Geodesy Principle

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Classes
class	SoChamferDistanceMapProcessing2d
	SoChamferDistanceMapProcessing2d engine More...

class	SoChamferDistanceMapProcessing3d
	SoChamferDistanceMapProcessing3d engine More...

class	SoChessboardDistanceMapProcessing
	SoChessboardDistanceMapProcessing engine More...

class	SoClosestBoundaryPointsProcessing2d
	SoClosestBoundaryPointsProcessing2d engine More...

class	SoClosestBoundaryPointsProcessing3d
	SoClosestBoundaryPointsProcessing3d engine More...

class	SoEuclideanDistanceMapProcessing3d
	SoEuclideanDistanceMapProcessing3d image filter More...

class	SoGeodesicDistanceMapProcessing
	SoGeodesicDistanceMapProcessing engine More...

class	SoGeodesicPropagationProcessing2d
	SoGeodesicPropagationProcessing2d engine More...

class	SoLocalThicknessMapProcessing3d
	SoLocalThicknessMapProcessing3d engine More...

class	SoTimeMapProcessing
	SoTimeMapProcessing engine More...

Detailed Description

Geodesy Principle

Geodesy is by definition the science of measuring the shape of the earth. When applied to image processing it is the science of measuring the exact shape of objects included in an image. The geodesic distance is defined as follows:

If two points $x$ and $y$ belong to $X$ then $d_X(x,y)$ is the shortest distance between the two points with the condition that the entire path between the points is included in the particle $X$ . If one of the points is outside then $d_X(x,z) = \infty$ . If the points belong to 2 disjointed components, then $d_X(x,y) = \infty$

This geodesic distance is actually a distance for any set $X$ without any hole. A geodesic disk, $B_x$ , is then defined, as shown in figure below.

Geodesic measurement

The geodesic notion implies that each particle is fully independent of its neighbours in the image. Moreover, one may introduce the geodesic erosion and dilation. The geodesic dilation is equivalent to a reconstruction in the continuous space. One can show that a discrete geodesic dilation of size $N$ is actually $N$ dilations of size 1, each dilation being followed by an intersection with the set $X$ . In this case, the underlying discrete distance is defined by the elementary discrete disk (a square or hexagon depending on the grid). The propagation function is then defined as:

$t_X(x) = Sup\{d_X(x,y), y \in X\}$

It corresponds to the geodesic distance between point $x$ and the furthest point of $X$ .

Open Inventor Release 2023.2.3

Geodesy Principle

Classes

Detailed Description

Geodesy Principle