One‐to‐one non‐linear transformation for RSS‐based localization with unknown transmit power

Perceptron Architecture Ensuring Pattern Description CompactnessThis paper examines conditions a neural network has to meet in order to ensure the formation of a space of features satisfying the compactness hypothesis. The formulation of compactness hypothesis is defined in more detail as applied to neural networks. It is shown that despite the fact that the first layer of connections is formed randomly, the presence of more than 30 elements in the middle network layer guarantees a 100% probability that the G-matrix of the perceptron will not be special. It means that under additional mathematical calculations made by Rosenblatt, the perceptron will with guaranty form a space of features that could be then linearly divided. Indeed, Cover's theorem only says that separation probability increases when the initial space is transformed into a higher dimensional space in the non-linear case. It however does not point when this probability is 100%. In the Rosenblatt's perceptron, the non-linear transformation is carried out in the first layer which is generated randomly. The paper provides practical conditions under which the probability is very close to 100%. For comparison, in the Rumelhart's multilayer perceptron this kind of analysis is not performed.

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Improved Piecewise Linear Transformation for Precise Warping of Very-High-Resolution Remote Sensing Images

Remote Sensing ◽

10.3390/rs11192235 ◽

2019 ◽

Vol 11 (19) ◽

pp. 2235 ◽

Cited By ~ 5

Author(s):

Han ◽

Kim ◽

Yeom

Keyword(s):

Remote Sensing ◽

High Resolution ◽

Linear Transformation ◽

Affine Transformation ◽

Piecewise Linear ◽

Transformation Model ◽

Reference Image ◽

Remote Sensing Images ◽

Non Linear ◽

Very High

A large number of evenly distributed conjugate points (CPs) in entirely overlapping regions of the images are required to achieve successful co-registration between very-high-resolution (VHR) remote sensing images. The CPs are then used to construct a non-linear transformation model that locally warps a sensed image to a reference image’s coordinates. Piecewise linear (PL) transformation is largely exploited for warping VHR images because of its superior performance as compared to the other methods. The PL transformation constructs triangular regions on a sensed image from the CPs by applying the Delaunay algorithm, after which the corresponding triangular regions in a reference image are constructed using the same CPs on the image. Each corresponding region in the sensed image is then locally warped to the regions of the reference image through an affine transformation estimated from the CPs on the triangle vertices. The warping performance of the PL transformation shows reliable results, particularly in regions inside the triangles, i.e., within the convex hulls. However, the regions outside the triangles, which are warped when the extrapolated boundary planes are extended using CPs located close to the regions, incur severe geometric distortion. In this study, we propose an effective approach that focuses on the improvement of the warping performance of the PL transformation over the external area of the triangles. Accordingly, the proposed improved piecewise linear (IPL) transformation uses additional pseudo-CPs intentionally extracted from positions on the boundary of the sensed image. The corresponding pseudo-CPs on the reference image are determined by estimating the affine transformation from CPs located close to the pseudo-CPs. The latter are simultaneously used with the former to construct the triangular regions, which are enlarged accordingly. Experiments on both simulated and real datasets, constructed from Worldview-3 and Kompsat-3A satellite images, were conducted to validate the effectiveness of the proposed IPL transformation. That transformation was shown to outperform the existing linear/non-linear transformation models such as an affine, third and fourth polynomials, local weighted mean, and PL. Moreover, we demonstrated that the IPL transformation improved the warping performance over the PL transformation outside the triangular regions by increasing the correlation coefficient values from 0.259 to 0.304, 0.603 to 0.657, and 0.180 to 0.338 in the first, second, and third real datasets, respectively.

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Comparison of non-linear palette usage for gamma-ray tomography imaging

Image Processing & Communications ◽

10.2478/v10248-012-0086-z ◽

2013 ◽

Vol 18 (2-3) ◽

pp. 119-125

Author(s):

Jan Budzisz ◽

Volodymyr Mosorov ◽

Sebastian Biedron

Keyword(s):

Least Squares ◽

Density Gradient ◽

Cross Section ◽

Linear Transformation ◽

Gamma Ray ◽

Correct Interpretation ◽

Tomography Imaging ◽

Non Invasive ◽

Non Linear ◽

Section Structure

Abstract Gamma-ray tomography is used for non-invasive studying of objects. To enable correct interpretation of such measurements, they need to be presented in analysis-friendly way. One method is to use ILST (Iterative Least Squares Technique) algorithm to visualize 1D detector data on a 2D grid, so that gammaray attenuation is visible with a resemblance to cross-section structure. However algorithm imperfections and thresholding do not always allow inferring shapes of the structure correctly. To remedy this, the analyses of the whole range of reconstructed values are to be used with a non-linear transformation function to visualize and emphasize density gradient.

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