JP2014055856A - Diffusion velocity calculation device and method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a diffusion velocity calculation device, a diffusion velocity calculation method, and a program for accurately obtaining velocity of flame and the like conforming to physical behavior.SOLUTION: A section 1 for deriving velocity of flame centroid movement derives centroid moving velocity of flame images, on the basis of time change of a plurality of flame images obtained by continuously shooting how a flame spreads as a diffusion object. After parallel moving each flame image so that each centroid of the plurality of flame images is fitted, a section 2 for deriving flame propagation velocity generates a continuous implicit function curved surface by interpolating each contour of the flame images by using a radial basis function, and derives velocity in a normal direction for each contour of the flame images on the generated implicit function curved surface, as propagation velocity. A flame velocity deriving section 3 derives velocity at which the flame propagates and spreads, on the basis of the propagation velocity derived by the section 2 for deriving flame propagation velocity and the centroid moving velocity derived by the section 1 for deriving velocity of flame centroid movement.

Description

  The present invention relates to a technique for calculating the diffusion speed of a diffusing object, and in particular, using a plurality of pieces of image information obtained by measuring in a continuous time, for example, the accuracy of a flame speed in an automobile engine or the like. The present invention relates to a diffusion rate calculation device, a diffusion rate calculation method, and a program suitable for measurement.

  Conventionally, for example, Patent Documents 1 and 2 describe a technique for calculating a flame speed as a diffusion speed of a diffusing object. In these techniques, the flame speed is calculated using image information photographed by the photographing means.

  In Patent Document 1, a luminance change signal on a specific scanning line constituting one screen of a flame video signal output from a TV camera, and a luminance change signal on the same scanning line constituting one screen after the next screen, A technique for measuring the speed of a flame by obtaining the correlation is described.

  In Patent Document 2, in a combustor equipped with a control device that controls the amount of fuel supplied, the shape of a flame is measured by a measuring device, and the flame combustion speed is calculated using the measurement value of the measuring device. Have been described. Specifically, there is an explanation using a boiler as an example, the combustion speed is defined as the speed at which unburned gas enters perpendicularly to the flame surface, the surface area of the flame is measured, the unburned gas flow velocity Uf in the burner, the burner Describes a technique for obtaining the combustion rate Su by “burning rate Su = (Ab / Af) Uf−1” using the cross-sectional area Ab and the total surface area Af of the flame.

  Further, in recent years, with the improvement of image acquisition technology using a computer, for example, it is possible to acquire the state of flame propagation in an automobile engine as a continuous image. And the demand for calculating the flame speed using the acquired continuous image information is increasing.

  Not only the flame but also the diffusion state of the diffusing object is obtained by analytically differentiating the interpolation function obtained by using multiple displacement information obtained by measuring the continuous displacement time. Non-patent literatures 1 and 2 provide the techniques to derive, for example.

  In Non-Patent Document 1, for the control of a robot and system identification, displacement data obtained at a constant sampling period is used as a radial basis function (Radial Basis Function (hereinafter referred to as “Radial Basis Function”). A technique is also described in which a continuous function is obtained by interpolation by linear combination such as RBF)), and further, an estimated value of speed / acceleration is obtained by analytically differentiating the continuous function.

  In Non-Patent Document 2, a curved surface method (implicit surface: Implicit Surface) is defined using a time-dependent implicit function, and the implicit function is differentiated with respect to time. A technique for determining the velocity in the linear direction is described.

Japanese Patent Laid-Open No. 01-269020 Japanese Patent Laid-Open No. 04-198617

Yuya Tachida, Hiroshi Yamaura “Speed and Acceleration Estimation Using RBF Interpolation” Transactions of the Japan Society of Mechanical Engineers (C) Volume 72, 721 (2006-9) pp. 2713-2720, paper no. 05-1043 JOS STAM and RYAN SCHMIDT "On the Velocity of an Implicit Surface" ACM Transactions on Graphics, Vol.30, No.3, Article21, Publication date: May 2011

  However, the techniques disclosed in Patent Documents 1 and 2 and Non-Patent Documents 1 and 2 cannot calculate the diffusion speed of a diffusing object in accordance with physical behavior, for example, the flame speed. There is.

