WO2002029355A2

WO2002029355A2 - Automatic method for meshing 3d virtual copies

Info

Publication number: WO2002029355A2
Application number: PCT/HU2001/000097
Authority: WO
Inventors: Loránt SZABO; Péter HERCZEG
Original assignee: Szabo Lorant; Herczeg Peter
Priority date: 2000-10-04
Filing date: 2001-10-03
Publication date: 2002-04-11
Also published as: HU0003886D0; AU2001295819A1; WO2002029355A3

Abstract

The solution according to the invention is an automatic method for preparing statue-like copies of bodies during which a three-dimensional virtual copy is created based on digitally recorded data of image points surveyed from multiple directions using a new image editing algorithm, a tactile copy is then created based on the original data file describing the copy. Steps of the procedure: scanning/data survey (1); data retrieval (2); creation of rough mesh (3); updating first cycle (4); densifying second cycle (5); refining third cycle (6); reduction/magnification (7); data saving to file / recording (8); printing / plotting (9). The procedure can be regarded as the spatial equivalent of photography.

Description

Automatic method for preparing statue-like copies

What is claimed is an automatic method for the preparation of a statue-like copy of a body that may ideally be approximated with a sphere, e.g. a human head.

Description of the related art: Ever since the invention of paper pictures realized through photography a solution has been sought for preparing lifelike copies of bodies based on no-contact data survey similar to photographic exposition.

There are known methods whereby digitally recorded data gathered by scanning are used to produce a virtual copy of a given body and for the reproduction of a stereoscopic image on screen or in printing.

- The image editing method according to US Patent 5. 748 865 generates a virtual body defined by a triangle mesh based on the entered digitally characterized image points where the resolution and the aspect of on-screen display can be chosen, that is the image may be rotated on the screen.

The initial step of the method places a virtual enveloping body around the picture point set, generates a spatial mesh made of triangles on its surface with a density defined by the desired resolution, and recursively modifies this mesh using the image point data. Upon inserting a new image point the new triangle edges are chosen based on the distances calculated on the projection plane defined by the aspect using the Delaunay method known from geometry. Since a part of the operations are performed on a plane, the spatial mesh relevant to the aspect stores the original spatial data only to a degree. When we define a new aspect the projection plane and projected distances are different, the Delaunay method select different edges, and the result is a significantly different spatial mesh that fits the original body also only from the selected aspect.

- The image editing method according to US Patent 5. 945 996 also produces a virtual copy defined by a triangle mesh that may be displayed on a screen and rotated, but aims for a smaller number of calculations. Recorded image points are entered into a table based on their distance from the center of the smallest enveloping sphere, and starting from the edge set of the tetrahedral pyramid constructed from the first four points the point closest according to the table is added connected to a face using the edge set which provides the tetrahedral pyramid with the smallest surface area, the latter being chosen using the Delaunay method after projection onto a plane. This method reduces the number of operations required for building the triangular mesh but the mesh is only free of distortion from one aspect owing to projection onto a plane. Upon moving to another aspect the digital data of the new triangular mesh on which the on-screen display of the virtual copy is based are calculated by means of a transformation matrix. In some methods, like the Hungarian patent claim case number P98 02241 the triangular mesh displayed on the screen is textured based on supplementary image information to enhance the spatial effect.

The automatic methods above are suited to produce a picture with a spatial effect displayed on a screen or in print but do not pursue rendering a concrete, statue-like display.

The aim of the invention is to develop a procedure that may be regarded as the spatial equivalent of photography, that is one that, after a relatively short, contact- free information survey, automatically produces a realistic, tactile copy of the body from the stored three-dimensional data. The aim furthermore is to be able to interrupt in time and space the process of producing the copy after the data survey and storage, and storage of the data file describing the copy. We also aim to have the procedure automatically filter contradictory data resulting from occurrent movement of the body and supplement overly information-free portions, furthermore to enable the reduction/magnification of the copy of the body should it be desired.

