A new algorithm for surface determination based on wavelets and its practical application

A new wavelets-based algorithm, FAST vision (facets stereo vision), is presented for an automatic and simultaneous determination of an object surface and its ortho image. Two families of orthogonal and C¹-continuous (continuously differentiable) object gray-value models, called 'S-D-model' and 'S-model,' respectively, were developed from the basic concept of multiresolution spaces. Both models establish two families of very simple gradient operators and enable FAST vision to do a very high resolution representation of an object surface and a fast solution of a very large system of normal equations. Test results using digitized aerial images at a scale of 1:4000 show that FAST vision is capable of a fast, highly resolved, reliable, and precise determination of an object surface in large windows and with rigorous error computations. The very high resolution of 2 by 2 pixels per height facet (0.12 by 0.12 m² in these tests) was obtained with the S-model in practical tests. The precision of the determined object surface was ± 0.02 to 0.06 m, i.e., 0.2 to 0.6 pixels or 0.03 to 0.1‰ of the flying height above ground, when compared with the control data measured by an operator on a Wild AC3 analytical stereoplotter. These figures correspond well with the natural roughness of the Earth's surface in the chosen test area.