Convolution

An adaptive two step paradigm for the super-resolution of optical images is developed in this paper. The procedure locally projects image samples onto a family of kernels that are learned from image data. First, an unsupervised feature extraction is performed on local neighborhood information from a training image. These features are then used to cluster the neighborhoods into disjoint sets for which an optimal mapping relating homologous neighborhoods across scales can be learned in a supervised manner. A superresolved image is obtained through the convolution of a low resolution test image with the established family of kernels. Results demonstrate the effectiveness of the approach.

Checking railway status is critical to guarantee high operating safety, proper maintenance schedule, and low maintenance and operating costs. This operation consists of the analysis of the rail profile and level as well as overall geometry and ondulation. Traditional detection systems are based on mechanical devices in contact with the track. Innovative approaches are based on laser scanning and image analysis. This paper presents an efficient composite technique for track profile extraction with real-time image processing. High throughput is obtained by algorithmic prefiltering to restrict the image area containing the track profile, while high accuracy is achieved by neural reconstruction of the profile itself.

In radionuclide therapy, absorbed dose is calculated by convolution of a three-dimensional activity matrix with a three-dimensional dose point kernel. A technique employing the fast Hartley Transform (FHT) has been developed to perform this calculation. An important part of that development was the indexing scheme for 3D data. The results of this new FHT convolution technique were compared to direct convolution. A cube was convolved with itself by these two techniques. The results differed by less than 2 percent. In an effort to show the practical applicability of 3D convolution, a three-dimensional activity matrix from a I-131-labeled 16.88 monoclonal antibody patient was convolved with beta and photon dose point kernels using direct convolution. Isodose contours were then generated from the calculated absorbed dose matrix and overlaid on a CT image of the patient

The growth of the brain of human embryo is changing through a long time in the body of mother. So it is very difficult to observe and to understand that process. Therefore, the embryologists found the realistic human organ models and animations necessary for their studies. But to create the realistic human embryo brain models and to do the animations it requires an appropriate methodology. The aim of this paper is to present a developing methodology based on the functional representation and the convolution of the surfaces . We employed this to create a growth simulation of the human embryo brain. The idea of this technique is the following. As a first step the 2D central skeleton is created from an artistic drawing and then the 3D skeleton is modeled by adding the thickness. As the next step, the skeletons representing key-frame models are used to create an animation. At the end the gap between the key-frame models is filled by the suitable interpolation techniques and finally the animation is composed.

After collecting a data base of fingerprint images, we design a neural network algorithm for fingerprint recognition. When presented with a pair of fingerprint images, the algorithm outputs an estimate of the probability that the two images originate from the same finger. In one experiment, the neural network is trained using a few hundred pairs of images and its performance is subsequently tested using several thousand pairs of images originated from a subset of the database corresponding to 20 individuals. The error rate currently achieved is less than 0.5%. Additional results, extensions, and possible applications are also briefly discussed.

In the individual risk model, the total claims on a portfolio of insurance contracts is the random variable of interest. The total claims is modelled as the sum of all claims on the individual policies, which are assumed independent. We present several techniques, such as convolution and recursions, to obtain results in this model.

This paper studies a novel decomposition technique, suitable for blind separation of linear mixtures of signals comprising finite-length symbols. The observed symbols are first modeled as channel responses in a multiple-input-multiple-output (MIMO) model, while the channel inputs are conceptually considered sparse positive pulse trains carrying the information about the symbol arising times. Our decomposition approach compensates channel responses and aims at reconstructing the input pulse trains directly. The algorithm is derived first for the overdetermined noiseless MIMO case. A generalized scheme is then provided for the underdetermined mixtures in noisy environments. Although blind, the proposed technique approaches Bayesian optimal linear minimum mean square error estimator and is, hence, significantly noise resistant. The results of simulation tests prove it can be applied to considerably underdetermined convolutive mixtures and even to the mixtures of moderately correlated input pulse trains, with their cross-correlation up to 10% of its maximum possible value.

By making an example of the earlier proposed cyclic convolution algorithms, the computational efficiency of the multidimensional techniques over finite fields is investigated. It is shown that the multidimensional techniques are inferior to the directly designed algorithms for all lengths except when applied to lengths whose exponents are relatively prime. Relations between the complexities of the directly designed algorithms and those derived through the multidimensional techniques are also established in various cases.

