JPH09134447A - Multidimensional volume data display method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To shorten the processing time for lay-casting by generating writing address and reading address by using a specified expression. SOLUTION: In this multidimensional volume data display method in which n-dimensional volume data is read from storage space to a cache memory in accordance with a determined reading address and the video of the n- dimensional solid within an observation area is displayed based on read n- dimensional volume data v, the writing address and the reading address are generated by using an expression. In the expression, Ij ,k shows the kth-bit of Ij , Ij shows the coordinate value = [Ij ,n-1 Ij ,n-2 ...Ij ,1 Ij ,0 ] along the jth axis of the axis constituting an n-dimensional coordinate system and n shows integrs of >=2, j shows natural numbers satisfying 0<=j<=n-1, k shows natural numbers satisfying 0<=k<=m-1, m shows natural numbers corresponding to the power of 2 and [.] shows the binary number obtained by arranging arguments in the entered order.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention generally relates to a multi-dimensional volume data display method for displaying an image on a screen based on n-dimensional volume data given in an n-dimensional space.

[0002]

2. Description of the Related Art Generally, an array of data obtained in an n-dimensional space is called an n-dimensional data array. Further, an n-dimensional data array of physical quantities relating to the observation area in the n-dimensional space will be referred to as n-dimensional volume data in the present application. This observation area is set so as to include an n-dimensional solid (in this application, an object existing in the n-dimensional space) to be observed. That is, the n-dimensional volume data includes information about the n-dimensional object in the observation area.

As an example of n-dimensional volume data of n = 3, that is, three-dimensional volume data, there are data on the affected part state in the living body, blood flow, etc., and data on fluid flow etc. The former is data obtained by medical-related devices such as X-ray CT, MRI, and ultrasonic diagnostic equipment, and based on this, images of the affected area etc. are displayed (visualized) on a two-dimensional screen such as a CRT in an easy-to-see manner. , Doctor's diagnosis,
It can contribute to the accuracy and speed of treatment. The latter is data obtained by scientific and technological calculations such as fluid analysis, and based on this data, it is possible to contribute to understanding and analysis of physical phenomena by visualizing the fluid flow on a two-dimensional screen such as a CRT.

An isosurface method is an example of a process for visualizing three-dimensional volume data on a two-dimensional screen. However, this method has a disadvantage in that it has few display functions as compared with the ray casting (ray tracing method) described below, although high-speed processing using dedicated hardware is required. That is, integrated display (display of integrated value of information obtained by data sampling along the line of sight)
Also, the maximum value display (display of the maximum value of information obtained by data sampling along the line of sight) cannot be executed without some modification of the isosurfaceization method itself.

Raycasting is a visualization process on a two-dimensional screen that can be executed by software using a general-purpose workstation, a personal computer or the like without such disadvantages. The basic idea of this method is that, as shown in the upper half of FIG. 1, generally, three-dimensional volume data including physical quantity data relating to a three-dimensional solid (a diseased part in the case of a medical device) is converted into Similar to the above, the idea is to observe from a predetermined viewpoint in a three-dimensional space, and display an image according to the observation result information on a two-dimensional screen arranged so as to cross the line of sight (ray) during this observation. . The constituent elements of the three-dimensional volume data are called voxels, and the value of the data in the voxels is simply called a voxel value.

As an example of the display method on the two-dimensional screen, there is a method shown in the lower half of FIG. In this method, voxel values are sampled along the ray and the resulting voxel values are thresholded. The position of a voxel whose voxel value exceeds the threshold can be regarded as (one of) the surface of the three-dimensional solid included in the three-dimensional volume data. Therefore,
The surface of a three-dimensional solid can be detected by performing a similar threshold determination on a large number of rays that are radially emitted from a single viewpoint. On the two-dimensional screen arranged as shown in the upper half of FIG. 1, the luminance is normalized according to the distance (Z value) from the viewpoint to the surface of the three-dimensional solid, that is, the farthest point on the surface is dark and By displaying the surface of the three-dimensional solid in shades with the brightness determined by the linear conversion of the Z value so that the closest point becomes bright, the three-dimensional solid can be displayed on the two-dimensional screen in an easy-to-see manner. Display methods that can be easily executed by ray casting include integrated display and maximum value display in addition to this method.

FIG. 2 shows an example of a ray casting execution environment. In the example of this figure, the three-dimensional volume data is stored in the main memory 20. CPU
10 performs ray casting on the volume data on the main memory 20. In this figure, the CPU 10 is shown as a functional part for executing display based on the Z value.
11 to 13 are shown inside (these may be hardware or software).
3D DDA (Digital Differential Analysis) 11
Determines the position of a voxel that intersects from the time the ray enters the three-dimensional volume data to the time it passes through based on the ray direction. The sampling unit 12 samples the value of the voxel at the obtained position, and the CPU 10
In the internal cache memory 14. The shading unit 13 uses the above-described 3 when the surface of the three-dimensional solid is displayed in gray scale based on the sampled voxel value.
Simulates the shadows that may be caused by the unevenness of a 3D solid.

