By Bernd Jahne, Horst Haussecker, Peter Geissler
ISBN-10: 0123797721
ISBN-13: 9780123797728
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Extra info for Handbook of Computer Vision and Applications
Example text
5, are more complex on these lattices than, for example, the 2-D hexagonal lattice. In 3-D or volumetric images the elementary cell is known as a voxel, an abbreviation of volume element . 3 Discrete signals 17 represents the mean gray value of a cuboid. The position of a voxel is given by three indices. The first, l, denotes the depth, m the row, and n the column (Fig. 4b). In higher dimensions, the elementary cell is denoted as a hyperpixel. 3 Irregular lattices Irregular lattices are attractive because they can be adapted to the contents of images.
This simple estimate is, however, biased towards a larger area because the cells at the border of the object are only partly covered by the object. In the mean, half of the border cells are covered. 14) where Nb is the number of border cells. With this equation, the variance of the estimate can be determined. Only the statistical error in the area of the border cells must be considered. 15) If we assume a compact object, for example, a square, with a length of D pixels, it has D 2 pixels and 4D border pixels.
15) are also valid for volumetric images if the area of the elementary cell is replaced by the volume of the cell. Only the number of border cells is now different. If we again assume a compact object, for example, a cube, with a length of D, we now have D 3 cells in the object and 6D 2 border cells. 5 %. Note that the absolute/relative error for volume measurements in/decreases faster with the size of the object than for area measurements. The computations for the error of the center of gravity are quite similar.
Handbook of Computer Vision and Applications by Bernd Jahne, Horst Haussecker, Peter Geissler
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