Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1997-04-16
2001-08-07
Teska, Kevin J. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C702S167000, C708S445000, C342S022000, C342S02500R, C342S191000
Reexamination Certificate
active
06272448
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and apparatus which reproduce a digital terrain model (DTM) with natural features including fine folds from contour data.
2. Description of the Related Art
The simplest DTM from contour data is obtained by dividing a region between contours and making the height of each part to be constant which is the average of the elevational values of the enclosing contours. It is called the stacking model. The information of the model is exactly equivalent to that of the contour data. In the model every elevational gap on contours and the flatness between contours become conspicuous where the density of contour is low. Hence it becomes a problem to vary the elevational data between contours and connect the contours by a continuous surface. This is called the terrain reproduction problem from contour data. The necessary information to vary the elevational data is not obtained directly from contour data. Therefore the problem is of an addition of the information that some adequate information ought to be added to contour data in order to obtain an appropriate height surface data. The problem can be divided into two partial problems; the framework of the addition and the content of the addition.
Most of conventional methods are classified into following four types.
(1) The profiles of a terrain are calculated for some directions using interpolation curves such as the spline, and averaged out with weights.
(2) Triangle patches are spanned throughout between contours, and elevational values are interpolated on the triangle patches.
(3) DTM is obtained by smoothing the initial model obtained by a simple procedure such as the stacking model by a two-dimensional low-pass filter.
(4) Regarding contours as a set of points, an estimating function is deliberately chosen with a fitting surface. The surface is then fitted by minimizing the estimating function.
The outputs of above methods have some problems; (1) artificial steps and ditches or starlike noises appear in DTM, (2) as shown in
FIG. 5
, the triangle patches
501
will remain as a peculiarity of the landform, (3) and (4) as shown in
FIG. 6
the landform becomes an unusual rounded shape without minute folds and wrinkles.
Such problems occur in the conventional methods because physical and geomorphological features of landforms are not given but only artificial and geometrical conditions as the content of the addition to contour data. Also from the viewpoint of the framework of the addition, the methods are faced with some difficulties. The above (1), (2) and (3) methods are in principle of unified processes that the contents of the addition are mostly determined according to the frameworks of the addition. Thus it is almost impossible to add or cut a part of the contents as the need arises.
In the method of (4), the content of the addition can be varied by exchanging the estimating function. However, the choice is small and it is very difficult to adopt a local requirement because the content is after all given by a global-optimization problem.
SUMMARY OF THE INVENTION
A purpose of the present invention is to provide a method and an apparatus which reproduce a DTM from contour data with geomorphological consistency and natural features including fine folds. It solves the problems of geometrical noises and unnatural landform-features appearing in the result owing to merely geometrical and artificial techniques of the conventional methods.
To solve above problems in the present invention, the terrain reproduction problem is formulated as a boundary value problem for an operator on a functional space defined on two-dimensional (2D) plane where contours are set as the boundaries.
The content of the addition can be selected by the choice of the operator and it is easy to adopt local requirements because the framework of the addition is the boundary value problem. Thus a wide range of physical-geomorphological features can be expressed.
Particularly, in an area where erosion by rain dominates the land formation, it is most natural to give the geomorphological feature that the elevational values are smoothed along flowing water lines to the content of the addition. It is fundamental in the terrain reproduction problem on such an area. Then in the present invention, an operator which smooths the elevational values along flowing water lines or neighborhoods of the lines is introduced and it makes possible to give at least the feature to a DTM.
Some other features of rain erosion may be also given to a DTM by constructing an operator to which corresponding operations are added. For example, an effect of accumulation can be adopted into a DTM with an operator which behaves like the Laplace operator in flat areas.
In this application, an operator which smooths the elevational values along flowing water lines or the neighborhood of the lines means an operator at least including this smoothing operation.
As a result, a method and an apparatus of the present invention solve the problems of geometrical noises and unnatural landform-features resulting from the conventional methods and it makes possible to reproduce a DTM from contour data with geomorphological consistency and natural features including fine folds.
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Muraki, Shigeru; Yokoya, Naokazu; Yamamoto, Kazuhiko, “3D surface reconstruction from contour line image by a Regularization method,” SPIE, vol. 1395, Close-Range Photogrammetry Meets Machine Vision, Proceedings ISPRS, Sep. 3-7, 1990, pp. 226-233.
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Kobashigawa
Marger & Johnson & McCollom, P.C.
Phan Thai
Teska Kevin J.
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