1. FITTING, PORTRAYAL AND MAPPING FOR THE PRODUCTION OF 2nd ORDER SURFACES PHOTOMOSAICS Artemis Valanis School of Rural and Surveying Engineering Laboratory of Photogrammetry National Technical University of Athens, Greece

2. GENERAL INFORMATION AND OBJECTIVES This presentation refers to an extensive study that has been carried out within the framework of a much greater project. The project was assigned to the Laboratory of Photogrammetry and involved the thorough survey and recording of the world famous Byzantine Daphni Monastery of Athens (11th century). The main objective of this study was the creation of large-scale (1:5) developments of 2nd-order surfaces.

3. COURSE OF STUDY Data collection Surface fitting Reference system definition Creation of the “Intermediary Model” Choice of the most suitable projection Production of the developed images Creation of the photomosaics

4. PROBLEMS ENCOUNTERED - The choice of the most suitable model - The calculation of the approximate values of the unknowns - The definition of a new reference system - The fact that the mathematically defined surface generally differs from the real object surface

5. DATA USED Photographs of scale: k= 1:25 Scanning resolution: 600 dpi Geodetically collected point coordinates Photo orientations DEMs

7. Calculation of the approximate values of the unknowns

8. Creation of the least-squares adjustment programs with computational optimization

9. Testing of the programs with simulation data

11. MODEL OR REAL OBJECT SURFACE ? However, the most important problem encountered was the fact that the mathematically defined surface generally differs from the real object surface. Thus, in order for the photomosaicking to be possible, the one-to-one correspondence between the points of the real and the model surface had to be ensured. This was achieved with the creation of the “Intermediary Model”, which is based on the DEM of the real surface.

12. THE PROBLEM CAUSED DUE TO THE DIFFERENCE BETWEEN THE MODEL AND THE REAL SURFACE (PP) (Ph1) (Ph2) (Xc,Yc,Zc) Model Real Surface

13. |dR|   3cm (68%) |dR|   6cm (95%) |dR|   9cm (99%) Least-squares adjustment σο dR =3cm ERROR PROPAGATION

14. ERROR PROPAGATION

15. ERROR PROPAGATION

16. PROJECTION Choice of the most proper projection Criteria: Suitability for the application Minimization of the distortions Implementation: Projection-plane (xp, yp) Sphere  “Intermediary Model”  Actual object-surface  Geodetical coordinates  Coordinates on the photographic plane  Acquisition of the colour for the corresponding position (xp, yp) on the projection plane  Developed Image creation

17. RESULTS- Mollweide Conformal Projection -

18. RESULTS- Oblique Mercator Projection -

19. CHARACTERISTICS OF THE METHOD DEVELOPED Accuracy and reliability High quality Ability to work with RGB images Capability to incorporate numerous images for a single object Successful mosaicking Program performance highly dependent on the platform and the resources of the system used