By the way, 3 in the main memory 20
The address of the dimensional volume data is generally an integer, whereas the voxel position obtained by the three-dimensional DDA generally has a fractional part. Therefore, the accuracy of sampling varies depending on how the fractional part of the voxel position obtained by the three-dimensional DDA is handled at the time of sampling. The simplest sampling method is 3D DDA
The point sampling is for sampling the voxel value at the position obtained by or by the position closest thereto, but this method causes an error due to rounding of the decimal part.
Compared to point sampling, tri-linear interpolation in which the values of 2 ³ = 8 voxels in the vicinity of the position obtained by the three-dimensional DDA are read from the main memory 20 to the CPU 10 and linearly interpolated along each axis of the three-dimensional space High accuracy.

FIG. 3 shows the principle of trilinear interpolation. In this figure, a three-dimensional space that can be represented by three axes Ir, Iθ, Iψ is considered, and the point to be sampled is represented by (Ir, Iθ, Iψ), and this point (Ir, I
The physical quantity data of θ, Iψ) is represented by g, and the voxel values of eight neighboring voxels located at the vertices of a cube or a rectangular parallelepiped surrounding this point (Ir, Iθ, Iψ) are represented by g0 to g7, respectively. ing. What is trilinear interpolation?

[Mathematical formula-see original document] g01 = g0 * dr1 + g1 * dr0 g23 = g2 * dr1 + g3 * dr0 g45 = g4 * dr1 + g5 * dr0 g67 = g6 * dr1 + g7 * dr0 (2) Linear interpolation is executed along the Ir axis according to the formula

## EQU00003 ## g0145 = g01 * d.theta.1 + g45 * d.theta.0 g2367 = g23 * d.theta.1 + g67 * d.theta.0 (3) Linear interpolation is performed along the I.theta.

G = g0145 * dψ1 + g2367 * dψ0 (4) A process of estimating the physical quantity data g at the point (Ir, Iθ, Iψ) to be sampled by performing linear interpolation along the Iψ axis according to the formula (4). Is. However, dr
1, dr0, dθ1, dθ0, dψ1 and dψ0 are points (I) on each side of a cube or a rectangular parallelepiped used for trilinear correlation.
r0, Iθ, Iφ) coordinate values, g0
1 to g67, g0145 and g2367 are interpolation values obtained in the intermediate process of trilinear interpolation.

[0010]

Problems to be Solved by the Invention and Principles for Solving Problems The three-dimensional volume data to be subject to ray casting is usually data having a very large amount of information. For example, 3
When performing raycasting on dimensional volume data, typically more than a few megabytes of data must be handled. This causes a long processing time, and the user strongly requests to shorten the processing time.

The inventor, in order to solve such a problem,
A study was conducted as to which of the ray casting processes is the process that occupies a long processing time. As a result, it became clear that it takes a long time to sample the three-dimensional volume data, and this tendency is the same for the point sampling and the trilinear correlation. Tables 1 and 2 and FIG. 4 show the measurement results of the treatment time under the conditions shown in the margin of Table 1, and FIG. 5 shows the results obtained by converting the results into the treatment time ratio. As is clear from these tables and figures, the time required for sampling occupies more than half of the total processing time of ray casting regardless of whether point sampling or trilinear correlation is used.

[0012]

[Table 1]

[Table 2] The inventor next examined the cause of the long sampling time. That is, the inventor examined the change in processing time due to the change in the line-of-sight direction under the conditions shown in Table 3. Table 4 and FIG. 6 show the results of measuring the change in the processing time depending on the ray direction in the conventional address structure (FIG. 7). As is clear from Table 4 and FIG. 6, the processing time depends on the ray direction in both the point sample and the trilinear interpolation. What becomes clear from this is that when the three-dimensional volume data to be processed is read from the storage space, a mistake (cache error) in data transfer from the storage space (for example, the storage space provided by the main memory) to the cache memory. (Missing) is likely to occur, so it takes time for sampling.

