Program for extracting the centerline of a 3D image

Abstract

To extract a center line from three-dimensional image data of a target object and draw a picture.SOLUTION: A power generation source is set which continuously outputs a constant amount of heat in the inside of all voxels representing a target object. In voxels of the outside, a heat absorption source is set which absorbs heat unlimitedly at the temperature of zero degree. The temperatures of all the voxels in a stationary state in which a constant temperature difference is maintained among voxels are calculated by a three-dimensional stationary heat conduction analysis using a finite element method. The temperature differences are read and the voxels are connected together except voxel groups which are hotter than voxels therearound.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present invention relates to a centerline extraction program for extracting and drawing a centerline by arithmetic processing from three-dimensional image data of an object.

Background Art

[0002] For example, the continuous pores formed inside a porous ceramic material, blood vessels inside the human body photographed by MRI, etc. are curved, and their thickness and cross-sectional shape are non-uniform. In order to analyze the state of such objects, the extraction and drawing of these centerlines are performed.

[0003] Various arithmetic processing techniques for extracting a centerline from three-dimensional image data obtained by photographing an object by arithmetic processing of a computer have been introduced (Patent Documents 1 to 4) (Non-Patent Documents 1 to 3).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Non-Patent Documents

[0005]

Non-Patent Document 1

Non-Patent Document 2

[0006] With existing methods as described above, the extracted centerlines can be distorted, especially at branching points of an object or in areas where the object forms a loop. In such cases, it has been difficult to automatically extract a centerline that can be easily perceived from an image of the object. This invention was made to solve these problems. [Means for solving the problem]

[0007] The following configurations are each means of solving the above-mentioned problems.

[0008] <Configuration 1> A centerline extraction device for extracting and drawing a centerline from three-dimensional image data of an object by computational processing, equipped with means for performing the following processes by computer. (a) Obtain a three-dimensional image representing the contour shape of the object, and assume that the entire three-dimensional image is filled without gaps with voxels corresponding to pixels. (b) Heat sources are set up inside all of the above voxels, or at regularly distributed grid points, that continuously emit a constant amount of heat per unit time. (c) The heat from the above heat source may be released in all directions from the center of the voxel. (d) The voxels on the outermost surface of the object and the adjacent external voxels are heat-absorbing sources that are at zero degrees Celsius and absorb heat indefinitely. (e) Calculate the temperature of all voxels when a steady state is reached in which heat exchange occurs between voxels with heat sources and voxels with heat sources, and between voxels with heat sources and other voxels with heat sources, and a constant temperature difference is maintained between each voxel. (f) Read the temperature difference described above and leave the group of voxels that are hotter than the surroundings. (g) Connect the remaining voxel groups that are hotter than the surrounding area in order to draw the center line.

[0009] <Configuration 2> The centerline extraction apparatus according to configuration 1, characterized by repeatedly removing voxels in order from the lowest temperature to the highest temperature, leaving a group of voxels that are higher in temperature than the surrounding area.

[0010] <Structure 3> The centerline extraction device according to configuration 1 or 2, characterized in that it calculates the temperature of all voxels using the thermal diffusion equation when a steady state is reached in which a constant temperature difference is maintained between each voxel.

[0011] <Structure 4> A computer program for centerline extraction that causes a computer to function as the means described in Configuration 1.

[0012] <Composition 5> A computer-readable recording medium on which the computer program described in Configuration 4 is recorded. [Effects of the Invention]

[0013] When extracting a centerline using the phenomenon of heat diffusion, if the cross-sectional shape of an object changes complexly when viewed along its longitudinal direction, changes in the external shape and irregularities do not immediately affect the irregularities of the centerline. Because heat flow occurs not only in the direction outward from the centerline but also along the centerline, the centerline is automatically smoothed. When using the finite element method, the obtained values are approximate values. However, it is only necessary to know the temperature difference (the relationship between the magnitudes) between adjacent voxels. Even when calculating the temperatures of a large number of all voxels, the calculation results can be obtained by a computer within a practical time