  For example, as a component of the flame speed, there are a component of propagation in which the flame spreads over the combustible mixture and a component in which the flame itself moves by wind or the like. In Patent Documents 1 and 2, consideration is not given to the characteristics of the diffusion speed of the diffusing object, and the speed of the diffusing object including the flame cannot be measured with high accuracy.

  The problem to be solved by the present invention is that, in the prior art, for example, the diffusion of a diffusing object such as a propagation component in which a flame spreads over a combustible mixture and a component in which the flame itself moves by wind or the like. This is a point in which no consideration is given to the speed characteristics.

  An object of the present invention is to provide a diffusion speed calculation device, a diffusion speed calculation method, and a program that can solve the problems of these conventional techniques and accurately measure the diffusion speed of a diffusing object including a flame. It is.

  In order to achieve the above object, the diffusion speed calculation device according to claim 1 is based on temporal changes of object images representing a plurality of the objects obtained by continuously photographing the state of diffusion of a diffusing object. The center-of-gravity movement speed deriving means for deriving the center-of-gravity movement speed of the object image, and each object image are translated so as to match the center of gravity of each of the plurality of object images, and then the contour of each object image is interpolated by a radial basis function. A continuous implicit function curved surface, and a propagation speed deriving means for deriving the velocity in the normal direction at each contour of the object image as the propagation speed on the generated implicit function curved surface, and the propagation speed deriving means Speed deriving means for deriving a speed at which the object diffuses based on the propagation speed and the gravity center moving speed derived by the gravity center moving speed deriving means.

  According to the diffusion speed calculation device according to claim 1, based on temporal changes of object images representing the plurality of objects obtained by continuously photographing the diffusion state of the diffusing object by the gravity center moving speed deriving unit. Then, the center of gravity moving speed of the object image is derived, and the propagation speed deriving means translates the object images so that the centers of gravity of the plurality of object images are aligned. A continuous implicit function curved surface is generated by interpolating with the function, and the velocity in the normal direction at each contour of the object image is derived as a propagation velocity on the generated implicit function curved surface, and the propagation velocity is derived by the velocity deriving means. A speed at which the object diffuses is derived based on the propagation speed derived by the deriving means and the gravity center moving speed derived by the gravity center moving speed deriving means.

  As described above, according to the diffusion speed calculation device of the first aspect, based on the temporal change of the object image representing a plurality of objects obtained by continuously photographing the diffusion state of the diffusing object, Deriving the center-of-gravity moving speed, translating each object image so that the center of gravity of each of the object images is aligned, and then generating a continuous implicit function curved surface by interpolating the contour of each object image with a radial basis function The velocity in the normal direction of each contour of the object image is derived as the propagation velocity on the generated implicit function curved surface, and the velocity at which the object diffuses is derived based on the derived propagation velocity and the gravity center movement velocity. The diffusion speed of the diffusing object including the flame in accordance with the physical behavior can be obtained with high accuracy.

  In the present invention, as in the invention described in claim 2, the centroid moving speed deriving means includes a centroid coordinate calculating means for calculating centroid coordinates of each of the plurality of object images, and the centroid coordinate calculating means. Interpolation function generation means for generating an interpolation function for interpolating between the calculated barycentric coordinates of each object image, and movement speed derivation for deriving the barycentric movement speed by time differentiation of the interpolation function generated by the interpolation function generation means And the propagation speed deriving means sets the contours of the plurality of object images along the respective outlines after translating the object images so that the barycentric coordinates of the plurality of object images coincide with each other. An implicit function curved surface generating means for generating a continuous implicit function curved surface by interpolating a plurality of contour points by a radial basis function, and time differentiation of the implicit functional curved surface generated by the implicit function curved surface generating means, The plurality of objects A velocity normal direction component deriving unit that derives a velocity in the normal direction at each contour point of the image as the propagation velocity, and the velocity deriving unit derives the propagation derived by the velocity normal direction component deriving unit. The velocity at which the object diffuses may be derived by combining the velocity and the gravity center moving velocity derived by the moving velocity deriving means. Even with this configuration, the diffusion speed of the diffusing object including the flame in accordance with the physical behavior can be obtained with high accuracy as in the first aspect.

