Browsing by Subject "Projections onto convex sets"

Now showing 1 - 9 of 9

Open Access
Entropi fonsiyonuna dayalı uyarlanır karar tümleştirme yapısı
(2012-04) Günay, Osman; Töreyin, B. U.; Köse, Kıvanç; Çetin, A. Enis
Bu bildiride, resim analizi ve bilgisayarla görü uygulamalarında kullanılmak üzere entropi fonksiyonuna dayanan uyarlanır karar tümleştirme yapısı geliştirilmiştir. Bu yapıda bileşik algoritma, herbiri güven derecesini temsil eden sıfır merkezli bir gerçek sayı olarak kendi kararını oluşturan birçok alt algoritmadan meydana gelir. Karar değerleri, çevrimiçi olarak alt algoritmaları tanımlayan dışbukey kümelerin üzerine entropik izdüşümler yapmaya dayalı bir aktif tümleştirme yöntemi ile güncellenen ağırlıklar kullanılarak doğrusal olarak birleştirilir. Bu yapıda genelde bir insan olan bir uzman da bulunur ve karar tümleştirme algoritmasına geribesleme sağlar. Önerilen karar tümleştirme algoritmasının performansı geliştirdigimiz video tabanlı bir orman yangını bulma sistemi kullanılarak test edilmiştir.
Open Access
Entropy-functional-based online adaptive decision fusion framework with application to wildfire detection in video
(IEEE, 2012-01-09) Gunay, O.; Toreyin, B. U.; Kose, K.; Çetin, A. Enis
In this paper, an entropy-functional-based online adaptive decision fusion (EADF) framework is developed for image analysis and computer vision applications. In this framework, it is assumed that the compound algorithm consists of several subalgorithms, each of which yields its own decision as a real number centered around zero, representing the confidence level of that particular subalgorithm. Decision values are linearly combined with weights that are updated online according to an active fusion method based on performing entropic projections onto convex sets describing subalgorithms. It is assumed that there is an oracle, who is usually a human operator, providing feedback to the decision fusion method. A video-based wildfire detection system was developed to evaluate the performance of the decision fusion algorithm. In this case, image data arrive sequentially, and the oracle is the security guard of the forest lookout tower, verifying the decision of the combined algorithm. The simulation results are presented.
Open Access
Equiripple FIR filter design by the FFT algorithm
(Institute of Electrical and Electronics Engineers, 1997-03) Çetin, A. Enis; Gerek, Ö. N.; Yardımcı, Y.
The fast Fourier transform (FFT) algorithm has been used in a variety of applications in signal and image processing. In this article, a simple procedure for designing finite-extent impulse response (FIR) discrete-time filters using the FFT algorithm is described. The zero-phase (or linear phase) FIR filter design problem is formulated to alternately satisfy the frequency domain constraints on the magnitude response bounds and time domain constraints on the impulse response support. The design scheme is iterative in which each iteration requires two FFT computations. The resultant filter is an equiripple approximation to the desired frequency response. The main advantage of the FFT-based design method is its implementational simplicity and versatility. Furthermore, the way the algorithm works is intuitive and any additional constraint can be incorporated in the iterations, as long as the convexity property of the overall operations is preserved. In one-dimensional cases, the most widely used equiripple FIR filter design algorithm is the Parks-McClellan algorithm (1972). This algorithm is based on linear programming, and it is computationally efficient. However, it cannot be generalized to higher dimensions. Extension of our design method to higher dimensions is straightforward. In this case two multidimensional FFT computations are needed in each iteration.
Open Access
Filtered Variation method for denoising and sparse signal processing
(IEEE, 2012) Köse, Kıvanç; Cevher V.; Çetin, A. Enis
We propose a new framework, called Filtered Variation (FV), for denoising and sparse signal processing applications. These problems are inherently ill-posed. Hence, we provide regularization to overcome this challenge by using discrete time filters that are widely used in signal processing. We mathematically define the FV problem, and solve it using alternating projections in space and transform domains. We provide a globally convergent algorithm based on the projections onto convex sets approach. We apply to our algorithm to real denoising problems and compare it with the total variation recovery. © 2012 IEEE.
Open Access
Projections onto convex sets (POCS) based optimization by lifting
(IEEE, 2013) Çetin, A. Enis; Bozkurt, Alican; Günay, Osman; Habiboglu, Yusuf Hakan; Köse, K.; Onaran, İbrahim; Tofighi, Mohammad; Sevimli, Rasim Akın
A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.