Brief Description of the Drawings

[0014] [Figure 1] Figure 1 is an explanatory diagram of the relationship between the object and the voxel group [Figure 2] Figure 2 is an explanatory diagram of the voxel and the heat source [Figure 3] Figure 3 is an explanatory diagram of the voxel on the outer surface of the object and the adjacent external voxel [Figure 4] Figure 4(a) is an explanatory diagram of an example of extracting the center line of an object with little change in the outer diameter. Figure 4(b) is an explanatory diagram of an example of extracting the center line of an object with a rapid change in the outer diameter according to the present invention. Figure 4(c) is an explanatory diagram of an example of extracting the center line of an object by a known method. Figure 4(d) is an explanatory diagram of an example of extracting the center line of a branched portion of an object according to the present invention [Figure 5] Figure 5 is an explanatory diagram of an example of the arithmetic formula used for center line extraction of the present invention [Figure 6] Figure 6 shows a case where the outer shape changes rapidly. (a) is a calculation example by a known method, and (b) is an explanatory diagram of a calculation example according to the present invention [Figure 7] Figure 7 shows a case where there is a bulge in the middle of a blood vessel. (a) is a calculation example according to the present invention, and (b) is an explanatory diagram of a calculation example by a known method [Figure 8] Figure 8 is an explanatory diagram of a calculation model by the finite volume method [Figure 9] Figure 9 is an explanatory diagram of the calculation procedure by the finite volume method (1) [Figure 10] Figure 10 is an explanatory diagram of the calculation procedure by the finite volume method (2) [Figure 11] Figure 11 is an explanatory diagram of the calculation procedure by the finite volume method (3) [Figure 12] Figure 12 is an explanatory diagram of comparing the temperatures of the extracted grid points

Embodiments for Carrying Out the Invention

[0015] The embodiments of the present invention will be described in detail below for each example. [Examples]

[0016] (Object to be analyzed) This extraction program can be used, for example, to extract and plot the centerlines of three-dimensional images of blood vessels in the brain. Other possible targets include rope-like or tubular bodies with non-uniform cross-sectional shapes. Continuous pores formed inside porous ceramic products can also be used as targets. In all cases, plotting the centerlines makes it possible to analyze the characteristics of the target and how they change over time.

[0017] (Extraction of voxels on the center line from a group of voxels) Here, we will proceed with the explanation assuming that the object from which the centerline is extracted is a blood vessel in the brain. Although blood vessels are tubular, their external shape and cross-sectional shape are inconsistent depending on the location, and their curvature and external shape change drastically even when viewed in the longitudinal direction. In this invention, first, a three-dimensional image representing the contour shape of the blood vessel is obtained. Figure 1 shows an example of this image of object 10. The process of extracting its centerline 16 from this image data will be explained.

[0018] Assume that the entire three-dimensional image of object 10 is filled without gaps by voxels 12 corresponding to pixels, as shown in Figure 1. Figure 1 shows an example of a portion of the voxel group extracted. The entire space is filled without gaps by voxels 12, but their illustration is omitted. Here, for example, set the pixel values ​​of all voxels 12 inside object 10 to "1", and set the pixel values ​​of voxels outside object 10 to "0".

[0019] Next, as shown in Figure 2, a heat source 14 is set up inside all voxels 12 with a pixel value of "1" to continuously emit a constant amount of heat per unit time, for example, Q (joules). This heat is assumed to be emitted in all directions from the center of the voxel 12.

[0020] As shown in Figure 3, the voxel 12b adjacent to the voxel 12a on the outermost surface of the object 10 is an external voxel that is at zero degrees Celsius and absorbs heat to an almost zero degree Celsius extent. Because it is adjacent to the heat-absorbing source, the voxel 12a, which has a heat-generating source 14, continues to emit heat and stabilizes in a steady state at a temperature very close to zero degrees Celsius.

[0021] In other words, when one voxel 12a continuously releases heat and the other voxel 12b continuously absorbs heat, the two reach a steady state while maintaining a constant temperature difference. Even when voxels 12 having heat sources 14 are adjacent to each other inside the object 10, if one voxel continues to release heat in either direction, a nearly steady state is reached where a constant temperature difference is maintained between them.

