scholarly journals Least Squares Optimization: From Theory to Practice

Robotics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 51 ◽  
Author(s):  
Giorgio Grisetti ◽  
Tiziano Guadagnino ◽  
Irvin Aloise ◽  
Mirco Colosi ◽  
Bartolomeo Della Corte ◽  
...  
Keyword(s):  
Computer Vision ◽  
Least Squares ◽  
Open Source ◽  
State Of The Art ◽  
Nonlinear Least Squares ◽  
Research Community ◽  
Specific Domain ◽  
Theory To Practice ◽  
Least Squares Optimization ◽  
Computer Vision Systems

Nowadays, Nonlinear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last few years, and this resulted in the development of several open-source solvers to approach constantly increasing classes of problems. In this work, we propose a unified methodology to design and develop efficient Least-Squares Optimization algorithms, focusing on the structures and patterns of each specific domain. Furthermore, we present a novel open-source optimization system that addresses problems transparently with a different structure and designed to be easy to extend. The system is written in modern C++ and runs efficiently on embedded systemsWe validated our approach by conducting comparative experiments on several problems using standard datasets. The results show that our system achieves state-of-the-art performances in all tested scenarios.

ON METHODS OF OBJECT DETECTION IN VIDEO STREAMS

2017 ◽  
Vol 2 (1) ◽  
pp. 80-87
Author(s):  
Puyda V. ◽  
◽  
Stoian. A.
Keyword(s):  
Computer Vision ◽  
Object Detection ◽  
Open Source ◽  
Feature Detection ◽  
Video Stream ◽  
Object Identification ◽  
Vision Systems ◽  
Modern Computer ◽  
Computer Vision Systems ◽  
Open Source Hardware

Detecting objects in a video stream is a typical problem in modern computer vision systems that are used in multiple areas. Object detection can be done on both static images and on frames of a video stream. Essentially, object detection means finding color and intensity non-uniformities which can be treated as physical objects. Beside that, the operations of finding coordinates, size and other characteristics of these non-uniformities that can be used to solve other computer vision related problems like object identification can be executed. In this paper, we study three algorithms which can be used to detect objects of different nature and are based on different approaches: detection of color non-uniformities, frame difference and feature detection. As the input data, we use a video stream which is obtained from a video camera or from an mp4 video file. Simulations and testing of the algoritms were done on a universal computer based on an open-source hardware, built on the Broadcom BCM2711, quad-core Cortex-A72 (ARM v8) 64-bit SoC processor with frequency 1,5GHz. The software was created in Visual Studio 2019 using OpenCV 4 on Windows 10 and on a universal computer operated under Linux (Raspbian Buster OS) for an open-source hardware. In the paper, the methods under consideration are compared. The results of the paper can be used in research and development of modern computer vision systems used for different purposes. Keywords: object detection, feature points, keypoints, ORB detector, computer vision, motion detection, HSV model color

scholarly journals Parameterized Nonlinear Least Squares for Unsupervised Nonlinear Spectral Unmixing

2019 ◽  
Vol 11 (2) ◽  
pp. 148 ◽  
Author(s):  
Risheng Huang ◽  
Xiaorun Li ◽  
Haiqiang Lu ◽  
Jing Li ◽  
Liaoying Zhao
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Nonnegative Matrix Factorization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Nonlinear Least Squares ◽  
Hyperspectral Data ◽  
Spectral Unmixing

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.

scholarly journals Near infrared nadir sounding of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (3) ◽  
pp. 3685-3737
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Nonlinear Least Squares ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b–2 processing of SCIAMACHY data a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed: BIRRA performs a nonlinear least squares fit of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

scholarly journals 2D shape deformation using nonlinear least squares optimization

2006 ◽  
Vol 22 (9-11) ◽  
pp. 653-660 ◽  
Author(s):  
Yanlin Weng ◽  
Weiwei Xu ◽  
Yanchen Wu ◽  
Kun Zhou ◽  
Baining Guo
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Shape Deformation ◽  
Least Squares Optimization

scholarly journals Forest Height Estimation Based on Constrained Gaussian Vertical Backscatter Model Using Multi-Baseline P-Band Pol-InSAR Data

2018 ◽  
Vol 11 (1) ◽  
pp. 42 ◽  
Author(s):  
Xiaofan Sun ◽  
Bingnan Wang ◽  
Maosheng Xiang ◽  
Shuai Jiang ◽  
Xikai Fu
Keyword(s):  
Least Squares ◽  
Incidence Angle ◽  
Nonlinear Least Squares ◽  
Estimation Accuracy ◽  
Height Estimation ◽  
Low Frequencies ◽  
Function Fitting ◽  
Forest Height ◽  
Vertical Heterogeneity ◽  
Least Squares Optimization

In the case of low frequencies (e.g., P-band) radar observations, the Gaussian Vertical Backscatter (GVB) model, a model that takes into account the vertical heterogeneity of the wave-canopy interactions, can describe the forest vertical backscatter profile (VBP) more accurately. However, the GVB model is highly complex, seriously reducing the inversion efficiency because of a number of variables. Given that concern, this paper proposes a constrained Gaussian Vertical Backscatter (CGVB) model to reduce the complexity of the GVB model by establishing a constraint relationship between forest height and the backscattering vertical fluctuation (BVF) of the GVB model. The CGVB model takes into account the influence of incidence angle on scattering mechanisms. The BVF of VBP described by the CGVB model is expressed with forest height and a polynomial function of incidence angle. In order to build the CGVB model, this paper proposes the supervised learning based on RANSAC (SLBR). The proposed SLBR method used forest height as a prior knowledge to determine the function of incidence angle in the CGVB model. In this process, the Random Sample Consensus (RANSAC) method is applied to perform function fitting. Before building the CGVB model, iterative weighted complex least squares (IWCLS) is employed to extract the required volume coherence. Based on the CGVB model, forest height estimation was obtained by nonlinear least squares optimization. E-SAR P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) data acquired during the BIOSAR 2008 campaign was used to test the performance of the proposed CGVB model. It can be observed that, compared with Random Volume over Ground (RVoG) model, the proposed CGVB model improves the estimation accuracy of the areas with incidence angle less than 0.8 rad and less than 0.6 rad by 28.57 % and 40.35 % , respectively.

scholarly journals Fast Nonlinear Least Squares Optimization of Large‐Scale Semi‐Sparse Problems

2020 ◽  
Vol 39 (2) ◽  
pp. 247-259 ◽  
Author(s):  
M. Fratarcangeli ◽  
D. Bradley ◽  
A. Gruber ◽  
G. Zoss ◽  
T. Beeler
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Nonlinear Least Squares ◽  
Least Squares Optimization ◽  
Sparse Problems
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