  On the other hand, in order to achieve the above object, the diffusion speed calculation device according to claim 3 is based on temporal changes of object images representing a plurality of the objects obtained by continuously photographing the diffusion state of the diffusing object. A center-of-gravity movement speed deriving unit for deriving the center-of-gravity movement speed of the object image, a body rotation speed deriving unit for deriving the rotation speed of the object image based on a temporal change of the object image representing the object, Each object image is translated so as to match the center of gravity of each of the object images, and each object image is rotated so as to match the inclination of the principal axis of inertia of each of the plurality of object images, and then the contour of each object image is defined as a radial basis. A propagation speed deriving means for generating a continuous implicit function curved surface by interpolation using a function, and deriving a velocity in the normal direction at each contour of the object image as a propagation speed on the generated implicit function curved surface; The speed at which the object diffuses based on the propagation speed derived by the degree deriving means, the gravity center moving speed derived by the gravity center moving speed deriving means, and the rotation speed derived by the object rotation speed deriving means And speed deriving means for deriving. Thereby, the diffusion speed of the diffusing object including rotation can be obtained with high accuracy.

  Thus, according to the diffusion speed calculation device according to claim 3, the object image is based on the time change of the object images representing the plurality of objects obtained by continuously photographing the diffusion state of the diffusing object. The rotational speed of the object image is derived based on the temporal change of the object image representing the object, and each object image is translated so as to match the center of gravity of each of the plurality of object images. After rotating each object image to match the inclination of each principal axis of inertia of each object image, the contour of each object image is interpolated with a radial basis function to generate a continuous implicit function surface, and on the generated implicit function surface The velocity in the normal direction at each contour of the object image is derived as the propagation velocity, and the velocity at which the object diffuses is derived based on the derived propagation velocity, center of gravity movement velocity, and rotation velocity. Physical The diffusion rate of the object to spread containing flame conforming to can be accurately obtained.

  In the present invention, as in the invention described in claim 4, the centroid movement speed deriving means includes a centroid coordinate calculating means for calculating centroid coordinates of each of the plurality of object images, and the centroid coordinate calculating means. Interpolation function generation means for generating an interpolation function for interpolating between the calculated barycentric coordinates of each object image, and movement speed derivation for deriving the barycentric movement speed by time differentiation of the interpolation function generated by the interpolation function generation means And the object rotation speed deriving means includes an inclination calculating means for obtaining an inclination of an inertia main axis of each of the plurality of object images, an inclination of the inertia main axis obtained by the inclination calculating means, and the barycentric coordinates. Rotation speed deriving means for deriving the rotation speed of the object image based on the barycentric coordinates of each of the plurality of object images calculated by the calculating means, and the propagation speed deriving means includes the plurality of objects Each object image is translated so that the center-of-gravity coordinates of each of the images coincide with each other, and each object image is rotated so as to match the inclination of each principal axis of inertia of each of the plurality of object images. An implicit function curved surface generating means for generating a continuous implicit function curved surface by interpolating a plurality of contour points set along the contour of the contour with a radial basis function, and an implicit function curved surface generated by the implicit function curved surface generating means A velocity normal direction component deriving unit for deriving the velocity in the normal direction at each contour point of the plurality of object images as the propagation velocity, and the velocity deriving unit includes the velocity normal A speed at which the object diffuses by combining the propagation speed derived by the direction component deriving means, the center of gravity moving speed derived by the moving speed deriving means, and the rotational speed derived by the rotational speed deriving means. It is also possible to derive. Even with this configuration, the diffusion speed of the diffusing object including the flame in accordance with the physical behavior including the rotation can be obtained with high accuracy as in the third aspect.