The solution according to the invention is an automatic method for preparing a statue-like copy of a body. The method comprises the preparation of a virtual copy based on the generation and recursive modification of a spatial mesh from the digitally recorded data of image points of the original body surveyed from multiple directions - using an apparatus that is known in itself - and the production - using an apparatus that is known in itself - of a tactile copy based on the digital data file characterizing the mesh.

The image editing algorithm according to the invention generates a narrowly enveloping virtual body and the C fictive center thereof based on the data of the image points, and divides the unordered set of image points into spatial regions through the proportional division of the enveloping virtual body. A point is selected in each of the spatial regions and a rough spatial mesh of triangles defining an approximating body is generated by connecting the thus selected points of all of the neighboring spatial regions.

The virtual copy is created in three cycles using recursive processing of the image point data and development of the spatial mesh where the data and vertex ordering of the triangles of the actual spatial mesh are stored.

- In the first cycle all thus far unprocessed P points are examined to see whether line PC intersects a triangle face in its own or a neighboring region of the actual spatial mesh and whether it is inside of a predefined di distance from it - if it does not fulfill these requirements it is set aside. If it does, a new tetrahedral pyramid is constructed using point P as a vertex and the intersected triangle as a base, and the triangle faces incident on the vertex are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while the base triangle is discarded. Every newly adopted image point is examined to find whether it is connected to the neighboring image points by the shortest possible set of edges - if not, the triangles defined by the longer body diagonal of the spatial quadrangle are replaced in the spatial mesh with the triangles defined by the shorter body diagonal. - In the second cycle the triangles listed in the actual spatial mesh are examined to see whether there are edge lengths greater than a predefined d₂ distance or triangle faces with areas larger than a t₂ If such are found Q fictive image point is generated using the data of the oversized triangle and its neighbors sharing an edge with it. A new tetrahedral pyramid is then constructed using the fictive point Q as a vertex and the oversized triangle as a base, and the triangle faces incident on the vertex are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while the base triangle is discarded.

- In the third cycle all P image points set aside in the first cycle are examined to see whether line PC intersects a triangle face in its own or a neighboring region of the actual spatial mesh and whether it is inside of a predefined d₃ distance from it. If it does not fulfill these requirements it is definitively set aside. If it does, a new tetrahedral pyramid is constructed using point P as a vertex and the intersected triangle as a base, and the triangle faces incident on the vertex are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while the base triangle is discarded. Every newly adopted image point is examined to find whether it is connected to the neighboring image points by the shortest possible set of edges - if not, the triangles defined by the longer body diagonal of the spatial quadrangle are replaced in the spatial mesh with the triangles defined by the shorter body diagonal.

Should it be desired the virtual created copy is reduced/magnified by a predefined scale after the third cycle by carrying out operations on the digital data series describing the actual spatial mesh. Thereafter data file of the desired format ready for direct automatic processing is generated for storing or producing a hard copy. Should it be desired the copy prepared using the data file is stuff-colored or coated. In an advantageous realization the input data of the image editing algorithm are the three-dimensional Descartes coordinates of the entered image points in millimeters, the factor of reduction/magnification; the output data is the STL file (Stereolithography file).

In a further advantageous realization the original body is a body well approximable by a sphere with a diameter of 100 - 350 mm, more advantageously a human head; a sphere is generated as a virtual body narrowly enveloping the image points, its center is selected as the C fictive center of the approximating body, sectioning is done using pyramids having C as a common vertex and fitting together with planar side faces where the sides of the pyramids intersect the spherical surface in a manner similar to geographic parallels and longitudinals.

In a further advantageous realization the geometrical center of gravity is calculated from the image point data for every spatial region, the image point nearest to it is selected and connected with the other such points in the neighboring regions to define triangles that construct the rough mesh.