Absfrucf-It is well known that the discrete Fourier transformation (DFT) of a real-valued sequence contains some redundancies. More precisely, approximately half of the DFT coefficients suffice to completely determine the DFT. In this paper, it is shown that the choice of the set of (nonredundant) DFT coefficients to be calculated affects the efficiency of the resulting algorithm. One especially interesting choice is discussed in detail for the case of mixed radix-(2, 3) DFT algorithms. Algorithms for the DFT calculation of both one and more dimensional real-valued arrays are discussed.

Convolutions of independent random variables are usually compared. In this paper, after a synthetic comparison with respect to hazard rate ordering between sums of independent exponential random variables, we focus on the special case where one sum is identically distributed. So, for a given sum of n independent exponential random variables, we deduce the "best" Erlang-n bounds, with respect to each of the usual orderings: mean ordering, stochastic ordering, hazard rate ordering and likelihood ratio ordering.

An explicit analytical formula for a short kernel fifth-order polynomial interpolator is obtained. It is also possible to obtain the explicit forms of even higher order interpolation kernels with the method of calculation used, but it is seen that these local kernels become "remainderdominated" as the order increases. The frequency domain properties and the accuracies of the obtained kernel and the known convolution kernels are compared. Frequency domain comparison with the cubic B-spline interpolators is also given. Some cases of proper use of the calculated kernels have been pointed out.

We present a hybrid neural-network for human face recognition which compares favourably with other methods. The system combines local image sampling, a self-organizing map (SOM) neural network, and a convolutional neural network. The SOM provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the Karhunen-Loeve transform in place of the SOM, and a multilayer perceptron (MLP) in place of the convolutional network for comparison. We use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression, pose, and facial details. We analyze the computational complexity and discuss how new classes could be added to the trained recognizer

In many engineering applications ranging from engineering seismology to petroleum engineering and civil engineering, it is important to process seismic data. In processing seismic data, it turns out to be very efficient to describe the signal's spectrum as a linear combination of Ricker wavelet spectra. In this paper, we provide a possible theoretical explanation for this empirical efficiency. Specifically, signal propagation through several layers is discussed, and it is shown that the Ricker wavelet is the simplest non-trivial solution for the corresponding data processing problem, under the condition that the described properties of the approximation family are satisfied.

In this paper, we present new algorithms for the calculation of convolutions by means of number theoretic transforms over modulo rings. Not only are these algorithms more efficient than currently used methods, but they are also very flexible. Indeed, using special algorithms for short convolutions allows trading computational efficiency for structural simplicity.

The normal inverse Gaussian (NIG) distribution is a recent flexible closed form distribution that may be applied as a model of heavy-tailed processes. The NIG distribution is completely specified by four real valued parameters that have natural interpretations in terms of the shape of the resulting probability density function. By choosing the parameters appropriately, one can describe a wide range of shapes of the distribution. In this paper, we discuss several of the desirable properties of the NIG distribution. In particular, we discuss the cumulant generating function and the cumulants of the NIG-variables. A particularly important property is that the NIG distribution is closed under convolution. Finally, we derive a set of very simple yet accurate estimators of the NIG parameters. Our estimators differ fundamentally from estimators suggested by other authors in that our estimators take advantage of the surprisingly simple structure of the cumulant generating function.

The time-of-arrival (TOA) estimation ofpulse signals is widely used in radar, sonar and other sensor systems for geo-locating targets. This paper presents a new estimator for the TOA and width (W) of a pulse. Three auto-convolutions of a full and partial pulse determine the location ofthree convolution peaks. These peak locations are given by linear equations that contain as unknowns TOA and W. Solving these equations yields estimates of the pulse parameters. Simulation results show the performance of the estimator in noise and are compared with results obtained using an existing estimator.

The main objective of image enhancement is to improve some characteristic of an image to make it visually better one. This paper proposes a method for enhancing the color images based on nonlinear transfer function and pixel neighborhood by preserving details. In the proposed method, the image enhancement is applied only on the V (luminance value) component of the HSV color image and H and S component are kept unchanged to prevent the degradation of color balance between HSV components. The V channel is enhanced in two steps. First the V component image is divided into smaller overlapping blocks and for each pixel inside the block the luminance enhancement is carried out using nonlinear transfer function. In the second step, each pixel is further enhanced for the adjustment of the image contrast depending upon the center pixel value and its neighborhood pixel values. Finally, original H and S component image and enhanced V component image are converted back to RGB image. The subjective and objective performance evaluation shows that the proposed enhancement method yields better results without changing image original color in comparison with the conventional methods.