  In particular, according to the second or fourth aspect of the present invention, as in the fifth aspect of the present invention, the interpolation function generation unit is configured to calculate the centroids of the plurality of object images calculated by the centroid coordinate calculation unit. The interpolation function may be generated by interpolating between coordinates with a spline curve. Thereby, the diffusion speed of the diffusing object including the flame according to the physical behavior can be obtained with higher accuracy.

  According to the present invention, as in the invention described in claim 6, the object to be diffused is a flame, and the propagation of the flame from a plurality of flame images obtained by continuously photographing the propagation state of the flame. The speed may be derived. Thereby, the speed according to the physical behavior of the flame as the diffusing object can be obtained with high accuracy.

  Further, according to the present invention, as in the invention described in claim 7, the contour point is one of the contour line of the image, the inner side of the contour line, and the outer side of the contour line. The number of contour points may be the same as the number of contour points outside the contour line. Thereby, an implicit function curved surface can be generated with good balance.

  On the other hand, in order to achieve the above object, the diffusion speed calculation method according to claim 8 is based on temporal changes of object images representing a plurality of the objects obtained by continuously photographing the diffusion state of the diffusing object. The centroid movement speed deriving step for deriving the centroid movement speed of the object image, and the parallel movement of each object image so that the centroids of each of the plurality of object images are aligned, and then the contour of each object image is expressed by a radial basis function. A continuous implicit function curved surface is generated by interpolation, a propagation speed deriving step for deriving a normal direction velocity at each contour of the object image on the generated implicit function curved surface as a propagation speed, and the propagation speed deriving step A speed deriving step of deriving a speed at which the object diffuses based on the derived propagation speed and the gravity center moving speed derived in the gravity center moving speed deriving step.

  Therefore, according to the diffusion speed calculation method according to the eighth aspect, since it operates in the same manner as the invention according to the first aspect, the flame according to the physical behavior is included as in the first aspect. The diffusion speed of the diffusing object can be obtained with high accuracy.

  According to the present invention, as in the invention described in claim 9, the centroid movement speed derivation step includes a centroid coordinate calculation step for calculating each centroid coordinate of the plurality of object images, and the centroid coordinate calculation step. An interpolation function generation step for generating an interpolation function for interpolating between the calculated center-of-gravity coordinates of each object image, and a movement speed derivation for deriving the center-of-gravity movement speed by time differentiation of the interpolation function generated in the interpolation function generation step And the step of deriving the propagation velocity is set along the outline of each of the plurality of object images after translating each object image so that the barycentric coordinates of each of the plurality of object images coincide with each other. An implicit function curved surface generating step for generating a continuous implicit function curved surface by interpolating a plurality of contour points by a radial basis function, and the implicit function curved surface generating step A velocity normal direction component deriving step of differentiating a number curved surface with respect to time and deriving a velocity in the normal direction at each contour point of the plurality of object images as the propagation velocity, and the velocity deriving step includes the velocity deriving step The speed at which the object diffuses may be derived by combining the propagation speed derived in the normal direction component deriving step and the gravity center moving speed derived in the moving speed deriving step.

  Therefore, according to the diffusion speed calculation method according to the ninth aspect, since it operates in the same manner as the invention according to the second aspect, the flame according to the physical behavior is included as in the second aspect. The diffusion speed of the diffusing object can be obtained with high accuracy.

  On the other hand, in order to achieve the above object, a diffusion speed calculation method according to claim 10 is based on temporal changes of object images representing a plurality of the objects obtained by continuously photographing the state of diffusion of a diffusing object. A center-of-gravity movement speed deriving step for deriving a center-of-gravity movement speed of the object image, an object rotation speed deriving step for deriving a rotation speed of the object image based on a temporal change of the object image representing the object, Each object image is translated so as to match the center of gravity of each of the object images, and each object image is rotated so as to match the inclination of the principal axis of inertia of each of the plurality of object images, and then the contour of each object image is defined as a radial basis. A continuous implicit function curved surface is generated by interpolating with a function, and a normal velocity direction in each contour of the object image on the generated implicit function curved surface is derived as a propagation velocity. And the object based on the propagation speed derived in the propagation speed deriving step, the gravity center moving speed derived in the center of gravity moving speed deriving step, and the rotation speed derived in the object rotation speed deriving step. Deriving the rate at which the light diffuses.

