JP2001005992A - Method and device for expressing volume data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a display that seems to be desired by a user in an objective manner in the case of making volume data visible. SOLUTION: An equivalent face extracting part 12 extracts an equivalent face string from volume data 50. A critical equivalent face detecting part 14 detects a critical equivalent face being a characteristically equivalent face from the equivalent face string. A hyper-Reeb graph outputting part 16 arranges critical equivalent faces in order of its field value and generates and outputs a hyper-Reeb graph. A conversion function setting part 30 converts a field value into an optical property so as to enhance the critical equivalent face on the basis of the hyper-Reeb graph.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

2. Description of the Related Art Direct volume rendering
A technique for directly visualizing by converting field values of the original data into colors and opacity and integrating them in the line of sight without extracting their geometric features from the volume data that is a multivariate three-dimensional distribution. It is. Volume rendering requires expensive computations while allowing visual search for hidden complex internal structures and dynamic behavior. Therefore, in order to efficiently obtain an image reflecting the intention of the user, it is necessary to reduce the number of times of re-rendering as much as possible.

[0002]

The quality of a volume-rendered image is affected by the definition of a conversion function that converts physical fields of the volume data into corresponding optical properties. The present invention has been made based on such considerations, and an object of the present invention is to provide a technique for expressing volume data in an appropriate method according to its characteristics.

[0003]

According to the volume data expressing method of the present invention, a step of determining volume data to be processed, a step of obtaining phase information of an iso-surface of the determined volume data, and a step of obtaining the phase information And detecting a characteristic isosurface based on the The present invention is applicable not only to three-dimensional distribution data but also to data of any dimension. Hereinafter, when referring to volume data in connection with the present invention,
Shall be construed as such.

[0004] The characteristic isosurface may be such that the phase or structure graph of the isosurface changes at the position. When the volume data changes between,
The characteristic iso-surface may be such that the phase or the structure graph of the iso-surface changes at a certain position at a certain time. That is, in this case, the volume data is treated as four-dimensional data including time. The present invention may further include a step of visualizing the characteristic isosurface.

[0005] The present invention may further include a step of determining a conversion function for converting a physical field of the volume data into a property according to a predetermined purpose, for example, an optical property for visualization. The conversion function may be determined such that the characteristic isosurface is emphasized. The method may further include recording the field value of the volume data in association with the characteristic isosurface. This association may be performed by expressing the field value by one axis and by using a graph showing the position of the characteristic isosurface on the axis.

In the obtaining step, the phase information of a set space of the isosurface determined by giving a width to the field value of the volume data is obtained, and the detecting step is characterized by a characteristic based on the phase information. A set space of the above isosurfaces may be detected. The set space of isosurfaces may be called an interval volume.

Another aspect of the volume data expression method of the present invention is a step of determining volume data to be processed, a step of obtaining a characteristic iso-surface of the determined volume data, Visualizing the value plane.

On the other hand, a volume data expression device of the present invention comprises: a unit for acquiring an iso-surface of volume data;
A unit for acquiring phase information of the isosurface and a unit for detecting a characteristic isosurface based on the phase information are included. These units may be realized by hardware such as a circuit, or may be realized by a software module executed by a device such as a CPU. The present invention may further include a unit for visualizing the characteristic isosurface, and may further include a unit for determining a conversion function for converting a physical field of the volume data into a property according to a predetermined purpose.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In shape modeling using a computer, a surface is often understood and designed by characteristic edges and vertices. The present inventor thought that a characteristic surface called a critical isosurface described later can deepen the understanding of the phase structure of volume data. The embodiment provides a technique of converting the analysis result of the phase structure of a volume field based on a critical iso-surface into a new expression called a hyper-reave graph, and improving the conversion function based on the content. Hereinafter, this embodiment does not limit the contents of the present invention.

FIG. 1 shows a volume data expression device 100.
FIG. The volume data expression device 100 mainly includes a hyper-reve graph generation unit 10 for generating a hyper-reve graph described later, and a conversion function setting unit for setting a conversion function based on the hyper-reve graph generated by the hyper reve graph generation unit 10. 30; a visualization unit 36 for visualizing volume data using a set conversion function; and a user interface 40 for giving user instructions to those units.

