fit the selected virtual glasses on the users face. The user can see his/her face as in a mirror with the 3D virtual glasses fitted on it. We also propose a method for handling the occlusion problem, to display only those parts of the glasses that are not occluded by the face. This system can be used for online shopping, or short listing a large set of available models to a few before physical try-on at a retailers site.

Eye HDR: gaze-adaptive system for displaying high-dynamic-range images

The human visual system (HVS) uses several methods to interactively adapt to the incredible real-world range of light intensities, continually changing to effectively perceive visual information. Eye HDR is a new approach to the problem of displaying high-dynamic-range (HDR) content on low-dynamic-range displays. Instead of creating a single static image, it uses a dynamic display system to naturally, interactively adapt to the users view, just as the HVS changes depending on the environment.

Face and arm-posture recognition for secure human-machine interaction

In this paper, we present a user identification technique based on face recognition for secure human-machine interaction. Users face is matched with the faces memorized by the machine, and if a match is found with a reliable matching score, the machine gets ready to accept the commands. Gabor Wavelet Transform coefficients are used as features for matching, and they are computed on a dedicated LSI to attain high computational speed. For matching, an algorithm based on the elastic graph matching is used, and that is also implemented on hardware. We also propose an arm tracking algorithm for communication with machines using arm gesture. The algorithm utilizes stereo vision to define search regions in left and right images iteratively, and looks for the arm posture by matching with a three dimensional four degrees-of-freedom kinematics-based arm model. Tracking procedure is computationally efficient, robust to small occlusions, and works in unconstrained environment, which makes it suitable for general applications in human-machine interaction.

Virtual try-on of eyeglasses using 3D model of the head

This work presents a system for virtual try-on of eyeglasses using a 3D model of users face and head. The 3D head model is reconstructed using only one image of the user. The 3D glasses model are then fitted onto this head model, and the users head movement is tracked in real-time to rotate the 3D head model with glasses accordingly.

Flat magnitude response FIR halfband low/high pass digital filters with narrow transition bands

MAXFLAT FIR low/high pass digital filters are traditionally designed to satisfy the constraints of maximal flatness at the ends of the frequency band. In this paper, we show that by moving the points of flatness to the inner band, halfband filters with narrow transition bands can be realized. This, however, affects the smoothness of their magnitude responses at the ends of the frequency band. We propose a new design of halfband filters having their points of flatness at the middle of the pass and stop bands. The resulting filters have significantly narrow transition bands as compared to the existing MAXFLAT designs, and yet their magnitude responses are quite smooth in the entire frequency band.

HDR image tone mapping using histogram adjustment adapted to human visual system

Tone-mapping operators are used to produce low dynamic range versions of the high dynamic range images, while preserving as much details as possible. We have proposed a tone-mapping operator which is built on an existing histogram adjustment technique. It incorporates certain characteristics of the human visual system, to restrain the problem of extreme contrast enhancement of certain segments and intensive compression of others, associated with histogram equalization based techniques. Test results show significant improvement over traditional histogram adjustment. The proposed method also does quite well compared to the other state of the art tone-mapping operators.