  Therefore, according to the diffusion speed calculation method according to the tenth aspect, since it operates in the same manner as the invention according to the third aspect, in accordance with the physical behavior including rotation, as in the third aspect. It is possible to accurately obtain the diffusion speed of the diffusing object including the flame.

  In the present invention, as in the invention described in claim 11, the centroid movement speed derivation step includes a centroid coordinate calculation step for calculating each centroid coordinate of the plurality of object images, and the centroid coordinate calculation step. An interpolation function generation step for generating an interpolation function for interpolating between the calculated center-of-gravity coordinates of each object image, and a movement speed derivation for deriving the center-of-gravity movement speed by time differentiation of the interpolation function generated in the interpolation function generation step The object rotational speed deriving step includes: an inclination calculating step for determining an inclination of an inertial main axis of each of the plurality of object images; an inclination of the inertial main axis determined in the inclination calculating step and the barycentric coordinates A rotational speed deriving step for deriving the rotational speed of the object image based on the barycentric coordinates of each of the plurality of object images calculated in the calculating step; Each of the plurality of object images is translated so that the center-of-gravity coordinates of each of the plurality of object images coincide with each other, and the respective principal axes of the plurality of object images are aligned with each other. After rotating the image, an implicit function curved surface generating step for generating a continuous implicit function curved surface by interpolating a plurality of contour points set along each contour of the plurality of object images with a radial basis function; A velocity normal direction component deriving step for differentiating the implicit function curved surface generated in the implicit function curved surface generation step with respect to time, and deriving a normal direction velocity at each contour point of the plurality of object images as the propagation velocity; In the velocity deriving step, the propagation velocity derived in the velocity normal direction component deriving step, the gravity center moving velocity derived in the moving velocity deriving step, and Wherein the object was derived at a rotational speed derivation step said rotational speed synthesized and may be derived the rate of diffusion.

  Therefore, according to the diffusion speed calculation method according to the eleventh aspect, since it operates in the same manner as the invention according to the fourth aspect, it follows the physical behavior including the rotation as in the fourth aspect. It is possible to accurately obtain the diffusion speed of the diffusing object including the flame.

  According to the present invention, as in the twelfth aspect of the present invention, the diffusing object is a flame, and the flame is diffused from a plurality of flame images obtained by continuously photographing the diffusion of the flame. You may make it derive | lead-out the speed to perform. Thereby, the speed according to the physical behavior of the flame as the diffusing object can be obtained with high accuracy.

  On the other hand, in order to achieve the above object, a program according to a thirteenth aspect causes a computer to function as each means of the diffusion speed calculation device according to any one of the first to seventh aspects. Therefore, according to the invention of the thirteenth aspect, since the computer can be operated in the same manner as the diffusion rate calculation device of the present invention, the physical behavior is in accordance with the diffusion rate calculation device. The diffusion speed of the diffusing object including the flame can be obtained with high accuracy.

  According to the present invention, it is possible to accurately obtain the diffusion speed of a diffusing object including a flame in accordance with physical behavior.