The hyper-reve graph generating unit 10 receives the volume data 50 and extracts an iso-surface from the iso-surface extracting unit 12, and a threshold for detecting a critical iso-surface from the output 52 of the iso-surface extracting unit 12. It includes an iso-surface detection unit 14 and a hyper-reve graph output unit 16 that outputs a hyper-reve graph with reference to the output 54 of the critical iso-surface detection unit 14. Also,
The critical iso-surface detection unit 14 includes a Reeb graph generation unit 20 that generates a Reeb graph described later, and a height direction setting unit 22 that sets a height direction to be determined at that time.

The conversion function setting unit 30 receives the output 56 of the hyper-reve graph output unit 16 and sets a hue setting unit 32 for setting a hue operation as a conversion function and a hue setting unit 32 for setting an opacity operation similarly. A transparency setting unit 34 is included. The output 56 of the hyper-reve graph output unit 16 and the output 60 of the conversion function setting unit 30 are data storage 4
2 is stored. The data storage 42 may exist outside the volume data expression device 100. Also, as to those skilled in the art, there is considerable freedom as to which unit is inside or outside the volume data expression device 100.

The output 60 of the conversion function setting unit 30 is provided to a visualization unit 36, where necessary processing for visualization is performed, and a desired image is displayed on the display device 38. Here, the concept necessary for understanding the operation will be described.

Reeb graph In general, terrain can be recognized by a peak, a pit, and a pass. The top is locally higher than the surroundings, the bottom is also lower than the surroundings,
A pass is also called a saddle point, which is the highest point in one direction and the lowest point in the other direction. These points are collectively called critical points.

As a method of expressing the relationship between the critical points,
A structural graph called a Reeb graph in a topology is known. The Reeb graph is a graph in which the surface of an object is represented by a group of contour lines along an axis that gives a height direction, and a connected component of each contour line is given as one point. A connected component is a physically connected part.

FIG. 2 shows a torus or donut, and FIG. 3 shows a group of contours of the torus. FIG.
Is the Reeb graph of the torus. Here, it is assumed that the height direction is given by an axis substantially parallel to the long axis of the torus. At this time, the torus shown in FIG.
6 and a first pass 202 near the top 200 and a second pass 204 near the bottom 206, for a total of four critical points. FIG.
Are a loop between the top 200 and the first pass 202, and between the second pass 204 and the bottom 206, and two loops between the first pass 202 and the second pass 204. It becomes a loop.

As shown in FIG. 4, in a place where the contour line group forms one loop, since there is only one connected component, the Reeb graph consists of one edge, that is, an edge. on the other hand,
Where the contour group consists of two loops, there are two connected components, and the Reeb graph is divided into two edges. Thus, the Reeb graph represents the topological "skeleton" of the object.

Consider the modeling of the distribution structure of field values in critical iso-surface volume data. First, the target volume data is decomposed into isosurface arrays according to the field values. Next, the topological skeleton of each isosurface is represented by a Reeb graph.
Then, while gradually increasing or decreasing the field value, a phase value of the isosurface or a field value at which the Reeb graph changes (hereinafter referred to as a critical field value) is detected, and the isosurface corresponding to the critical field value is detected. It is named Critical Iso-surface (Critical Iso-surface).

Nodes corresponding to the minimum value, the critical field value, and the maximum value of the hyper-reve graph field data are prepared, and these nodes are connected linearly in the order of the field values. Thus, an upper graph is obtained. Next, a Reeb graph of an isosurface corresponding to the field value is associated with each node. Similarly, the Reeb graph is associated with the edge.

The operation of the volume data expression device 100 will be described based on the above definitions.

FIG. 5 shows the volume data expression device 100.
It is a flowchart which shows a process. At the start of processing
First, target volume data is determined (S1).
0). Here, hydrogen is used as the volume data to be processed.
Consider the three-dimensional charge density distribution of a molecule. The distribution ρ is
It is expressed by an equation. ρ (r (x, y, z)) = (a^Two(rA) + b^Two(rB) + 2sa (rA) b (rB)) /
(2 + s^Two) S = (1 + δR + (δR)^Two/ 3) e^-δR  a (rA) = (δ^Three/ Π)^1/2 e^{−δ | rA |} b (rB) = (δ^Three/ Π)^1/2 e^{−δ | rB |}  Where R and δ are constants

The iso-surface extraction unit 12 inputs volume data 50 corresponding to this distribution (S12), and extracts an iso-surface for its field value, that is, the charge density (S12).
14). FIG. 6 shows the extracted isosurfaces 300, 302, 30.
4, 306 and 308 are shown.

