New Variational Problems with an Action Depending on Generalized Fractional Derivatives, the Free Endpoint Conditions, and a Real Parameter

This work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize well-known results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.

Laplace Graph Embedding Class Specific Dictionary Learning for Face Recognition

The sparse representation based classification (SRC) method and collaborative representation based classification (CRC) method have attracted more and more attention in recent years due to their promising results and robustness. However, both SRC and CRC algorithms directly use the training samples as the dictionary, which leads to a large fitting error. In this paper, we propose the Laplace graph embedding class specific dictionary learning (LGECSDL) algorithm, which trains a weight matrix and embeds a Laplace graph to reconstruct the dictionary. Firstly, it can increase the dimension of the dictionary matrix, which can be used to classify the small sample database. Secondly, it gives different dictionary atoms with different weights to improve classification accuracy. Additionally, in each class dictionary training process, the LGECSDL algorithm introduces the Laplace graph embedding method to the objective function in order to keep the local structure of each class, and the proposed method is capable of improving the performance of face recognition according to the class specific dictionary learning and Laplace graph embedding regularizer. Moreover, we also extend the proposed method to an arbitrary kernel space. Extensive experimental results on several face recognition benchmark databases demonstrate the superior performance of our proposed algorithm.

A digital arbitrary size kernel convolution smart image sensor based on in-pixel pulse width processors

Purpose The purpose of this study is to propose a pulse width based, in-pixel, arbitrary size kernel convolution processor. When image sensors are used in machine vision tasks, large amount of data need to be transferred to the output and fed to a processor. Basic and low-level image processing functions such as kernel convolution is used extensively in the early stages of most machine vision tasks. These low-level functions are usually computationally extensive and if the computation is performed inside every pixel, the burden on the external processor will be greatly reduced. Design/methodology/approach In the proposed architecture, digital pulse width processing is used to perform kernel convolution on the image sensor data. With this approach, while the photocurrent fluctuations are expressed with changes in the pulse width of an output signal, the small processor incorporated in each pixel receives the output signal of the corresponding pixel and its neighbors and produces a binary coded output result for that specific pixel. The process is commenced in parallel among all pixels of the image sensor. Findings It is shown that using the proposed architecture, not only kernel convolution can be performed in the digital domain inside smart image sensors but also arbitrary kernel coefficients are obtainable simply by adjusting the sampling frequency at different phases of the processing. Originality/value Although in-pixel digital kernel convolution has been previously reported however with the presented approach no in-pixel analog to binary coded digital converter is required. Furthermore, arbitrary kernel coefficients and scaling can be deployed in the processing. The given architecture is a suitable choice for smart image sensors which are to be used in high-speed machine vision tasks.