CAMERA CONSTANT IN THE CASE OF TWO MEDIA PHOTOGRAMMETRY

Transcription

1 CAMERA CONSTANT IN THE CASE OF TWO MEDIA PHOTOGRAMMETRY Panagiotis Agrafiotis and Andreas Georgopoulos Laboratory Of Photogrammetry, School of Rural and Surveying Engineering National Technical University of Athens users.ntua.gr/pagraf

2 Introduction refraction : the main cause of geometric distortions in multimedia photogrammetry This effect cannot be compensated and corrected by a suitable camera calibration In this work are presented... the problem of two-media calibration which is also analysed the relation of the effective camera constant of twomedia to the one in air through the application of calibration methods using different test fields 2

3 Motivation Lavest et al. (2000) : when the camera is underwater, the effective camera constant is approximately equal to that in the air (x) by the refractive index of water (n=1.33) However... In two media photogrammetry, the 1.33 factor used for underwater cases does not apply and the most probable relation of the effective camera constant to the one in air is depending of the percentages of air and water in the total camera-toobject distance 3

4 The Refraction Effect Review A Camera A Camera B B This research assumes that the water surface is planar Flying Height Normal r P A P' Normal P B air Light rays passing through the air/water interface are refracted according to Snell s law: Water Height Apparent Depth P'' i water sin r sin i = h h A = n Real Depth P The geometry of two-media Photogrammetry (Fryer and Kniest, 1985) 4

5 About Two-Media Calibration Underwater Camera Calibration Also considered as two media calibration. However, is differentiated from the through water camera calibration by the amount of the percentages of the media intervening between the camera lens and the test field Through Water (two-media) Calibration Most applications do not overcome the refraction effects by a camera calibration but try to correct them Why? 5

6 The problem of a suitable camera calibration The sea surface alteration due to waves The solar reflections The effects of refraction that differ in each image,...lead to unstable solutions The refraction is affected by the amount of the water that covers the point of origin and the angle of incidence of the beam in the air/water interface Shots from different angles and different distances alter the amount of water that covers the points of the test field AND they significantly alter the angles of incidence of the light rays Calibration techniques do not succeed and fail to provide a reliable result 6

7 Theoretical Approach for retrieving the effective camera constant in two media cases A A z z y c y c x x ri r r ri image plane rii r r rii image plane H air/water interfaceii H air/water interface I Pa'' Pa' Pb' Pb'' hii h I Pa Pb It is obvious that the increase of the water depth implies a decrease of the solid angle of view. This variation seems to be directly proportional to the camera constant because the sensor size (and hence the image size) is constant 7 Pa Pb

8 Methodology Applied (1) Proving the misleading results of a camera calibration in two media cases 3 different calibration methods in air and water in order to achieve objective results 1. Photomodeler Calibration Suite 2. FAUCCAL 3. Camera Calibration Toolbox for Matlab 2 different test fields were used It was decided to rotate the test fields and not move the camera around in order to keep the system camerarefractive surface constant and avoid different angles of 8 incidence

9 Methodology Applied (2) Retrieving the effective Camera Constant in the case of Two Media Images of a specially graduated stable planar test field with increasing water percentages, each time by 5% maintaining the camera position and the test field constant The images were also checked for lens distortions The coefficient of the camera constant is retrieved by measuring and comparing the decreasing field of view and accordingly the scale 9

10 Experimental Results (1) Camera calibration in two media cases Photomodeler 1.34 FAUCCAL 1.32 CCT Photomodeler FAUCCAL CCT % 30% 45% The computed camera constant according to the water percentages R15% R30% R45% The ratio between the camera constant in two-media and the one in air. The amount of the refraction is affected by the amount of the water that covers the point of origin and the angle of incidence of the beam in the interface air/water This varies with the rotations of the planar test fields and leads to wrong results unstable solutions 10

11 Experimental Results (2) Camera Constant in the case of Two Media 25% 0% 25% Translating the described theoretical approach into mathematical terms, the camera constant coefficient is expressed by: P air n air + P water n water 11

12 Experimental Results (3) Camera Constant in the case of Two Media (2) The reduction of the FOV leads to the increasing of the scale of the image Since the camera - to - test field distance is remaining constant and by the well known Equation 1 P air n air + P water n water k = H c Theoretical and Experimental coefficient comparison regarding to the intervening water percentages 12

13 Conclusions In two media photogrammetry the 1.33 factor used for clean water in underwater cases does not apply the camera calibration in two-media photogrammetry leads to misleading results The effective camera constant to the one in air is given by: c two media = c air (P air n air + P water n water ) This relation bridges the gap between the camera constant in air applications and the one in underwater cases. However it is not applicable the refraction effect needs to be corrected 13

14 Thank you! users.ntua.gr/pagraf The research leading to these results has been supported by European Union funds and National funds (GSRT) from Greece and EU under the project 3D ORO: Efficient and Effective 3D Computer Vision Tools for Improving the Performance of 3D Digitalization funded under the cooperation framework. 14