[0022] Furthermore, the calculation methods employed in this invention, such as the finite element method and the finite volume method, tolerate errors that are practically negligible, and the term "steady state" refers to a state that is practically stable.

[0023] When all voxels are in a steady state, a temperature gradient is generated from the voxel closest to the center line 16 of the object 10 outwards. The center line can be extracted by tracing the temperature gradient generated inside the object. Alternatively, the center line can be drawn by extracting the parts that maintain a locally high temperature and drawing lines between them.

[0024] As described above, the process of calculating the temperature of all voxels when they reach a steady state will be called the centerline mapping process. Then, the display of voxels is deleted in order from the lowest temperature, leaving only the voxels with a higher temperature than their surroundings. This process will be called the trimming (thinning) process. After that, lines are drawn sequentially to connect the remaining voxels with a higher temperature than their surroundings, and the process of drawing the centerline will be called the line tracing process.

[0025] In this invention, these three types of processes are executed sequentially by a computer, allowing the center line of an object to be automatically drawn on a display.

[0026] The relative positions of all voxels in the three-dimensional image remain unchanged from the initial state. The calculation involves determining the temperature of a heat source arranged on a grid of points at regular intervals. Since the center point is extracted only after the temperature of all voxels reaches a steady state, the time element does not need to be considered in this calculation.

[0027] Since this invention does not seek an analysis of natural phenomena, but only the results of schematic calculations, the parameters for heat conduction calculations can be minimized, and units can be ignored, thus simplifying the calculation formula. Therefore, even when calculating the temperature of a large number of voxels or grid points, the calculation results can be obtained by computer in a practical amount of time.

[0028] (Calculation example) For the mapping process calculation, for example, a three-dimensional steady-state heat conduction analysis program using the finite element method (authored by Kengo Nakajima, provided by the Information Technology Center, University of Tokyo (Non-Patent Literature 3)) can be used. Figure 5 shows the calculation formula. Voxels correspond to the elements of this calculation, and the temperature of each element can be expressed by this formula.

[0029] This formula, which states that the sum of the heat inflow and outflow in three dimensions and the heat generated by the element itself is zero, indicates a steady state. For all voxels, we simply need to calculate the temperature in this state. A computer program for this calculation is also described in this document. By providing boundary conditions, the temperature distribution of all elements (voxels) can be calculated as shown on page 3 of this document. Using the finite element method, the obtained values ​​are approximate, but the thinning process can be performed if the temperature difference (magnitude relationship) between adjacent voxels is known.

[0030] Thus, when performing centerline extraction calculations using the phenomenon of heat diffusion, changes in the external shape and irregularities do not immediately affect the irregularities of the centerline when extracting the centerline of an object whose cross-sectional shape changes complexly when viewed in the longitudinal direction. This is because heat flow occurs not only in the direction outward from the centerline but also along the centerline, causing the centerline to be automatically smoothed.

[0031] In particular, even in areas where the external shape changes in a complex way, such as when blood vessels branch into multiple lines, it is possible to extract and draw the centerline by focusing only on the temperature gradient, thereby drawing a smooth centerline.

[0032] In the thinning process, for example, by repeatedly setting the pixel values ​​of voxels with relatively low temperatures to "0" one by one, voxels with a pixel value of "1" remain near the center of the object 10. For example, in this process, voxels near the center line of the smaller outer diameter appear earlier, and voxels of the largest outer diameter are extracted last. By connecting these at appropriate intervals, the center line can be obtained.

[0033] Furthermore, if the temperature gradient is small, it may be difficult to extract voxels along the centerline. The shape of the object may also make it difficult to clearly express the temperature gradient. In such cases, it is best to find the optimal value by increasing or decreasing the value of Q.

[0034] The following shows images of centerlines extracted using specific calculation examples to illustrate the effect.