The critical iso-surface detector 14 is provided with an iso-surface extractor 12
, The height direction of the Reeb graph is first set in the height direction setting unit 22. Here, it is assumed that the height direction is set substantially perpendicular to the direction connecting the atoms of the hydrogen molecules. The Reave graph generation unit 20 acquires the phase information of the iso-surface according to the height direction.
The phase information is shown in the form of a Reeb graph (S16). The Reeb graph generation unit 20 further detects an isosurface where a change occurs in the shape of the Reeb graph when the charge density is changed, as a characteristic isosurface, that is, a critical isosurface (S18).

A hydrogen molecule is composed of two hydrogen atoms, and the closer to each atomic nucleus the higher the charge density. Therefore, there are two isosurfaces in the region where the charge density is highest. This state is maintained just before the critical isosurface 306, and the critical isosurface 30
At 6, the two isosurfaces join at one point. The output 54 of the critical iso-surface detection unit 14 includes information on the critical iso-surface and information on the shape of the Reeb graph constant between the critical iso-surfaces.

Subsequently, the hyper-reve graph output unit 16
Receives the output 54 of the critical iso-surface detector 14 and generates a hyper-reve graph (S20). FIG. 7 is a generated hyper-reve graph. Since the distribution of the charge density is infinite, the minimum and maximum field values are introduced here for convenience. In the figure, the minimum field value is V1,
The critical field value is represented by V2 and the maximum field value is represented by V3, and one upper graph 330 having three nodes V1, V2, and V3 is provided. Field values corresponding to the node are shown in parentheses next to the node. The nodes of the maximum and minimum field values generated due to the finite volume area are represented by white nuclei to distinguish them from the true critical isosurface.

A corresponding Reeb graph is associated with each node of the upper graph 330 and each edge between the nodes. From the node V1 to just before the node V2, the Reeb graph of the isosurface is composed of one side, so the Reeb graphs 340 and 342 each composed of one side are drawn at the edge connecting the node V1 and the nodes V1 and V2. Have been. At the node V2, as can be understood from the contour line group as shown in FIG. 3, there are two connected components, that is, two loops where the height is large and where the height is small, and there is one loop at a certain point between them. Therefore, the Reeb graph 344 of the node V2 takes the form of “X”. Immediately after the node V2 to the node V3, since the Reeb graph of the isosurface includes two sides, the nodes V1 and V2
And the node V3 are drawn with Reeb graphs 346 and 348 each having two sides.
The generated hyper-reve graph is provided to the data storage 42 as an output 56 of the hyper-reve graph output unit 16. As described above, the internal schematic structure of the volume data can be grasped more easily than the original distribution formula by drawing the hyper-reve graph.

The output 5 of the hyper-reve graph output unit 16
6 is also given to the conversion function setting unit 30. The conversion function setting unit 30 sets a conversion function that emphasizes the critical isosurface based on the generated hyper-reve graph (S2).
2). Here, the hue setting unit 32 and the opacity setting unit 34
Performs the following processing with the critical isosurface as a boundary.

[Setting 1] Make the conversion function to hue discontinuous at the critical field value [Setting 2] Increase the conversion function value to opacity slightly near the critical field value [Setting 3] Combine

FIGS. 8 and 9 show graphs of conversion functions to hue and opacity, respectively. The x-axis is the field value, and the y-axis is the hue and opacity, respectively. The field value, hue, and opacity are all normalized to [0, 1].

First, assuming that αi is a critical field value and βi is the hue value of the hue, α0 = 0 αk ≦ x <αk + 1 y = (βk + 1−βk) / (αk + 1−αk) ) X + (αk + 1βk−
The hue can be linearly changed by αkβk + 1) / (αk + 1−αk). Suppose there are N critical isosurfaces, the rate of change and the increment a of the hue value at the critical field value are constant, and α0 = 0, β0 = 0, βn
If = 1, the hue y of the field value x can be represented by the following equation. y = (1-Na) x + ia where 0 <a <N ⁻¹ , αi <x <αi + 1, i = 0,1,
.. N Although a linear change is considered here, this may of course be a non-linear change.

On the other hand, with respect to the opacity, a method of slightly projecting by δ1−δ0 near the critical field value and adopting a constant value δ0 can be adopted for the other opacity. However, there are various modified examples. The conversion function thus set is provided to the data storage 42 as an output 60 of the conversion function setting unit 30.

The visualizing unit 36 receives the output 60 of the conversion function setting unit 30 and the volume data 50, visualizes the volume data, and displays it on the display device 38 (S2).
4).

