WAVELETS BASED OBJECT SURFACE RECONSTRUCTION BY FAST VISION
Jaan-Rong Tsay, Bernhard P. Wrobel
Department of Photogrammetry and Cartography, University of Technology, Darmstadt (Germany)
Reinhold Schneider
School of Mathematics, University of Technology, Darmstadt (Germany)
International Society of Photogrammetry and Remote Sensing, Commission IIT, Working Group III/2
XVIII ISPRS Congress, Vienna, Austria, 9-19 July 1996
KEY WORDS: Texture, Geometry, DEM/DTM, Radiometry, Orthoimage, Object Surface Reconstruction,
Facets Stereo Vision (FFAST Vision), Orthogonal Wavelets
ABSTRACT:
An algorithm is presented for the reconstruction of object surfaces with the method of FAST Vision(FFV) using new
models derived from wavelets. Firstly, the method of FV will be described briefly. A new, orthogonal and Cl.
continuous object grey value model, called 'S-model', was developed from the basic concept of the multiresolution
spaces in the theory of wavelets. A high resolution representation of object surface and a fast solution of the
corresponding normal equations can then be performed. Test results using digitized aerial images with image scale
1:4000 show that FV can perform a fast, highly resolved, reliable and precise determination of object surface in large
windows with strict computation of the covariance matrix under the application of the proposed algorithm. The very
high resolution of 2 x 2 pixels per height facet (= 0.12x0.12m” in these tests) is applicable in this algorithm. The
precision of the determination of object surface in these tests is +0.02-0.06m, i.e. 0.2-0.6 pixel or 0.03-0.1%% ac
flying height above ground, comparing with the control data measured by an operator on the analytical stereo plotter
WILD AC3. These figures correspond already to the natural roughness of earth surface and to errors of interior and
exterior orientation of the used images.
1. FAST VISION (=FV)
FV is a method to compute simultaneously image
matching, digital terrain reconstruction and ortho image
generation using digital data from image space and - if
available - from object space. It provides very good
quality control.
The theory of FV was firstly proposed by Wrobel in
1985 [5,6]. It's basic equation (1) is derived from the
inversion of an image formation model:
TÍG'G. y) *vo (y), 7G (X9. Y?) +a6°(x y), +
O0 , 0 x0 su 0 /
ea^ (x? Y); Xi-X 40 YY -Y |
ex 2 un E mi Ims
dZ(X9, v^ Q)
where
(G(x, vy), vg (X, y} =observation of the image grey
value for the pixel i and its residual;
T=transfer function between image grey value and its
corresponding object grey value;
dG°(X, Y); "correction of the approximate object grey
value G°{X°,Y°). that is a function of the
corrections of the parameters of the object grey
value model;
Xp, Y6, Zy7object coordinate of the projection center
of the used image;
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
ES YY? ; z0 — approximate object coordinate of the
surfel i;
dz(x°, vhs, correction of the height for the surfel i,
that is a function of the height corrections for the
height grid points used in the object height model.
In the past, we used a linear function to approximate
the transfer function 7, and bilinear approximation
functions for the object grey value model and the object
height model. One can find detailed descriptions about
FV in [2,3,4,5,6] and extended tests in [8].
The well-known il/-posed problem in the object surface
reconstruction is caused e.g. by a possible deficiency of
the necessary image information in the matching
window. This problem in FV can be solved by utilizing
image and object information. For example, the adaptive
regularization [7] uses the smoothness conditions of the
geometrical object surface to solve this problem. These
conditions are one type of object information.
The bigger the window size, the more image
information is available. In this paper we present a
wavelets based representation not only to enable the
object surface reconstruction in a large matching
window, but also to give a good representation of the
radiometrical model of the object surface (ortho image).
The orthogonal compactly supported wavelets given by
Daubechies [1] are applied. We use them to develop an
orthogonal and C'-continuous object grey value model,