It is a block diagram which shows the functional structure of the diffusion speed calculating apparatus which concerns on embodiment. It is a block diagram which shows the structural example by the computer of the diffusion speed calculating apparatus which concerns on embodiment. It is a top view which shows an example of the continuous image used with the diffusion speed calculating apparatus which concerns on embodiment. It is explanatory drawing which shows an example of the spline interpolation curve produced | generated by the diffusion speed calculating apparatus which concerns on embodiment. It is a schematic diagram which shows the structure of the coordinate information (point group) of each contour point in the 1st flame image used with the diffusion speed calculating apparatus which concerns on embodiment. It is a schematic diagram which shows the structure of the coordinate information (point group) of each outline point in the 2nd flame image used with the diffusion speed calculating apparatus which concerns on embodiment. It is explanatory drawing which shows an example of the interpolation curve produced | generated by the diffusion rate calculating apparatus which concerns on embodiment. It is explanatory drawing which shows an example of the output image of the process result by the diffusion speed calculating apparatus which concerns on embodiment. It is explanatory drawing which shows the other example of the output image of the process result by the diffusion speed calculating apparatus which concerns on embodiment. It is explanatory drawing which shows an example of the output image of the process result of the diffusion rate of the flame produced | generated only from the conventional RBF curved surface. It is a flowchart which shows the flow of a process of the diffusion rate calculating process program which concerns on embodiment. It is a block diagram which shows the other functional structure of the diffusion rate calculating apparatus which concerns on embodiment. It is a flowchart which shows the flow of the other process of the diffusion rate calculating process program which concerns on embodiment.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The diffusion speed calculation apparatus 10 according to the present embodiment has the functional configuration shown in FIG. 1 and has the hardware configuration of the computer shown in FIG. First, the configuration of the computer will be described with reference to FIG.

  The diffusion speed calculation device 10 according to the present embodiment is a CPU (Central Processing Unit) 22 that performs the processing according to the present embodiment of the diffusion speed calculation device 10 based on a program, and the CPU 22 performs, for example, FIG. A RAM (Random Access Memory) 24 used as a work area at the time of execution of various programs showing the processing routine in the flowchart of FIG. 13, and a ROM (Read Only Memory) 26 in which various control programs, various parameters, and the like are stored in advance. Various information is exchanged between the hard disk 28 (described as “HDD” 28 in the figure) used for storing various information, the keyboard 14, the mouse 16, and the display 18, and an externally connected device. And an interface unit 20 (denoted as “IF” 28 in the figure) that controls the system. Is constructed are connected to each other by the scan BUS.

  The CPU 22 accesses the RAM 24, ROM 26 and hard disk 28, acquires various information via the keyboard 14 and mouse 16, displays various information on the display 18, and exchanges various information with external devices connected to the interface unit 20. Etc. can each be performed.

  When the CPU 22 executes the diffusion rate calculation processing program stored in the hard disk 28 or the like, the function of each processing unit in the diffusion rate calculation device 10 according to the present embodiment shown in FIG. 1 is realized.

  A diffusion speed calculation device 10 according to the present embodiment shown in FIG. 1 is intended to calculate the flame speed for a flame as a diffusing object. FIG. 11 and FIG. As a function realized by the processing based on the diffusion speed calculation processing program shown in the flowchart, the flame center-of-gravity moving speed deriving unit 1, the flame propagation speed deriving unit 2, the flame speed deriving unit 3, and the storage unit 4 are provided.

  The storage unit 4 stores, in advance, a plurality of pieces of image information illustrated in FIG. 3 obtained by continuously capturing the state of propagation of the flame in a storage device such as the HDD 28 together with the respective shooting time information.

  The flame center-of-gravity moving speed deriving unit 1 calculates the center of gravity of the flame image based on temporal changes of a plurality of flame images obtained by continuously photographing the state of diffusion (hereinafter also referred to as propagation) of the flame as a diffusing object. Deriving the moving speed. For example, a plurality of flame images are read from the HDD 28, the respective center-of-gravity coordinates x, y in the plurality of read-out flame images are calculated, and the center of gravity of the flame is calculated using the movement amounts of the calculated center-of-gravity coordinates x, y. Deriving the moving speed.