FIG. 10 shows a display obtained for the volume data (64 × 64 × 64 voxels) of the three-dimensional charge density distribution of hydrogen molecules. In this figure, the critical isosurface 400
Is highlighted. In addition, a portion 402 corresponding to an isosurface outside the portion is schematically drawn in a light color.
In practice, the outer edge of this part will be blurred. This figure also makes it easier to understand the features of the three-dimensional charge density distribution of the hydrogen molecules, and shows the usefulness of the embodiment.

In addition to the three-dimensional charge density distribution of hydrogen molecules, a two-dimensional scalar field called a Cartesian regular leaf shape (Folium of Descartes) is uniquely expanded in three dimensions (100 × 100 × 100 volume). Voxel). Field values are defined as follows:

F (x, y, z) = ((x ³ + y ³ + 3z ² (x
+ Y + 1) / 2-3xy) / 92 + 1/2 where | x, y, z | ≦ 2

If the height axis is set so as to pass through the critical point, f (x, y, z) = 0.5 becomes the critical field value, and the hyper-reave graph is as shown in FIG. Although the visualization result is omitted because the drawing is difficult, a display that is very easy to understand is obtained.

Similarly, an experiment was conducted on a scalar field called a 3 Blobbies model. This model uses volume data (128 x 1) containing two critical isosurfaces.
28 × 64 voxels). The field value ρ (r) of an arbitrary point r includes three points A (0.17, 0.098, 0.25), B (0.33,
0.098, 0.25), distance from C (0.25, 0.34, 0.25) to rA, r
Assuming B and rC, the following equation can be used. ρ (r) = (a ² (rA) + b ² (rB) + c ² (rC)) / Sa (rA) = e− ^{| rA |} , b (rB) = e− ^{| rB |} , c (rC) = ^{E-| rC |} S = 0.273

The critical field values are 0.70 and 0.89. The hyper-reave graph is shown in FIG. In the above experiments, it has been found that, when the optical properties are determined by the conversion function, generally, the method of changing both the hue and the opacity gives the best result.

Any combination of the functions of the above embodiments may be provided by being recorded on a computer-readable and executable recording medium. In addition, the following modifications or extensions are also possible in the embodiment.

First, here is an example in which the critical iso-surface can be specified by analytical prediction. However, the critical iso-surface may be extracted from volume data obtained by actual simulation or measurement.

Second, the function of the height direction setting unit 22 may be extended to set the height direction interactively. In addition, a user support function that suggests the most effective direction for the visual search from the system side may be added. As an example of automatic setting of the height direction, a direction in which the isosurface of interest is the longest in the height direction may be selected, or a direction in which the number of critical isosurfaces is maximized may be selected. .

Third, the conversion function setting technique according to the embodiment can be directly applied to a volume rendering method based on other principles such as a sputtering method, in addition to a ray-casting method. .

Fourth, the conversion function setting technique according to the embodiment is also effective for indirect volume visualization. Among them, in the widely used isosurface extraction, the critical isosurface can be regarded as the most valuable candidate as a default for starting a visual search.

Fifth, when a plurality of isosurfaces are displayed simultaneously, the critical isosurfaces closest to the isosurfaces are selected as indices for determining the relative opacity values. The distance between them or the section width may be used.

Sixth, even when extracting a solid area in which field values are given an allowable range as a general form of an isosurface, that is, an “interval volume” expressing a set space of isosurfaces, a critical area is also used. The isosurface gives a characteristic boundary surface. With multiple interval-type volumes, each corresponding to a field interval that can be represented by the same Reeb graph,
The given volume data may be automatically segmented.

Seventh, when it is expected that the hyper-reave graph will be complicated to some extent, weights may be added to the critical iso-surface to simplify it. For example, volume data may be described hierarchically using a wavelet transform, a Laplacian pyramid, or the like, and a hyper-reave graph may be extracted from an upper layer. Further, after extracting the isosurface groups, simplification may be performed using a polygon expression.

Eighth, after a hyper-reve graph is obtained, a function of editing the hyper-reave graph may be added.

Ninth, a plurality of hyper-reave graphs corresponding to respective times are searched in the time direction with respect to time-varying volume data such as a collision problem between a hydrogen atom and a proton, and the phase of the isosurface is determined. Alternatively, when the Reeb graph changes over time, its isosurface may be detected as a temporal critical isosurface. This realizes an expression method that can be called a four-dimensional hyper-reave graph.

