The 3D surface is approximated by a triangular mesh to reduce geometric complexity and to tailor the model to the requirements of computer graphics visualization systems. A simple approach consists of overlaying a 2D triangular mesh on top of the image and then build a corresponding 3D mesh by placing the vertices of the triangles in 3D space according to the values found in the depth map. To reduce noise it is recommended to first smooth the depth image (the kernel can be chosen of the same size as the mesh triangles). The image itself can be used as texture map (the texture coordinates are trivially obtained as the 2D coordinates of the vertices).
It can happen that for some vertices no depth value is available or that the confidence is too low (see Section 7.1.2). In these cases the corresponding triangles are not reconstructed. The same happens when triangles are placed over discontinuities. This is achieved by selecting a maximum angle between the normal of a triangle and the line of sight through its center (e.g. 85 degrees).
This simple approach works very well on the depth maps obtained after multi-view linking. On simple stereo depth maps it is recommended to use a more advanced technique described in [90]. In this case the boundaries of the objects to be modeled are computed through depth segmentation. In a first step, an object is defined as a connected region in space. Simple morphological filtering removes spurious and very small regions. Then a bounded thin plate model is employed with a second order spline to smooth the surface and to interpolate small surface gaps in regions that could not be measured.
The surface reconstruction approach is illustrated in Figure 8.1. The obtained 3D surface model is shown in Figure 8.2 with shading and with texture. Note that this surface model is reconstructed from the viewpoint of a reference image. If the whole scene can not be seen from one image, it it necessary to apply a technique to fuse different surfaces together (e.g. [205]).
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