In a further advantageous realization fictive image point Q for an oversized triangle is created in the second cycle through performing operations on real image points, by intersecting line CH containing the center point C and the point H contained by the oversized triangle with a continuous differential surface fitted onto the vertices of the oversized triangle and the neighboring triangles. The procedure according to the invention is explained through figures Figure 1 Illustration of the processing of image point P Figure 2 Illustration of edge replacement

Figure 3 Illustration of the adoption of fictive image point Q in the second cycle Figure 4 Flowchart of the procedure

Figure 1 illustrates a portion of the actual spatial mesh during the adoption of a new image point. P_j is the selected image point, C is the fictive center of the spatial mesh, T| is the triangle first intersected by line P_jC. Intersection point D is considered to be contained in triangle T_t if D is no closer to any of the sides of the triangle than distance d₀, where d₀ is expediently 10 % of the shortest side of T|. Using d₀ we can set which image points close to each other to consider significantly different data and which to consider only an interfering effect of movement. In the first cycle of the procedure image point P_j is set aside if the distance between P_j and Ti is greater than the predefined distance d_1t where the distance of a point from a triangle is understood to be the smallest line segment that can be found between point P_j and any point of the triangle TV, di is a parameter characteristic of the cycle, expediently 2%d<d₁<5%d. In the third cycle of the procedure image point P_j is definitively set aside if the distance between P_j and T. is greater than the predefined distance d₃, where d₃ is a parameter characteristic of the cycle, expediently 1%d<d <3%d. Distances d₁ and d₃ enable keeping prominently incorrect data from being adopted and triangles too pointed for the measurements of the body to be created. If image point P_j is close enough to triangle T| and the intersection point is contained by T| then a tetrahedral pyramid is created using point P_j as a vertex and the intersected triangle T_t as a base, and the triangle faces incident on vertex P_j are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while triangle T₍ is discarded. Vertex ordering is set in a way that it yields a normal vector pointing outside the body, this important piece of information can be stored by fixed vertex listing order. Figure 2 illustrates edge replacement in neighboring triangles of the actual spatial mesh that may be needed to have a spatial mesh made of triangles having edges as short as possible. Let Pj be a newly adopted image point; P1P2P3 is the triangle neighboring the triangle discarded upon adoption in the spatial mesh. Triangles P₁P₂P₃ and PιP₃P_j appearing in the actual spatial mesh are replaced in the spatial mesh by triangles PιP₂P_j and P₂P₃P_j if distance P₂P_j is smaller than distance P_tP₃. Thus the same image points now construct smaller triangles thereby making the body defined by the spatial mesh appear less angular.

Figure 3 illustrates densification of the spatial mesh with fitting fictive image points in the second cycle in the case of oversized triangles.

C is the fictive center of the body, T_k is a triangle in the actual spatial mesh having an edge longer than the predefined distance d or an area larger than the given area t₂. Parameters d₂ and t₂ are characteristic of the cycle, expediently 1%d<d₂<10%d and t₂=^s0,1%d² respectively; with regard to d, the diameter of the body.

Let us select point D inside triangle T_k, and generate the continuous (expediently polynomial) surface F based on calculations with coordinates to include the vertices of triangle T_k and its neighboring triangles. Intersecting line CD with surface F results in intersection point Q, which is a point well adoptable at T_k-nέl as a fitting fictive image point.

Notations in Figure 4. the flowchart of the procedure: 1 , Scanning / data recording 2, Data retrieval

3, Rough mesh

3A, Sectioning into regions 3B, Mesh generation

4, First cycle 4A, Selection of unprocessed image point

4B, finding a nearby triangle 4C, is it within d,? 4D, is it within d₀?

4E, Adoption of point with tetrahedral pyramid construction and triangle replacement

4F, Investigation of the neighboring triangles of the spatial mesh 4G, Edge replacement

5, Second cycle

5A, Search for triangles with great edge lengths or areas 5B, Insertion of fictive image point

6, third cycle 6A, Selection of unprocessed image point

6B, finding a nearby triangle

6C, is it within d₃?

6D, is it within d₀?