Tenth, in the embodiment, the volume data is analyzed from the viewpoint of the iso-surface, but this need not necessarily be the iso-surface. Analyzing volume data from a topological viewpoint while paying attention to its field value,
It may be a process of relating the topological features found as a result to the volume data. For example, a function g (x, x) with a field value f (x, y, z)
y, z), a solution may be calculated by gradually changing the function g, and a topologically characteristic solution may be extracted from the shape of the solution. .

[Brief description of the drawings]

FIG. 1 is a configuration diagram of a volume data expression device.

FIG. 2 is a diagram showing a torus.

FIG. 3 is a diagram showing a contour group of the torus.

FIG. 4 is a diagram showing a Reeb graph of the torus.

FIG. 5 is a flowchart showing processing of the volume data expression device.

FIG. 6 is a diagram showing an isosurface of the charge density of a hydrogen molecule.

FIG. 7 is a diagram showing a generated hyper-reve graph.

FIG. 8 is a diagram showing a graph of a conversion function to hue.

FIG. 9 is a diagram showing a graph of a conversion function to opacity.

FIG. 10 is a diagram showing a display obtained for volume data of a three-dimensional charge density distribution of a hydrogen molecule.

FIG. 11 is a diagram showing a hyper-reave graph obtained for a three-dimensional Cartesian regular leaf shape.

FIG. 12 is a diagram showing a hyper-reave graph obtained for a three-blobby model.

[Explanation of symbols]

 REFERENCE SIGNS LIST 10 hyper-reave graph generation unit 12 iso-surface extraction unit 14 critical iso-surface detection unit 16 hyper-reve graph output unit 20 reave graph generation unit 22 height direction setting unit 30 conversion function setting unit 32 hue setting unit 34 opacity setting unit 36 visualization unit 38 display device 40 user interface 42 data storage 50 volume data 100 volume data expression device

Claims (19)

[Claims] 1. A step of determining volume data to be processed; a step of acquiring phase information of an iso-surface of the determined volume data; and detecting a characteristic iso-surface based on the phase information. A method for expressing volume data, comprising: 2. The method according to claim 1, wherein the characteristic isosurface is one in which the phase of the isosurface changes at the position. 3. The method according to claim 2, wherein the volume data causes a temporal change, and the characteristic iso-surface has a phase that changes at a certain position at a certain time. Item 1. The method according to Item 1. 4. The method according to claim 1, wherein the characteristic isosurface is such that the structure graph of the isosurface changes at the position. 5. The volume data causes a temporal change, and the characteristic isosurface is such that the structure graph of the isosurface changes at a certain position at a certain time. The method of claim 1. 6. The method according to claim 1, further comprising the step of visualizing the characteristic isosurface. 7. The method according to claim 1, further comprising a step of determining a conversion function for converting a physical field of the volume data into a property according to a predetermined purpose. 8. The method of claim 7, wherein the property is an optical property. 9. The method of claim 8, wherein the optical properties include hue information. 10. The method of claim 8, wherein the optical properties include information about opacity. 11. The method according to claim 7, wherein the conversion function is determined such that the characteristic isosurface is emphasized. 12. The method according to claim 1, further comprising a step of recording a field value of the volume data and the characteristic isosurface in association with each other. 13. The acquiring step acquires phase information of a set space of an isosurface determined by giving a width to a field value of the volume data, and the detecting step comprises: acquiring the phase information based on the phase information. 13. The method according to claim 1, wherein a characteristic set space of the isosurfaces is detected. 14. A method for determining volume data to be processed, obtaining a characteristic iso-surface of the determined volume data, and visualizing the characteristic iso-surface. A volume data expression method characterized by the following. 15. A unit for acquiring an iso-surface of volume data, a unit for acquiring phase information of the iso-surface, and a unit for detecting a characteristic iso-surface based on the phase information. An apparatus for expressing volume data, comprising: 16. The apparatus according to claim 15, further comprising a unit for visualizing the characteristic isosurface. 17. The apparatus according to claim 15, further comprising a unit that determines a conversion function for converting a physical field of the volume data into a property according to a predetermined purpose. 18. A function of determining volume data to be processed, a function of acquiring phase information of an iso-surface of the determined volume data, and detecting a characteristic iso-surface based on the phase information. A computer-readable recording medium characterized by including a function and a program for causing a computer to execute the function. 19. analyzing the volume data from a topological point of view while focusing on its field values; and associating the topological characteristics of the volume data determined as a result with the volume data. A volume data expression method comprising: