scholarly journals Reconstruction Error Analysis of Skin Lesion Images using Orthogonal Moments

2019 ◽  
Vol 8 (4) ◽  
pp. 10910-10915
Keyword(s):  
Image Reconstruction ◽  
Skin Lesion ◽  
Error Analysis ◽  
Scale Invariance ◽  
Reconstruction Error ◽  
Zernike Moments ◽  
Shape Descriptors ◽  
Orthogonal Moments ◽  
Precise Calculation ◽  
The Impact

Orthogonal moments (OMs) are amongst the superlative region centered shape descriptors. These OMs retain lowest facts redundancy. Zernike Moments (ZM) and pseudo Zernike Moments (PZM) are tested with respect to rotation invariance, and scale invariance for skin lesion images. Image reconstruction is executed for various orders of two different orthogonal moments; ZM and PZM. Reconstruction errors are also computed. This paper examines the impact of these errors on the features of OMs and executes a relative study of these errors on the precise calculation of the two major OMs: ZMs and PZMs.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

scholarly journals Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Neural Network ◽  
Maximum Likelihood ◽  
Image Reconstruction ◽  
Image Recognition ◽  
Shannon Entropy ◽  
Reconstruction Error ◽  
Likelihood Method ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
D Wave

AbstractRestricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter ($$\beta $$ β ) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

scholarly journals Gradient Projection with Approximate L0 Norm Minimization for Sparse Reconstruction in Compressed Sensing

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3373 ◽  
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yongmei Huang ◽  
Yong Liu ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Objective Function ◽  
Signal Reconstruction ◽  
Reconstruction Error ◽  
Sparse Signal ◽  
Reconstruction Accuracy ◽  
L1 Norm ◽  
Function Model ◽  
L2 Norm

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L1 norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L0 norm algorithm. However, because the L0 norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L0 norm from the approximate L2 norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L2 norm and the L1 norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.

scholarly journals Simulation of the Operation of a Single Pixel Camera with Compressive Sensing in the Long-Wave Infrared

2021 ◽  
Vol 25 (2) ◽  
pp. 53-60
Author(s):  
Anna Szajewska
Keyword(s):  
Case Analysis ◽  
Calibration Method ◽  
Reconstruction Error ◽  
Infrared Observation ◽  
Long Wave ◽  
Reference Images ◽  
The Impact ◽  
Long Wave Infrared ◽  
Single Pixel

Imaging with the use of a single pixel camera and based on compressed sensing (CS) is a new and promising technology. The use of CS allows reconstruction of images in various spectrum ranges depending on the spectrum sensibility of the used detector. During the study image reconstruction was performed in the LWIR range based on a thermogram from a simulated single pixel camera. For needs of reconstruction CS was used. A case analysis showed that the CS method may be used for construction of infrared-based observation single pixel cameras. This solution may also be applied in measuring cameras. Yet the execution of a measurement of radiation temperature requires calibration of results obtained by CS reconstruction. In the study a calibration method of the infrared observation camera was proposed and studies were carried out of the impact exerted by the number of measurements made on the quality of reconstruction. Reconstructed thermograms were compared with reference images of infrared radiation. It has been ascertained that the reduction of the reconstruction error is not directly in proportion to the number of collected samples being collected. Based on a review of individual cases it has been ascertained that apart from the number of collected samples, an important factor that affects the reconstruction fidelity is the structure of the image as such. It has been proven that estimation of the error for reconstructed thermograms may not be based solely on the quantity of executed measurements.

Wavefront Reconstruction Error Analysis Method for Diffraction Optical System

2019 ◽  
Vol 39 (11) ◽  
pp. 1105002
Author(s):  
乔凯 Qiao Kai ◽  
智喜洋 Zhi Xiyang ◽  
杨冬 Yang Dong ◽  
于頔 Yu Di ◽  
王达伟 Wang Dawei
Keyword(s):  
Error Analysis ◽  
Optical System ◽  
Reconstruction Error ◽  
Analysis Method ◽  
Wavefront Reconstruction

scholarly journals Bivariate Hahn moments for image reconstruction

2014 ◽  
Vol 24 (2) ◽  
pp. 417-428 ◽  
Author(s):  
Haiyong Wu ◽  
Senlin Yan
Keyword(s):  
Image Reconstruction ◽  
Numerical Stability ◽  
Parameter Selection ◽  
Experimental Results ◽  
Grayscale Image ◽  
Orthogonal Moments ◽  
Binary Images ◽  
Hahn Polynomials ◽  
Discrete Orthogonal ◽  
Computational Aspects

Abstract This paper presents a new set of bivariate discrete orthogonal moments which are based on bivariate Hahn polynomials with non-separable basis. The polynomials are scaled to ensure numerical stability. Their computational aspects are discussed in detail. The principle of parameter selection is established by analyzing several plots of polynomials with different kinds of parameters. Appropriate parameters of binary images and a grayscale image are obtained through experimental results. The performance of the proposed moments in describing images is investigated through several image reconstruction experiments, including noisy and noise-free conditions. Comparisons with existing discrete orthogonal moments are also presented. The experimental results show that the proposed moments outperform slightly separable Hahn moments for higher orders.

scholarly journals Image reconstruction from limited range projections using orthogonal moments

2007 ◽  
Vol 40 (2) ◽  
pp. 670-680 ◽  
Author(s):  
H.Z. Shu ◽  
J. Zhou ◽  
G.N. Han ◽  
L.M. Luo ◽  
J.L. Coatrieux
Keyword(s):  
Image Reconstruction ◽  
Limited Range ◽  
Orthogonal Moments
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