[0013]

[Table 3]

[Table 4] As a cause of the sampling time depending on the ray direction, firstly, a problem in the address structure has been revealed.
That is, when storing the above-mentioned three-dimensional volume data in the main memory, conventionally, the voxel value of the voxel at the position (x, y, z) is set to the address a = x + on the main memory.
Since the data is stored in n · y + n · n · z, the block (storage area including a plurality of consecutive addresses) on the cache memory forms an elongated rectangular parallelepiped on the three-dimensional volume data as shown in FIG. Was. Under such an address structure, if the longitudinal direction of the rectangular parallelepiped corresponding to the block does not match the ray direction, cache misses frequently occur. The second cause of the cache miss has been clarified. Since the read address a is generated along a single ray, the longitudinal direction of the rectangular parallelepiped corresponding to the block coincides with the ray direction. This means that cache misses are more likely to occur when there is no cache.

A basic point of view of the present invention and an object of the present invention are to store n-dimensional volume data to be processed by improving an addressing method or structure when executing n-dimensional data processing such as ray casting. It is to meet the user's request to reduce the processing time by suppressing the occurrence of cache miss from the storage space.

[0015]

Means for Solving the Problems and Effects of the Invention In order to achieve such an object, the present invention provides n-dimensional volume data v whose position is described by n-dimensional coordinates in an n-dimensional space, A viewpoint for observing the observation area in the n-dimensional space and a screen that crosses a ray from the viewpoint to the observation area according to a writing address determined according to the coordinate value, The n
It is defined in a three-dimensional space, its n-dimensional coordinate values are obtained with respect to the points constituting the portion penetrating the observation region of the ray, the read address is determined according to the obtained n-dimensional coordinate value, and the read address is determined according to the determined read address. In the multidimensional volume data display method of reading the n-dimensional volume data v from the storage space to the cache memory and displaying the image of the n-dimensional solid in the observation area based on the read n-dimensional volume data v, the write address and The read address is generated by using the following equation (5).

[0016]

## EQU5 ## a = [I _{n-1, m-1} I _{n-2, m-1} ... I _{0, m-1} I _{n-1, m-2} I _{n-2, m-2} ... I _{0, m-2} ... I _n-1,1 I _n-2,1 I _0,1 I _n-1,0 I _n-2,0 I _0,0 ] (5) where I _{j, k} : the k-bit I _j, I _j: coordinates along the j-th axis of the shaft constituting the n-dimensional coordinate system _{= [I j, m-1} I j, m-2 ... I j, 1 I j, ₀ ] n: integer of 2 or more, j: natural number satisfying 0 ≦ j ≦ n−1, k: natural number satisfying 0 ≦ k ≦ m−1, natural number corresponding to power of m: 2, [·]: A binary number obtained by arranging its arguments in the order they are listed.

According to this structure, a plurality of data v occupying an n-dimensional cube or an area close thereto in the n-dimensional space.
Are written in the storage space so as to be stored in the same block on the cache memory (n-dimensional localization of the address a). Therefore, when accessing the storage space along a ray, even if the ray is not parallel to any coordinate axis in the n-dimensional space, mistakes regarding access from the storage space are unlikely to occur. Therefore, the hit rate related to the access is improved, and the processing time is shortened. Further, since the process of generating the address a is a process of rearranging the bits forming each coordinate value I ₀ , I ₁ , ..., I _n-1 , the wiring is simply performed to implement this configuration in hardware. You can set the order of. That is, this configuration is relatively easy to implement in terms of hardware.

In the multidimensional volume data display method according to the second configuration of the present invention, in the first configuration, the calculation of the n-dimensional coordinate value, the determination of the read address, and the readout of the n-dimensional volume data are mutually performed. The present invention is characterized in that a plurality of adjacent rays are executed simultaneously or in parallel. According to this configuration, since the access is also localized in the n-dimension, an access miss is further unlikely to occur, the hit rate is improved, and the processing time is shortened.

In the multidimensional volume data display method according to the third configuration of the present invention, in the first or second configuration, the n-dimensional volume data v read from the storage space is subjected to trilinear interpolation, and then the above-mentioned method is applied. Characterized by being used for video display. According to this configuration, good accuracy can be obtained by trilinear interpolation. In addition, since the probability that the voxel to be accessed in Trilia interpolation belongs to a single block is increased, the processing time is further shortened.

[0020]

BEST MODE FOR CARRYING OUT THE INVENTION Preferred embodiments of the present invention will be described below with reference to the drawings. Since the present invention can be applied to ray casting regarding three-dimensional volume data, the following description is based on the apparatus and method shown in FIGS. 1 to 3, but the present invention is generally n.
It can be applied to dimensional volume data (n is an integer of 2 or more). For example, it can be applied to 3 × 3 filter processing in image processing.