[0035] (Extraction of the center line) In the cylindrical object 18 shown in Figure 4(a), where the outer diameter changes little, the voxels of the centerline 16 can be extracted almost seamlessly in a steady state. On the other hand, Figures 4(b) and (c) show examples of centerline extraction for an object 20 in which the outer diameter changes abruptly when viewed in the longitudinal direction. Figure 4(b) is an example of the present invention, and Figure 4(c) is an example of a known method. Figure 4(d) shows an example of centerline extraction at a branched portion. Figure 5 shows an example of the calculation formula used for this extraction.

[0036] In this invention, as shown in Figure 4(b), a center line 16 that curves relatively smoothly can be extracted even in parts where the outer shape of the object 20 changes abruptly. When extracted using known methods, as shown in Figure 4(c), the center line 16 is unnaturally curved in parts where the outer shape of the object 20 changes abruptly.

[0037] As in the present invention, when the centerline is extracted by focusing on the temperature gradient, each centerline is connected by a gentle curve. Because heat is radiated in all directions from the heat source, the centerline can be naturally extracted far from any of the outer wall surfaces of the object. On the other hand, in known methods, the centerline is extracted based on the distance to the nearest outer wall surface, so in the case of an object whose outer diameter changes rapidly, the centerline becomes significantly curved, as shown in Figure 4(c).

[0038] For example, in a branched section like the one shown in Figure 4(d), the external shape cannot be determined, resulting in the generation of numerous candidate centerlines using known methods. On the other hand, in the present invention, the high-temperature sections are connected as shown in the figure, allowing for the extraction of a centerline with an intuitively understandable shape.

[0039] Figure 6 shows an image of the centerline extracted by performing calculations using the program according to the present invention. In the calculation in Figure 6, a model was used in which two rectangular prisms 24 and 26, with large and small cross-sectional areas, were connected asymmetrically by shifting their central axes when viewed from the cross-section.

[0040] Figure 6(a) shows the result of plotting the centerline 16 based on the temperature distribution calculated according to the present invention. The dashed lines connect regions with the same temperature, clearly indicating the temperature distribution like contour lines. To avoid making the figure too complex, these contour lines have been omitted in the high-temperature regions.

[0041] Figure 6(b) is a magnified view of the area near the step in (a). Centerline A shows the result obtained based solely on the distance from the outer surface for comparison. Centerline 16 shows the result drawn based on the temperature gradient according to the present invention. Near the step, the effect of heat dissipation from the vertical wall surface 28 of the step is significant, and centerline B curves slowly and gently. In contrast, centerline A bends sharply near the step. This clearly shows the difference in their calculation capabilities.

[0042] By using the calculation method described in Non-Patent Document 3 above, it is possible to calculate the steady-state temperature for all voxels regularly arranged in the three-dimensional image data of the object. [Examples]

[0043] According to the steady-state equation shown in Figure 5, calculations can also be performed using methods other than the finite element method. In this embodiment, we will specifically explain a method of calculation using the finite volume method, which is simpler than the finite element method described above.

[0044] The heat diffusion phenomenon in a circular pipe with a constant cross-sectional area over its entire length, as shown in Figure 8, is calculated using a discretization method based on the finite volume method. This is a circular pipe model of arbitrary length at any location inside the object. The heat diffusion equation in the steady state is shown in Figure 9(f1), which is the same as that shown in Figure 5. This equation shows how the temperature φ at each grid point changes in the steady state when boundary conditions are given, given that there are heat sources with heat quantity S at five grid points in the initial state. Note that the units of all parameters below are omitted and only numerical values ​​are shown.

[0045] The cross-sectional area of ​​the circular pipe is 1.0. Assume that there are five grid points within this pipe, spaced apart by δx = 0.004, with heat sources arranged at these points. The distance between the leftmost heat source and the interface (side wall of the object) is 0.002. The distance between the rightmost heat source and the interface is also 0.002.

[0046] The boundary conditions are 100.0 at the left end of the figure and 200.0 at the right end. This means, for example, that the temperature at the left end of the cylinder in the figure is set to 100 and the temperature at the right end is set to 200. The diffusion coefficient k is set to 0.5, where k corresponds to the thermal conductivity. The amount of generated heat S is set to 1000.0, where S is the amount of heat contained in each voxel and is a constant value equal to all lattice points.