Focal plane processing applications present a growing computing need for portable telecomputing and videoputing systems. This paper demonstrates the integration of digital processing, analog interface circuitry, and thin film OE devices into a compact computing package. The SIMPil architecture provides a programmable, silicon efficient SIMD processor for effective execution of early image processing applications such as edge detection, convolution, and compression. Results from a demonstration SIMPil node are presented including its microarchitecture, and performance on image processing applications.

For high fidelity sound reproduction, it is necessary to use long filter coefficients in audio crosstalk cancellation. To implement these long filters on real-time DSP processors, conventional overlap save technique suffers from more computational power as well as processing delay. To overcome these technical problems, mixed uniform partitioned convolution technique is proposed. This method is derived by combining uniform partitioned convolution with mixed filtering technique. With the proposed method, it is possible to perform audio crosstalk cancellation even at the order of ten thousand filter taps with less computations and short processing delay. The proposed technique was implemented on 32-bit floating point DSP processor and design was provided with efficient memory management to achieve optimization in computational complexity. The computational comparison of this method with conventional methods shows that the proposed technique is very efficient for long filters.

Abstract: Hand gestures recognition provides a natural way to interact and communicate with machines of different kinds. The process is known and referred to as static hand gesture recognition in which images of a hand gesture are stored in the database and analyzed in order to determine the meaning of the hand gesture. The implementation has been done using Scale Invariant Feature Transform (SIFT), Principal Component Analysis(PCA) which present an interface used to recognize  hand gestures from the American Sign Language.
Keywords:  Distance ratio, Threshold, convolution, Gaussian Filters, Eigen Vector.
Title: Analysis and Implementation of Hand Gesture Recognition System
Author:  Mrs. Poonam Verma, Utkarsh Mor, Puneet Singh, Arpan Khandelwal
International Journal of Computer Science and Information Technology Research
ISSN 2348-1196 (print), ISSN 2348-120X (online)
Research Publish Journals

In this paper, we derive a relation for the circular convolution operation in the discrete sine and cosine transform domains. The transform coefficients are either symmetric or asymmetric and hence we need to calculate only half of the total coefficients. Since fast algorithms are available for the computation of discrete sine and cosine transforms, the proposed method is an alternative to the discrete Fourier transform method for filtering applications.

Convolutional neural networks (CNNs) represent an interesting method for adaptive image processing, and form a link between general feed-forward neural networks and adaptive filters. Two-dimensional CNNs are formed by one or more layers of two-dimensional filters, with possible non-linear activation functions and/or down-sampling. Convolutional neural networks (CNNs) impose constraints on the weights and connectivity of the network, providing a framework well suited to the processing of spatially or temporally distributed data. CNNs possess key properties of translation invariance and spatially local connections (receptive fields). The so- called “weight-sharing” property of CNNs limits the number of free parameters. Although CNNs have been applied to face and character recognition, it is fair to say that the full potential of CNNs has not yet been realised. This chapter presents a description of the convolutional neural network architecture, and reports some of our work applying CNNs to theoretical and real-world image processing problems.

Structural health monitoring (SHM) and vibration-based structural damage detection have been a continuous interest for civil, mechanical and aerospace engineers over the decades. Early and meticulous damage detection has always been one of the principal objectives of SHM applications. The performance of a classical damage detection system predominantly depends on the choice of the features and the classifier. While the fixed and hand-crafted features may either be a sub-optimal choice for a particular structure or fail to achieve the same level of performance on another structure, they usually require a large computation power which may hinder their usage for real-time structural damage detection. This paper presents a novel, fast and accurate structural damage detection system using 1D Convolutional Neural Networks (CNNs) that has an inherent adaptive design to fuse both feature extraction and classification blocks into a single and compact learning body. The proposed method performs vibration-based damage detection and localization of the damage in real-time. The advantage of this approach is its ability to extract optimal damage sensitive features automatically from the raw acceleration signals. Large-scale experiments conducted on a grandstand simulator revealed an outstanding performance and verified the computational efficiency of the proposed real-time damage detection method.