6E, Adoption of point with tetrahedral pyramid construction 6F, Investigation of the neighboring triangles of the spatial mesh

6G, Edge replacement

7, Reduction/magnification

8, Data output to file / recording

9, Printing / plotting

The procedure according to the invention fits the goals set and has the advantage over previously known methods of preparing sculptures and copies of producing a display that does not only provide a spatial effect but is also really tactile. The procedure is completely automatic, not even the reparatory steps require outside control. The procedure may also be applied to prepare a copy based on previously recorded data, or in a way where the data survey, the preparation of the data file describing the virtual copy, and the construction of the body take place in geographical locations very far from each other. The efficacy of the procedure is illustrated through the intermediate results of a concrete copying process:

As the procedure can be regarded as the spatial equivalent of photography it is suited to be widely spread and utilized. Its most direct potential use is the preparation of a sculpture of a living human head using fully automatic technology.

Claims

PATENT CLAIM

1. Automatic method for the preparation of a statue-like copy of a body comprising the preparation of a virtual copy based on the generation and recursive modification of a spatial mesh from the digitally recorded data of image points of the original body surveyed from multiple directions - using an apparatus that is in itself known - and the production - using an apparatus that is in itself known- of a tactile copy based on the digital data file characterizing the mesh, provided that during the image editing algorithm: - a narrowly enveloping virtual body containing the virtual center C is generated based on the image point data, and that the unordered set of image points is divided into spatial regions;

- a point is selected in each of the spatial regions and a rough spatial mesh of triangles defining an approximating body is generated by connecting the thus selected points of all of the neighboring spatial regions;

- the virtual copy is created in three cycles using recursive processing of the image point data and refining of the spatial mesh where the data and vertex ordering of the triangles of the actual spatial mesh are stored;

- in the first updating cycle all thus far unprocessed P points are examined to see whether line PC intersects a triangle face in its own or a neighboring region of the actual spatial mesh and whether it is inside of a predefined di distance from it - if it does not fulfill these requirements it is set aside. If it does, a new tetrahedral pyramid is constructed using point P as a vertex and the intersected triangle as a base, and the triangle faces incident on the vertex are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while the base triangle is discarded;

- in the second updating cycle the triangles listed in the actual spatial mesh are examined to see whether there are triangle edge lengths greater than a predefined d₂ distance; if such are found Q fictive image point is generated using the data of the oversized triangle and its neighbors sharing an edge with it and a new tetrahedral pyramid is then constructed using the fictive point Q as a vertex and the oversized triangle as a base, and the triangle faces incident on the vertex are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while the base triangle is discarded;

- in the third updating cycle all P image points set aside are examined to see whether line PC intersects a triangle face in its own or a neighboring region of the actual spatial mesh and whether it is inside of a predefined d₃ distance from it - if it does not fulfill these requirements it is definitively set aside - if it does, a new tetrahedral pyramid is constructed using point P as a vertex and the intersected triangle as a base, and the triangle faces incident on the vertex are adopted with a suitable vertex ordering into the spatial mesh and the table describing it while the base triangle is discarded;

- should it be desired the virtual created copy is reduced/magnified by a predefined scale after the third cycle by carrying out operations on the digital data series describing the actual spatial mesh, then the data file of the desired format ready for direct automatic processing is generated for storing or producing a hard copy.

2. The procedure according to claim 1. provided that the input of the image editing algorithm is: the three-dimensional Descartes coordinates of the surveyed image points in mm, the scale of magnification/reduction; the output is a Stereolithography file.

3. The procedure according to claim 1. or 2. provided that the original body has a diameter of 100 - 350 mm and is well approximable by a sphere; a sphere is generated to narrowly envelope the image points, it center point is chosen as the C fictive center point of the approximating body; the sectioning into spatial regions is done using pyramids having C as a common vertex and fitting together with planar side faces where the sides of the pyramids intersect the spherical surface in a manner similar to geographic parallels and longitudinals.

4. The procedure according to any of claims 1 - 3. provided that the geometrical center of gravity is calculated from the image point data for every spatial region, the image point nearest to it is selected and connected with the other such points in the neighboring regions to define triangles that construct the rough mesh.

5. The procedure according to claim 1. provided that fictive image point Q for an oversized triangle is created in the second cycle through performing operations on real image points, by intersecting line CH containing the center point C and the point H contained by the oversized triangle with a continuous polynomial surface fitted onto the vertices of the oversized triangle and the neighboring triangles.