[0047] When equation 9(f1) is expressed in component form, it can be represented as equation 9(f2). Integrating equation 9(f2) over the control volume CV yields equation 9(f3).

[0048] Equation 9(f3) can be expanded as shown in Equation 9(f4). This can be generalized to Equation 9(f5).

[0049] Here, the diffusion coefficients Ke and Kw in equation 9(f4) are related by equation 9(f6). Therefore, the coefficients in equation 9(f5) are as shown in equation 9(f7). The discretization equations at each grid point are all shown in Figure 10(f8). The coefficients at grid point 1, which is closest to the left end of the cylindrical model in Figure 8, are as shown in Figure 10(f9).

[0050] The coefficients for grid points 2, 3, and 4, other than the ends of the cylindrical model in Figure 8, are as shown in Figure 10(f10). The coefficient for grid point 5, which is closest to the right end of the cylindrical model in Figure 8, is as shown in Figure 10(f11).

[0051] The above results can be expressed as a determinant as shown in Figure 11(f12). Calculating φ from this equation yields the result shown in Figure 11(f13).

[0052] When this is represented graphically, it looks like Figure 12. That is, it becomes an upward-opening quadratic curve as shown in equation (f14) in Figure 11. The third and fourth grid points, which show the maximum value, are the parts with the highest temperature. For each voxel that makes up the three-dimensional image of the object, the temperature of each grid point (voxel) can be determined by unfolding this cylindrical model in the three-dimensional direction, performing calculations, and superimposing the results.

[0053] In Example 1, we explained how to calculate the temperature of each voxel in a steady state after it has transitioned from an initial state to a nearly steady state, for all voxels that exist without gaps in the three-dimensional image data of the object. On the other hand, Example 2 explains a calculation example in which grid points are arranged at regular intervals within the object and heat sources are placed there.

[0054] In other words, all voxels or grid points to be calculated must be regularly arranged at equal intervals in three dimensions and capable of transferring heat to each other in an equivalent manner. Furthermore, an appropriate calculation method should be adopted depending on the computing power of the computer used and the allowable calculation time.

[0055] Furthermore, if the resolution required to draw the desired center line can be lower than the resolution of the target image, for example, the drawing can be performed using a single voxel at the center of a cube with sides of 5 voxels as a representative voxel. [Explanation of symbols]

[0056] 10 Objects 12 voxels 12a Internal voxel 12b External voxels 14. Heat source 16 Center line 18. Object 20 Objects 22 Center line ·

Claims

1. A centerline extraction device for extracting and drawing a centerline from three-dimensional image data of an object by computational processing, equipped with means for performing the following processes by computer. (a) A three-dimensional image representing the contour shape of the object is obtained, and the entire three-dimensional image is assumed to be filled without gaps with voxels corresponding to pixels. (b) Heat sources are set up inside all of the above voxels, or at regularly distributed grid points, that continuously emit a constant amount of heat per unit time. (c) The heat from the above heat source may be released in all directions from the center of the voxel. (d) The voxels on the outermost surface of the object and the adjacent external voxels are heat-absorbing sources that are at zero degrees and absorb heat to the greatest extent possible. (e) Calculate the temperature of all voxels when a steady state is reached in which heat exchange occurs between voxels with heat sources and voxels with heat absorption sources, and between voxels with heat sources and other voxels with heat sources, and a constant temperature difference is maintained between each voxel. (f) Read the temperature difference described above and leave the group of voxels that are hotter than the surroundings. (g) Connect the remaining voxel groups that are hotter than the surrounding area in order to draw the center line.

2. The centerline extraction apparatus according to claim 1, characterized in that it repeatedly removes voxels in order from the lowest temperature to the highest temperature, leaving a group of voxels that are higher in temperature than the surrounding area.

3. The centerline extraction device according to claim 1 or 2, characterized in that it calculates the temperature of all voxels when a steady state is reached in which a constant temperature difference is maintained between each voxel, using a thermal diffusion equation.

4. A computer program for centerline extraction that causes a computer to function as the means described in claim 1.

5. A computer-readable recording medium on which the computer program described in claim 4 is recorded.

Images