On Frequency Matching and the Explicit Calculation of Prior Probabilities from Training Images

2011 ◽  
Author(s):  
Klaus MOSEGAARD
Keyword(s):  
Explicit Calculation ◽  
Prior Probabilities ◽  
Frequency Matching ◽  
Training Images

scholarly journals A Frequency Matching Method for Generation of a Priori Sample Models from Training Images

2011 ◽  
Author(s):  
Katrine LANGE ◽  
Knud Skou CORDUA ◽  
Jan FRYDENDALL ◽  
Thomas Mejer HANSEN ◽  
Klaus MOSEGAARD
Keyword(s):  
A Priori ◽  
Matching Method ◽  
Frequency Matching ◽  
Training Images

CNN performance dependence on linear image processing

2020 ◽  
Vol 2020 (10) ◽  
pp. 310-1-310-7
Author(s):  
Khalid Omer ◽  
Luca Caucci ◽  
Meredith Kupinski
Keyword(s):  
Image Processing ◽  
Texture Classification ◽  
Full Rank ◽  
Detection Performance ◽  
Ideal Observer ◽  
Training Data ◽  
Image Texture ◽  
Training Images ◽  
Analytic Expressions ◽  
Linear Compression

This work reports on convolutional neural network (CNN) performance on an image texture classification task as a function of linear image processing and number of training images. Detection performance of single and multi-layer CNNs (sCNN/mCNN) are compared to optimal observers. Performance is quantified by the area under the receiver operating characteristic (ROC) curve, also known as the AUC. For perfect detection AUC = 1.0 and AUC = 0.5 for guessing. The Ideal Observer (IO) maximizes AUC but is prohibitive in practice because it depends on high-dimensional image likelihoods. The IO performance is invariant to any fullrank, invertible linear image processing. This work demonstrates the existence of full-rank, invertible linear transforms that can degrade both sCNN and mCNN even in the limit of large quantities of training data. A subsequent invertible linear transform changes the images’ correlation structure again and can improve this AUC. Stationary textures sampled from zero mean and unequal covariance Gaussian distributions allow closed-form analytic expressions for the IO and optimal linear compression. Linear compression is a mitigation technique for high-dimension low sample size (HDLSS) applications. By definition, compression strictly decreases or maintains IO detection performance. For small quantities of training data, linear image compression prior to the sCNN architecture can increase AUC from 0.56 to 0.93. Results indicate an optimal compression ratio for CNN based on task difficulty, compression method, and number of training images.

scholarly journals Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

scholarly journals Cotton Stand Counting from Unmanned Aerial System Imagery Using MobileNet and CenterNet Deep Learning Models

2021 ◽  
Vol 13 (14) ◽  
pp. 2822
Author(s):  
Zhe Lin ◽  
Wenxuan Guo
Keyword(s):  
Deep Learning ◽  
Cotton Plant ◽  
Unmanned Aerial System ◽  
Learning Models ◽  
Training Images ◽  
Testing Dataset ◽  
Cotton Plants ◽  
Detection And Counting ◽  
Different Dimensions ◽  
The Mean

An accurate stand count is a prerequisite to determining the emergence rate, assessing seedling vigor, and facilitating site-specific management for optimal crop production. Traditional manual counting methods in stand assessment are labor intensive and time consuming for large-scale breeding programs or production field operations. This study aimed to apply two deep learning models, the MobileNet and CenterNet, to detect and count cotton plants at the seedling stage with unmanned aerial system (UAS) images. These models were trained with two datasets containing 400 and 900 images with variations in plant size and soil background brightness. The performance of these models was assessed with two testing datasets of different dimensions, testing dataset 1 with 300 by 400 pixels and testing dataset 2 with 250 by 1200 pixels. The model validation results showed that the mean average precision (mAP) and average recall (AR) were 79% and 73% for the CenterNet model, and 86% and 72% for the MobileNet model with 900 training images. The accuracy of cotton plant detection and counting was higher with testing dataset 1 for both CenterNet and MobileNet models. The results showed that the CenterNet model had a better overall performance for cotton plant detection and counting with 900 training images. The results also indicated that more training images are required when applying object detection models on images with different dimensions from training datasets. The mean absolute percentage error (MAPE), coefficient of determination (R2), and the root mean squared error (RMSE) values of the cotton plant counting were 0.07%, 0.98 and 0.37, respectively, with testing dataset 1 for the CenterNet model with 900 training images. Both MobileNet and CenterNet models have the potential to accurately and timely detect and count cotton plants based on high-resolution UAS images at the seedling stage. This study provides valuable information for selecting the right deep learning tools and the appropriate number of training images for object detection projects in agricultural applications.