موضوعات مورد مطالعه :
 کدگذاری کانال با استفاده از کدهای کانولوشنال
 شبیه سازی کانال چند مسیره با نویز گوسی سفید جمع شونده
 طراحی همسان‌ساز MLSE برای حذف اثر ISI ، به کمک الگوریتم ویتربی
 آشکارسازی کدهای کانوشنال، به کمک الگوریتم ویتربی

Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradientbased learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of two dimensional (2-D) shapes, are shown to outperform all other techniques.

Convolution reverb is the process used for reverberating a signal by an impulse response of an actual space. The product of this operation is a third signal, containing reverberation of the space where the impulse response is captured. This project is based on creating a convolution reverb plugin on MaxMSP and evaluating the perceptual quality of convolution reverb.
The real-time fast convolution reverb plugin was implemented using multiple frequency delay line non-uniform partitioned convolution method on MaxMSP. An experimental design methodology was introduced in order to evaluate the perceptual quality of convolution reverb. In order to realise, anechoic drum kit music samples were recorded and re-recorded in a chamber to form the control signal. Also, using same equipment and setup, an impulse response was captured in the same chamber to form the test sample. These samples were then used for subjective analysis in a pair-wise categorical preference type listening test. The samples were also analysed in their spectrogram views in order to analyse the quality objectively.
Listening tests were designed so that realism, quality and personal preference categories were present. Null hypothesis was proved, where the realism difference of the two samples resulted in 52% of the participants preferring chamber reverb (control signal). However personal preference category resulted in 61%of the subjects preferring the chamber reverb. This was justified by objective analysis, where the convolution reverb shown to be having a faster decay rate for high frequency bands, thus sounding unnatural.

An introduction to Dirac delta function$ and its salient properties are presented. The experience of having taught  subjects in physics such as quantum mechanics, electromagnetism, optics, mathematical physics for the past three decades, the presentation in this communication is distinct and different. Many situations wherein Dirac delta function plays important roles are listed and discussed. It is hoped that this pedagogical paper will help the beginners to understand and appreciate this important singular function.
$ P. A. M. Dirac, “The Principles of Quantum mechanics”, Oxford Science Publications, 1970.

All physical subjects, involving random phenomena, something depending upon chance, naturally find their own way to theory of Statistics. Hence there arise relations between the results derived for hose random phenomena in different physical subjects and the concepts of Statistics. Convolution theorem has a variety of applications in field of Fourier transforms and many other situations, but it bears beautiful applications in field of statistics also .Here in this paper authors want to discuss some notions of Electrical Engineering in terms of convolution of some probability distributions.

La convolución es una operación fundamental en procesamiento de señales por su estrecha relación con los procesos de transmisión de las señales, filtrada, entre otros, cuando se trabaja en el dominio temporal. Se denomina convolución a una función, que de forma lineal y continua, transforma una señal de entrada en una nueva señal de salida. La función de convolución se expresa por el símbolo *

Face recognition is an emergent research area, spans over multiple disciplines such
as image processing, computer vision and signal processing, machine learning. Face
recognition is mainly used for identity authentication/identification, security access
control and intelligent human-computer interaction.
This work compares holistic and hybrid face recognition methods. The hybrid face
feature extraction in which local features were derived using Multi Scale Block Local
Binary Patterns (MB-LBP) and global features are derived using Principal Component
Analysis (PCA). For a facial image a spatially enhanced, concatenated representation
is obtained by deriving a histogram from each grid that an input image
is divided. These histograms were projected to lower dimensions by applying PCA
to create eigenfaces. The holistic face representation of a subject was derived by
projecting several images of the subject into lower dimensions applying PCA.
There are several parameters affect the performance of local descriptor based face
recognition system viz: image size, grid size, operator scale and available codes. Impact
of these parameters on performance of FRS are not explored much in literature.
This thesis aims to study empirically the effect of these parameters for FRS configured
in verification mode.

Absfrucf-Cubic convolution interpolation is a new technique for resampling discrete data. It has a number of desirable features which make it useful for image processing. The technique can be performed efficiently on a digital computer. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero, With the appropriate boundary conditions and constraints on the interpolation kernel, it can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines.

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature.

