The document presents a method for registering geophysical images from different modalities to increase the information obtained. It uses mutual information as a similarity measure to find the translation between image pairs. It then introduces an algorithm that applies local distortions through a windowing approach while maintaining grid continuity, improving upon simple rigid registration. The method is tested on archaeological image datasets, successfully registering image pairs in agreement with their known coordinates and increasing their mutual information.

1. Registration of Geophysical Images Alexandra A. Karamitrou Laboratory of Exploration Geophysics Aristotle University of Thessaloniki, Greece, Maria Petrou Informatics & Telematics Institute, CERTH, Thessaloniki, Greece Gregory N. Tsokas Laboratory of Exploration Geophysics Aristotle University of Thessaloniki, Greece [email_address] [email_address] [email_address] ARISTOTLE UNIVERSITY OF THESSALONIKI FACULTY OF SCIENCES

2. Geophysical methods The target is to increase the information obtained from the 2 original images independently. Archaeology Brizzolari et al., 1992a Garrison, 2003 Piro et al., 1998 Tsokas et al., 1994

3. Magnetic method Detect magnetic anomalies produced by the existence of buried features Instrument: Gradiometer sensors

4. Electrical method Determines the underground resistivity anomalies Electrodes that induce electric current Electrodes that measure the electric potential

5. Ruins from the temple of Dionisos ( 323 - 146 B.C ) Ceramic objects Archaeological area of Kampana (Maronia-NE Greece) Ancient Theater ( 323 - 146 B.C ) Mosaic floor from an aristocratic house ( 323 - 146 B.C )

6. Vertical Gradient of the local magnetic field Magnetic method Apparent Resistivity Electrical method Archaeological area of Kampana (Maronia-NE Greece) Tsokas G. et al., 2004

7. Ancient temple of Roman period (63 B.C – 476 A.D ) and an old Christian church ( 450–600 A.D ) Aero photography by Κ. Κ iriagos Archaeological area of Argos-Orestiko (West Greece)

8. Archaeological area of Argos-Orestiko (West Greece) Tsokas et al., 2006 Vertical Gradient of the local magnetic field Magnetic method Apparent Resistivity Electrical method

9. Vertical Gradient of the local magnetic field Magnetic method Apparent Resistivity Electrical method Archaeological area of Argos-Orestiko (West Greece) Tsokas et al., 2006

12. Left column Vertical Gradient of the local magnetic field (magnetic method) Right column Apparent Resistivity (electrical method) Training set Test data

13. Image Registration We used a simplified version of the cost function (Kovalev V. A. and Petrou M., 1998) , where exhaustive search is used to find the parameters of the global translation that would maximize the mutual information between the pairs of images as well as their overlapping area. The geophysical images are from different modalities Mutual Information was used as a similarity measure Mutual Information 0.1204 Mutual Information 0.5431 Mutual Information 0.2234

14. In all three cases the results agreed exactly with the known shift between the pairs of images from their geographical coordinates. Preliminary registration of training set Preliminary registration of test data Registration Results

15. Affine Transformation Affine transformation is a linear 2-D geometric transformation which maps variables, through a linear combination of rotation, scaling and shearing followed by a translation, into new variables. Original Image Rotation Scaling Shearing

16. Proposed Methodology

17. “ continuity” parameter The Delaunay triangulation method (Delaunay B., 1934) was used. (2M+3)x(2M+3) Μ=1 25 pixels (2M+1)x(2M+1) Μ=1 9 pixels + + + + + + + + + + + + + + + + o o o o o o o o o x x x x x x x x x For the pixels at the places of the window with the maximum distortion, Selecting , the pixels at the periphery do not move much. Parameter is calculated as,

18. The randomly selected central pixel and the (2M+3)x(2M+3) window are selected with the condition that the whole window does not contain uncharted pixels.

19. Windows that succeed to increase the Mutual information Windows that fail to increase the Mutual information

20. Different values of mutual information for the training pair of images (Maronia). Argos Orestiko 1 st case Argos Orestiko 2 nd case Different values of mutual information for the two testing pair of images The algorithm was run without any change of the parameters for the 2 testing pair of images 0.5  0.98 0.57  0.76 0.8  1.46 Mutual Information Results

21. Transformed Images Results Archaeological area of Kampana Archaeological area of Argos Orestiko

22. Conclusions Registration method with rigid body translations succeeded to register the geophysical images in agreement with the geographical coordinates. Local inaccuracies (offsets) during the measurements degrade the overall mutual information between the images. We selected the parameters of the algorithm by using a training pair of images and then tested it, without changing these parameters on two other sets of images. In all cases the algorithm increased the mutual information between the images beyond the benchmark value of rigid body registration. We introduced a new efficient and effective semi-stochastic optimization algorithm which applies randomly distortions with randomly selected parameters, and accepts the changes only when they help increase the mutual information between the images. We proposed a method that applies local distortion while preserves the continuity of the grid.

23. Alexandra A. Karamitrou Laboratory of Exploration Geophysics Aristotle University of Thessaloniki, Greece, Maria Petrou Informatics & Telematics Institute, CERTH, Thessaloniki, Greece Gregory N. Tsokas Laboratory of Exploration Geophysics Aristotle University of Thessaloniki, Greece [email_address] [email_address] [email_address] Thank you for your attention !