scholarly journals Minimax-Optimal Bounds for Detectors Based on Estimated Prior Probabilities

2012 ◽  
Vol 58 (9) ◽  
pp. 6101-6109 ◽  
Author(s):  
Jiantao Jiao ◽  
Lin Zhang ◽  
Robert D. Nowak
Keyword(s):  
Prior Probabilities ◽  
Optimal Bounds

scholarly journals Fields Connected with Particles in Terms of Complex-Riemannian Geometry

1990 ◽  
Vol 45 (2) ◽  
pp. 81-94
Author(s):  
Julian Ławrynowicz ◽  
Katarzyna Kędzia ◽  
Leszek Wojtczak
Keyword(s):  
Field Potential ◽  
Riemannian Metrics ◽  
Interaction Matrix ◽  
Explicit Calculation ◽  
Maxwell System ◽  
Curved Space ◽  
Starting Point ◽  
Autocorrelation Time ◽  
The Fourier Transform ◽  
Convolution Equations

AbstractA complex analytical method of solving the generalised Dirac-Maxwell system has recently been proposed by two of us for a certain class of complex Riemannian metrics. The Dirac equation without the field potential in such a metric appeared to be equivalent to the Dirac-Maxwell system including the field potentials produced by the currents of a particle in question. The method proposed is connected with applying the Fourier transform with respect to the electric charge treated as a variable, with the consideration of the mass as an eigenvalue, and with solving suitable convolution equations. In the present research an explicit calculation based on linearization of the spinor connections is given. The conditions for the motion are interpreted as a starting point to seek selection rules for curved space-times corresponding to actually existing particles. Then the same method is applied to solids. Namely, by a suitable transformation of the configuration space in terms of elements of the interaction matrix corresponding to the Coulomb, exchange, and dipole integrals, the interaction term in the hamiltonian becomes zero, thus leading to experimentally verificable formulae for the autocorrelation time

Frequency Shift in Drilling due to Margin Engagement

2005 ◽  
Vol 127 (2) ◽  
pp. 271-276 ◽  
Author(s):  
D. N. Dilley ◽  
D. A. Stephenson ◽  
P. V. Bayly ◽  
A. J. Schaut
Keyword(s):  
Frequency Shift ◽  
Three Dimensional ◽  
Hole Drilling ◽  
Frequency Increase ◽  
Element Analysis ◽  
Pilot Hole ◽  
Frequency Matching ◽  
The Past ◽  
Chatter Prediction ◽  
Embedded Model

Drill chatter degrades hole roundness, hole size, and tool life. This wastes time and money in tools, scrap, and hole rework. Chatter prediction in milling and turning has shown significant benefit to industry; however, researchers have been unable to accurately predict chatter in drilling applications. In the past, the drill, including the chisel edge, was modeled as either a fixed-fixed or fixed-pinned beam (Tekinalp, O., and Ulsoy, A. G., 1989, “Modeling and Finite Element Analysis of Drill Bit Vibrations,” ASME J. Eng. Indust. 111, pp. 148–154), but more recent research (Dilley, D. N., Bayly, P. V., and Schaut, A. J., 2005, “Effects of the Chisel Edge on the Chatter Frequency in Drilling,” J. Sound Vib., 281, pp. 423–428) has shown that a fixed-embedded model using springs improves frequency matching. The effects of the drill margins on dynamics have not been studied. The fixed-fixed or fixed-pinned model will be shown to be inappropriate for modeling the effects of margin engagement, while the spring-end boundary condition can better approximate the frequency increase observed experimentally as the drill margins engage deeper into the hole. In addition, the shifted frequency is well below the frequency found from an analytical fixed-fixed or fixed-pinned beam. Evidence that the margins cause the frequency shift is seen in three-dimensional waterfall plots that show this shift for pilot hole drilling (in which the margins are engaged), but not for tube drilling (in which margins are not engaged).

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