scholarly journals Motion Invariance in Visual Environments

2019 ◽  
Author(s):  
Alessandro Betti ◽  
Marco Gori ◽  
Stefano Melacci
Keyword(s):  
Computer Vision ◽  
Differential Equations ◽  
Invariance Principle ◽  
Visual Learning ◽  
Feature Learning ◽  
Video Signals ◽  
Convolutional Networks ◽  
Natural Vision ◽  
Cognitive Action ◽  
Well Posed

The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams, just as it happens in nature. In this paper, we claim that the processing of a stream of frames naturally leads to formulate the motion invariance principle, which enables the construction of a new theory of visual learning based on convolutional features. The theory addresses a number of intriguing questions that arise in natural vision, and offers a well-posed computational scheme for the discovery of convolutional filters over the retina. They are driven by the Euler- Lagrange differential equations derived from the principle of least cognitive action, that parallels the laws of mechanics. Unlike traditional convolutional networks, which need massive supervision, the proposed theory offers a truly new scenario in which feature learning takes place by unsupervised processing of video signals. An experimental report of the theory is presented where we show that features extracted under motion invariance yield an improvement that can be assessed by measuring information-based indexes.

scholarly journals Going Deep into Remote Sensing Spatial Feature Learning

2020 ◽  
Author(s):  
Keiller Nogueira ◽  
William Robson Schwartz ◽  
Jefersson Alex Dos Santos
Keyword(s):  
Remote Sensing ◽  
Deep Learning ◽  
Feature Learning ◽  
Aerial Images ◽  
Morphological Operations ◽  
Pixel Classification ◽  
Specific Data ◽  
Convolutional Networks ◽  
Spatial Features ◽  
New Strategy

A lot of information may be extracted from the Earth’s surface through aerial images. This information may assist in myriad applications, such as urban planning, crop and forest management, disaster relief, etc. However, the process of distilling this information is strongly based on efficiently encoding the spatial features, a challenging task. Facing this, Deep Learning is able to learn specific data-driven features. This PhD thesis1 introduces deep learning into the remote sensing domain. Specifically, we tackled two main tasks, scene and pixel classification, using Deep Learning to encode spatial features over high-resolution remote sensing images. First, we proposed an architecture and analyze different strategies to exploit Convolutional Networks for image classification. Second, we introduced a network and proposed a new strategy to better exploit multi-context information in order to improve pixelwise classification. Finally, we proposed a new network based on morphological operations towards better learning of some relevant visual features.

scholarly journals Nonlinear Manifold Learning Integrated with Fully Convolutional Networks for PolSAR Image Classification

2020 ◽  
Vol 12 (4) ◽  
pp. 655
Author(s):  
Chu He ◽  
Mingxia Tu ◽  
Dehui Xiong ◽  
Mingsheng Liao
Keyword(s):  
Image Classification ◽  
Manifold Learning ◽  
Feature Learning ◽  
Learning Ability ◽  
High Dimensional ◽  
Compact Representation ◽  
Deep Network ◽  
Convolutional Networks ◽  
Fully Convolutional Networks ◽  
Spatial Features

Synthetic Aperture Rradar (SAR) provides rich ground information for remote sensing survey and can be used all time and in all weather conditions. Polarimetric SAR (PolSAR) can further reveal surface scattering difference and improve radar’s application ability. Most existing classification methods for PolSAR imagery are based on manual features, such methods with fixed pattern has poor data adaptability and low feature utilization, if directly input to the classifier. Therefore, combining PolSAR data characteristics and deep network with auto-feature learning ability forms a new breakthrough direction. In fact, feature learning of deep network is to realize function approximation from data to label, through multi-layer accumulation, but finite layers limit the network’s mapping ability. According to manifold hypothesis, high-dimensional data exists in potential low-dimensional manifold and different types of data locates in different manifolds. Manifold learning can model core variables of the target, and separate different data’s manifold as much as possible, so as to complete data classification better. Therefore, taking manifold hypothesis as a starting point, nonlinear manifold learning integrated with fully convolutional networks for PolSAR image classification method is proposed in this paper. Firstly, high-dimensional polarized features are extracted based on scattering matrix and coherence matrix of original PolSAR data, whose compact representation is mined by manifold learning. Meanwhile, drawing on transfer learning, pre-trained Fully Convolutional Networks (FCN) model is utilized to learn deep spatial features of PolSAR imagery. Considering complementary advantages, weighted strategy is adopted to embed manifold representation into deep spatial features, which are input into support vector machine (SVM) classifier for final classification. A series of experiments on three PolSAR datasets have verified effectiveness and superiority of the proposed classification algorithm.

scholarly journals Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Esmael Samei ◽  
Ahmad Ahmadi ◽  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Schauder Fixed Point Theorem ◽  
Stability Of Solution ◽  
The Stability ◽  
Well Posed ◽  
Schauder Fixed Point ◽  
Schäuder Fixed Point Theorem

AbstractIn this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

scholarly journals Boundary-value problems in a layer for evolutionary pseudo-differential equations with integral conditions

2018 ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Well Posedness ◽  
Integral Conditions ◽  
Pseudo Differential Equation ◽  
Necessary And Sufficient ◽  
Well Posed

Boundary-value problems for evolutionary pseudo-differential equations with an integral condition are studied. Necessary and sufficient conditions of well-posedness are obtained for these problems in the Schwartz spaces. Existence of a well-posed boundary-value problem is proved for each evolutionary pseudo-differential equation.

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