FIG. 8 shows an address structure when the present invention is applied to three-dimensional volume data. That is, in the embodiment of FIG. 8, the three-dimensional volume data is written in the main memory 20 in advance according to the address a generated by using the following equation (6) according to the coordinate values (X, Y, Z). The address a is generated by the same equation when read. Since such an address structure is employed, in the present embodiment, one block of the cache memory 14 corresponds to a cube or a rectangular parallelepiped close to this in the three-dimensional volume data. 3 of such addresses
As a result of the dimensional localization, a situation in which a cache miss is likely to occur depending on the ray direction is less likely to occur. Furthermore, since the probability that 8 neighboring points belong to the same block increases, the speed can be further increased by combining with the trilia interpolation.

[0022]

A = [Z _m-1 Y _m-1 X _m-1 Z _m-2 Y _m-2 X _m-2 ... Z ₁ Y ₁ X ₁ Z ₀ Y ₀ X ₀ ] (6) _{, X = [X m-1} X m-2 ... X 1 X 0] Y = [Y m-1 Y m-2 ... Y 1 Y 0] Z = [Z m-1 Z m-2 ... Z 1 Z ₀ ] 2 ^m is the length of one side of the volume data Further, in the present embodiment, the access at the time of reading is also localized three-dimensionally. That is, as shown in FIG.
Since access is performed in a ray bundle including a plurality of rays that are adjacent to each other (side by side with respect to each ray forming the ray bundle), the same or adjacent blocks are simultaneously or consecutively accessed. (Three-dimensional localization of access), and as a result, a situation in which a cache miss is likely to occur depending on the ray direction is unlikely to occur.

[Brief description of the drawings]

FIG. 1 is a conceptual diagram showing the principle of ray casting.

FIG. 2 is a block diagram showing an example of an environment for performing ray casting.

FIG. 3 is a spatial diagram showing the principle of trilinear interpolation.

FIG. 4 is a diagram showing a time required for sampling processing in comparison with other processing times.

FIG. 5 is a diagram showing a ratio of a time required for sampling processing to a total processing time.

FIG. 6 is a diagram showing a change in sampling time due to a change in a ray direction.

FIG. 7 is a conceptual diagram showing a conventional address structure.

FIG. 8 is a conceptual diagram for explaining three-dimensional localization of addresses according to an embodiment of the present invention.

FIG. 9 is a conceptual diagram for explaining the three-dimensional localization of access in this embodiment.

[Explanation of symbols]

 10 CPU, 20 main memory.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Shoji Ishikawa 5-1-1 Shimorenjaku, Mitaka-shi, Tokyo Within Japan Radio Co., Ltd. (72) 5-1-1 1-1 Shihrenjaku, Mitaka-shi, Tokyo Inventor Incorporated (72) Inventor Kengo Toeda 5-1-1 Shimorenjaku, Mitaka-shi, Tokyo Within Japan Radio Co., Ltd.

Claims (3)

[Claims] 1. The n-dimensional volume data v, the position of which is described in n-dimensional coordinates related to an n-dimensional space, is written in a storage space in accordance with a write address determined according to the coordinate values, and the n-dimensional volume is written. A viewpoint for observing an observation region in space and a screen that crosses the line of sight from the viewpoint to the observation region are defined in the n-dimensional space, and a portion of the line of sight that penetrates the observation region is defined. The n-dimensional coordinate values of the constituent points are determined, the read address is determined according to the determined n-dimensional coordinate value, the n-dimensional volume data v is read from the storage space to the cache memory according to the determined read address, and the read n-dimensional volume is read. A multidimensional volume data display method for displaying an image of an n-dimensional solid in the observation region based on the data v, Multidimensional volume data display method characterized in that the write address and the read address, generated using the following equation (1). ## EQU1 ## a = [I _{n-1, m-1} I _{n-2, m-1} ... I _{0, m-1} I _{n-1, m-2} I _{n-2, m-2} ... I _{0, m-2} ... I _n-1,1 I _n-2,1 I _0,1 I _n-1,0 I _n-2,0 I _0,0 ] (1) where I _{j, k} : the k-bit I _j, I _j: coordinates along the j-th axis of the shaft constituting the n-dimensional coordinate system _{= [I j, m-1} I j, m-2 ... I j, 1 I j, ₀ ] n: integer of 2 or more, j: natural number satisfying 0 ≦ j ≦ n−1, k: natural number satisfying 0 ≦ k ≦ m−1, natural number corresponding to power of m: 2, [·]: A binary number obtained by arranging its arguments in the order they are listed. 2. The method according to claim 1, wherein the calculation of the n-dimensional coordinate value, the determination of the read address, and the reading of the n-dimensional volume data are performed simultaneously or in parallel with respect to a plurality of lines of sight that are close to each other. A method for displaying multidimensional volume data, characterized in that 3. The method according to claim 1, wherein the n-dimensional volume data v read from the storage space.
A method for displaying multi-dimensional volume data, characterized by being used for the above-mentioned image display after being subjected to trilinear interpolation.