A Note on the Estimation of Linear Regression Models with Heteroskedastic Measurement Errors

2002 ◽  
Author(s):  
Daniel G. Sullivan
Keyword(s):  
Linear Regression ◽  
Measurement Errors ◽  
Regression Models ◽  
Linear Regression Models

Measurement Error Correction of y Coordinate in Three Dimensional Localization of Tomatoes Using Binocular Stereo Vision

2014 ◽  
Vol 610 ◽  
pp. 209-215 ◽  
Author(s):  
Rong Xiang ◽  
Huan Yu Jiang ◽  
Yi Bin Ying
Keyword(s):  
Linear Regression ◽  
Measurement Errors ◽  
Regression Models ◽  
Stereo Matching ◽  
Three Dimensional ◽  
Linear Regression Models ◽  
Matching Methods ◽  
Binocular Stereo Vision ◽  
Binocular Stereo ◽  
Binary Linear Regression

Accuracy three dimensional coordinates of fruits and vegetables are very important to harvesting robots to harvest fruits and vegetables correctly. To decrease the measurement errors of the y coordinates of tomatoes, we analyzed the measurement errors of y coordinate acquired using binocular stereo vision based on three stereo matching methods. These three stereo matching methods were centroid-based, area-based, and combination stereo matching methods. After stereo matching, the three dimensional coordinates of tomatoes could be acquired based on the triangle ranging principle. Tests of 225 pairs of stereo images of three plastic balls used as normal balls acquired at the distances from 300 to 1000 mm showed that the ranges of the measurement errors of y coordinate acquired based on three stereo matching methods changed with the image acquisition distances obviously. Moreover, the measurement errors of y coordinate appeared linear decreasing trends approximately. Therefore, binary linear regression models were set up to reduce the ranges of the measurement errors of y coordinate of three balls. These models were used as correction models of the measurement values of y coordinate and were helpful to reduce the measurement errors of y coordinate. However, there were owe correction and overcorrection conditions when the image acquisition distances were smaller and larger than 750 mm separately. Then, the correction models based on piecewise binary linear regression were used to solve this problem. The ranges of the measurement errors of y coordinate were reduced further. Tests of 225 pairs of stereo images of three tomatoes acquired at the distances from 300 to 1000 mm showed that the ranges of the measurement errors of y coordinate acquired based on three stereo matching methods were separately from [-20.9, -6.6], [-19.9, -3.44], [-19.9, -3.48] mm to [-6.84, -0.06], [-5.84, -0.82], [-5.85, -0.83] mm after the correction using the piecewise binary linear regression models. It proved that the piecewise binary linear regression models were helpful to reduce the measurement errors of y coordinate in three dimensional localization of tomatoes using binocular stereo vision.

Sign in / Sign up

Export Citation Format

Share Document