We propose a 16-bit non-pipelined RISC processor, which is used for signal processing applications. The processor consists of the blocks, namely, program counter, clock Control unit, ALU, IDU and registers. Advantageous architectural modifications have been made in the incrementer circuit used in program counter and carry select adder unit of the ALU in the RISC CPU core. Furthermore, a high speed and low power modified Wallace tree multiplier has been designed and introduced in the design of ALU. The RISC processor has been designed for executing 27-instruction set. Convolution is an important signal processing application which is used in filter design. Many algorithms have been proposed in order to achieve an optimized performance of the filters by optimizing the convolution design. Modified Winograd algorithm is notable among them. They require 4 multiplication operations only, when compared to 6 for a 3*2 normal convolution methodology with an additional rise in the number of adders to 9 from 4.

Necessary and sufficient conditions for a direct sum of local rings to support a generalized discrete Fourier transform are derived. In particular, these conditions can be appled to any finite ring. Tle function O(N) defined by Agarwal and Burrus for transforms over ZN is extended to any finite ring R as O(R)and it isshown that R supports a length m discrete Fourier transform if and only if m is a divisor of O(R) Tlhis result is applied to the homomorphic images of rings-of algebraic integers

"Kubla Khan" and "This Lime-Tree Bower My Prison" are constructed on utterly different schemes, though they share some of the same underlying components. "Kubla Khan" is ontological and impersonal in character and makes extensive use of convolution in calculating meanings. It reveals the structure of being. "Lime-Tree Bower" is narrative and personal and makes little or no use of convolution. It reveals the unfolding of subjectivity in time. The two poems also differ in their versification, a differences which is related to their different strategies of meaning.

With the advent of inventions of laser and fiber optics, communication through fiber optics with laser light and the modes of propagation of pulses in different types of channels receive considerable attention. In this context, a study of free propagation of Gaussian beam issuing from a Helium-Neon laser or semiconductor laser becomes important. A similar situation arises in quantum mechanics: free propagation of Gaussian wave packet. Both have same mathematical structure. Propagation distance of a Gaussian beam and propagation time of a Gaussian wave packet are analogous. In this brief communication, a simple and elegant approach, based on Convolution Theorem in Fourier transform, is presented to derive the width and radius of curvature of the Gaussian beam.

It is a common practice in the development of point focus solar concentrators to use multiple identical reflecting facets, as a practical and economic alternative for the design and construction of large systems. This kind of systems behaves in a different manner than continuous paraboloidal concentrators. A theoretical study is carried out to understand the effect of the size of facets and of their optical errors in multiple facet point focus solar concentrating systems. For this purpose, a ray tracing program was developed based on the convolution technique, in which the brightness distribution of the sun and the optical errors of the reflecting surfaces are considered. The study shows that both the peak of concentration and the optimal focal distance of the system strongly depend on the size of the facets, and on their optical errors. These results are useful to help concentrator developers to have a better understanding of the relationship between manufacturing design restrictions and final optical behavior.

Research in human action recognition has accelerated significantly since the introduction of powerful machine learning tools such as Convolutional Neural Networks (CNNs). However, effective and efficient methods for incorporation of temporal information into CNNs are still being actively explored in the recent literature. Motivated by the popular recurrent attention models in the research area of natural language processing, we propose the Attention-aware Temporal Weighted CNN (ATW CNN) for action recognition in videos, which embeds a visual attention model into a temporal weighted multi-stream CNN. This attention model is simply implemented as temporal weighting yet it effectively boosts the recognition performance of video representations. Besides, each stream in the proposed ATW CNN framework is capable of end-to-end training, with both network parameters and temporal weights optimized by stochastic gradient descent (SGD) with back-propagation. Our experimental results on the UCF-101 and HMDB-51 datasets showed that the proposed attention mechanism contributes substantially to the performance gains with the more discriminative snippets by focusing on more relevant video segments.

In image processing one of significant perspective is the image compression. It is concerned in reducing the quantity of fundamental element to represent of an image. An immense memory and high data transfer capacity are required for transmission of pictures continuously. Hereafter to build the organization capacities of winning organizations in a successful way and furthermore to make the interest for capacity to an economical level, image compression gives a quick solution for this arrangement. In this proposed work, an effective discrete wavelet transform (DWT) is designed for compression of image by utilizing fundamental cell strategy and a streamlined controller pathway laterally with a capable design architecture is suggested. The architecture design is thought by reasonably interconnecting the units and is realized in Verilog HDL. The task complier is been utilized to synthesize and confirm the design functional practically by utilizing the EDA tool. The result of the approach shows decline in power use, repetition in memory utilization, high-throughput and less latency contrasted with other existing techniques.