We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered "non serious", a cutting plane is added and a new search direction is computed. This procedure is repeated until a "serious" step is obtained. When this happens, the search direction is a feasible descent direction of the constrained equivalent problem. The search directions are computed with FDIPA, the Feasible Directions Interior Point Algorithm. We prove global convergence and solve several test problems very efficiently.
Abstract. We propose a method for the assessment and visualization of high frequency regions of a multiresolution image. We combine both orientation tensor and multiresolution analysis to give a scalar descriptor of high frequency regions. High values of this scalar space indicate regions having coincident detail vectors in multiple scales of a wavelet decomposition. This is useful for finding edges, textures, collinear structures and salient regions for computer vision methods. The image is decomposed into several scales using the Discrete Wavelet Transform (DWT). The resulting detail spaces form vectors indicating intensity variations which are combined using orientation tensors. A high frequency scalar descriptor is then obtained from the resulting tensor for each original image pixel. Our results show that this descriptor indicates areas having relevant intensity variation in multiple scales.
Salient object detection plays a vital role in image processing applications like image retrieval, security and surveillance in authentic-time. In recent times, advances in deep neural network gained more attention in the automatic learning system for various computer vision applications. In order to decrement the detection error for efficacious object detection, we proposed a detection classifier to detect the features of the object utilizing a deep neural network called convolutional neural network (CNN) and discrete quaternion Fourier transform (DQFT). Prior to CNN, the image is pre-processed by DQFT in order to handle all the three colors holistically to evade loss of image information, which in-turn increase the effective use of object detection. The features of the image are learned by training model of CNN, where the CNN process is done in the Fourier domain to quicken the method in productive computational time, and the image is converted to spatial domain before processing the fully connected layer. The proposed model is implemented in the HDA and INRIA benchmark datasets. The outcome shows that convolution in the quaternion Fourier domain expedite the process of evaluation with amended detection rate. The comparative study is done with CNN, discrete Fourier transforms CNN, RNN ad masked RNN.
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