A Preliminary Study on the Theory of Polar Coordinates Digital Photogrammetry and the Coordinate System of Spatial Information

doi:10.11947/j.JGGS.2018.0108

Abstract

Abstract:

The development of new aeronautics and astronautics technologies has been constrained by strict mathematical rules for data processing among the diverse methods used to obtain spatial information.The acquisition of spatial information has been affected by various choices including the applied technologies (e.g.,push broom sensors),techniques (e.g.,zoom imaging),and equipment settings (e.g.,swing angle,aerial platform attitude,camera angle) in terms of the convergence,efficiency,and accuracy of the data.Based on the principle of the bionic machine parallax angle and pyramidal projection of the aerial space platform to the surface,this study explored solutions for high-resolution image sparsity,ill-conditioned singularity,and non-convergence by building a set of mathematical models to process the polar coordinates of the parallax angular vector.This study also formed a polar information theory for initial spatial information.This method improved the ranges of accuracy,efficiency,and anti-interference in close-range photogrammetry and the free net bundle adjustment model by several orders of magnitude.The open source code was made globally available more than 3 years ago,and has received positive reactions.The method’s effectiveness was verified using aerophotogrammetry and absolute network adjustment model experiments,and its performance was better than that of the Cartesian coordinate processing method.Finally,the higher-order solution characteristics of various applications and spaceflight platforms were provided,which are expected to provide a foundation for construction of a new polar coordinate system for aerospace multi-scale all-attitude spatial information acquisition,organization,management,storage,processing,and application.

Key words: astringency; bionic machine vision; convergence precision; intelligent photogrammetry; polar coordinates vector; spatial information

Lei YAN,Ruihua ZHANG,Yanbiao SUN. A Preliminary Study on the Theory of Polar Coordinates Digital Photogrammetry and the Coordinate System of Spatial Information[J]. Journal of Geodesy and Geoinformation Science, 2018, 1(1): 61-78.

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Vaihingen		G20 GN Cartesian coordinates	G20 LM Cartesian coordinates	sSBA Cartesian coordinates	ParallaxBA GN Polar coordinates	ParallaxBA LM Polar coordinates
Initial MSE		144707.21	144707.21	144707.21	144707.18	144710.18
Convergence MSE		N/A	135.060663	0.126012	0.126012	0.126012
Number of iterations		N/A	200	8	6	20
Linear equation		N/A	214	8	6	25
Single iteration time	Win	N/A	N/A	N/A	1.21	1.21
Single iteration time	Linux	N/A	1.2	0.8	1.45	1.45
total time	Win	N/A	N/A	N/A	8.46	26.43
total time	Linux	N/A	263.6	6.8	8.86	35.24

College		G20 GN Cartesian coordinates	G20 LM Cartesian coordinates	sSBA Cartesian coordinates	ParallaxBA GN Polar coordinates	ParallaxBA LM Polar coordinates
Initial MSE		202329.64	202329.64	202329.64	202329.44	202329.44
Convergence MSE		N/A	25.723307	9.272481	0.734738	0.734738
Number of iterations		N/A	200	200	12	17
Linear equation		N/A	349	228	12	17
Single iteration time	Win	N/A	N/A	N/A	2.71	2.71
Single iteration time	Linux	N/A	2.51	2.72	3.85	3.85
total time	Win	N/A	N/A	N/A	37.14	49.68
total time	Linux	N/A	674.83	453.22	51.55	69.58

Village		G20 GN Cartesian coordinates	G20 LM Cartesian coordinates	sSBA Cartesian coordinates	ParallaxBA GN Polar coordinates	ParallaxBA LM Polar coordinates
With or without ground control points		Yes	Yes	Yes	No	No
Initial MSE		28174.10	28174.10	28968.73	28170.98	28170.98
Convergence MSE		N/A	0.083716	0.083716	0.083716	0.083716
Number of iterations		N/A	34	8	6	11
Linear equation		N/A	55	8	6	11
Single iteration time	Win	N/A	N/A	N/A	0.67	0.67
Single iteration time	Linux	N/A	0.62	0.56	0.96	0.96
total time	Win	N/A	N/A	N/A	5.07	7.92
total time	Linux	N/A	27.46	4.54	6.98	12.23

	Village data	Taian data
Number of images	90	737
Number of belts	4	12
terrain	hills	mountain
scale	1∶1000	1∶5000
Area size	2km*3.5km	53km*35km
camera	DMC	DMC
Image frame	7680*13824	7680*13824
Resolution (m)	0.1	0.5
Control point	6	32
checking point	6	20

	Village	Taian
Encryption points	305719	2743625
Image points	779320	6017028
Initial error	56432.16	590764.93
Convergence error	0.09013	0.138706
Number of iterations	11	18
total time(second)	11.2	126.4