Open Access
Pulse shape design using iterative projections
(IEEE, 2005-09) Güven, H. Emre; Çetin, A. Enis
In this paper, the pulse shape design for various communication systems including PAM, FSK, and PSK is considered. The pulse is designed by imposing constraints on the time and frequency domains constraints on the autocorrelation function of the pulse shape. Intersymbol interference, finite duration and spectral mask restrictions are a few examples leading to convex sets in L 2. The autocorrelation function of the pulse is obtained by performing iterative projections onto convex sets. After this step, the minimum phase or maximum phase pulse producing the autocorrelation function is obtained by cepstral deconvolution.
Open Access
Signal recovery from partial fractional fourier domain information and pulse shape design using iterative projections
(2005) Güven, H. Emre
Signal design and recovery problems come up in a wide variety of applications in signal processing. In this thesis, we first investigate the problem of pulse shape design for use in communication settings with matched filtering where the rate of communication, intersymbol interference, and bandwidth of the signal constitute conflicting themes. In order to design pulse shapes that satisfy certain criteria such as bit rate, spectral characteristics, and worst case degradation due to intersymbol interference, we benefit from the wellknown Projections Onto Convex Sets. Secondly, we investigate the problem of signal recovery from partial information in fractional Fourier domains. Fractional Fourier transform is a mathematical generalization of the ordinary Fourier transform, the latter being a special case of the first. Here, we assume that low resolution or partial information in different fractional Fourier transform domains is available in different intervals. These information intervals define convex sets and can be combined within the Projections Onto Convex Sets framework. We present generic scenarios and simulation examples in order to illustrate the use of the method.
Open Access
Three-dimensional motion and dense-structure estimation using convex projections
(SPIE, 1997-02) Alatan, A. Aydın; Erdem, A. Tanju; Onural, Levent
We propose a novel method for estimating the 3D motion and dense structure of an object form its two 2D images. The proposed method is an iterative algorithm based on the theory of projections onto convex sets (POCS) that involves successive projections onto closed convex constraint sets. We seek a solution for the 3D motion and structure information that satisfies the following constraints: (i) rigid motion - the 3D motion parameters are the same for each point on the object. (ii) Smoothness of the structure - depth values of the neighboring points on the object vary smoothly. (iii) Temporal correspondence - the intensities in the given 2D images match under the 3D motion and structure parameters. We mathematically derive the projection operators onto these sets and discuss the convergence properties of successive projections. Experimental results show that the proposed method significantly improves the initial motion and structure estimates.
Open Access
Video processing algorithms for wildfire surveillance
(2015-05) Günay, Osman
We propose various image and video processing algorithms for wild re surveillance. The proposed methods include; classi er fusion, online learning, real-time feature extraction, image registration and optimization. We develop an entropy functional based online classi er fusion framework. We use Bregman divergences as the distance measure of the projection operator onto the hyperplanes describing the output decisions of classi ers. We test the performance of the proposed system in a wild re detection application with stationary cameras that scan prede ned preset positions. In the second part of this thesis, we investigate di erent formulations and mixture applications for passive-aggressive online learning algorithms. We propose a classi er fusion method that can be used to increase the performance of multiple online learners or the same learners trained with di erent update parameters. We also introduce an aerial wild re detection system to test the real-time performance of the analyzed algorithms. In the third part of the thesis we propose a real-time dynamic texture recognition method using random hyperplanes and deep neural networks. We divide dynamic texture videos into spatio-temporal blocks and extract features using local binary patterns (LBP). We reduce the computational cost of the exhaustive LBP method by using randomly sampled subset of pixels in the block. We use random hyperplanes and deep neural networks to reduce the dimensionality of the nal feature vectors. We test the performance of the proposed method in a dynamic texture database. We also propose an application of the proposed method in real-time detection of ames in infrared videos. Using the same features we also propose a fast wild re detection system using pan-tilt-zoom cameras and panoramic background subtraction. We use a hybrid method consisting of speeded-up robust features and mutual information to register consecutive images and form the panorama. The next step for multi-modal surveillance applications is the registration of images obtained with di erent devices. We propose a multi-modal image registration algorithm for infrared and visible range cameras. A new similarity measure is described using log-polar transform and mutual information to recover rotation and scale parameters. Another similarity measure is introduced using mutual information and redundant wavelet transform to estimate translation parameters. The new cost function for translation parameters is minimized using a novel lifted projections onto convex sets method.