  Further, the flame propagation speed deriving unit 2 translates each flame image so as to match each center of gravity of the plurality of flame images, and then interpolates the outline of each flame image with a radial basis function to obtain a continuous implicit function curved surface. Then, the velocity in the normal direction at each contour of the flame image is derived as the propagation velocity on the generated implicit function curved surface. That is, the flame propagation speed deriving unit 2 translates the coordinates of the contour points of each of the plurality of flame images so as to cancel the movement amounts of the center-of-gravity coordinates x and y of the flame images, and then converts each contour point to a radial basis function. A continuous implicit function curved surface is generated by interpolation using (RBF), and the velocity in the normal direction at each contour point of the flame image is derived as a flame propagation velocity on the generated implicit function curved surface.

  The flame speed deriving unit 3 derives the speed at which the flame diffuses based on the flame propagation speed derived by the flame propagation speed deriving unit 2 and the gravity center moving speed derived by the flame center of gravity moving speed deriving unit 1. .

  The flame center-of-gravity moving speed deriving unit 1 includes a flame center-of-gravity coordinate calculating unit 1a, an interpolation function generating unit 1b, and a moving speed deriving unit 1c. The flame propagation speed deriving unit 2 includes an implicit function curved surface generating unit 2a, and a velocity normal line. A direction component deriving unit 2b is provided.

  The flame center-of-gravity moving speed deriving unit 1 derives the moving speed of the center of gravity of the flame in the plurality of pieces of image information as a propagation speed at which the flame itself moves. And the barycentric coordinates x and y of each of the read-out flame images are calculated.

  Then, in the interpolation function generation unit 1b, an interpolation function x (t) for interpolating between the centroid coordinates of each flame image from the temporal change of the centroid coordinates x, y of the plurality of flame images calculated by the centroid coordinate calculation unit 1a. y (t) is generated, and the moving speed deriving unit 1c derives the center of gravity moving speed by differentiating the interpolation functions x (t) and y (t) generated by the interpolation function generating unit 1b with respect to time.

  The flame propagation speed deriving unit 2 derives the normal direction component of the velocity on the implicit function curved surface as a propagation velocity at which the flame spreads on the combustible mixture. After each flame image is translated so that the barycentric coordinates of each flame image match, a plurality of contour points set along each contour of the plurality of flame images are interpolated by a radial basis function. Generate an implicit function surface. That is, by subtracting the barycentric coordinates x and y of the flame image calculated by the barycentric coordinate calculation unit 1a from the coordinates of the contour points determined for the plurality of flame images stored in the HDD 28 or the like, After translating the coordinates of each contour point, each contour point of a plurality of flame images is interpolated by RBF to generate a continuous implicit function curved surface.

  Then, in the velocity normal direction component deriving unit 2b, the implicit function curved surface generated by the implicit function curved surface generating unit 2a is time-differentiated, and the velocity in the normal direction at each contour point of the plurality of flame images is set as the flame propagation velocity. To derive.

  The flame speed deriving unit 3 derives the flame speed by combining the center of gravity moving speed derived by the flame center of gravity moving speed deriving unit 1 and the flame propagation speed derived by the flame propagation speed deriving unit 2.

  As described above, the diffusion speed calculation device 10 stores in advance a plurality of flame images obtained by continuously shooting the state of flame propagation in a storage device such as the HDD 28 together with each shooting time t. The center-of-gravity moving speed deriving unit 1 reads out a plurality of flame images from the storage device, calculates the respective center-of-gravity coordinates x, y in the plurality of read-out flame images, and calculates the center-of-gravity coordinates x, y of the calculated plurality of flame images. The center of gravity movement speed of the flame is derived using the amount of movement.

  Further, the flame propagation speed deriving unit 2 translates the coordinates of the contour points of each of the flame images so as to cancel the movement amounts of the center-of-gravity coordinates x and y of the flame images, and then interpolates the contour points by RBF. Then, a continuous implicit function curved surface is generated, and the normal direction velocity at each contour point of the flame image is derived as the flame propagation velocity on the generated implicit function curved surface.

  Then, the flame velocity deriving unit 3 adds the flame propagation velocity derived by the flame propagation velocity deriving unit 2 and the gravity center moving velocity derived by the flame gravity center moving velocity deriving unit 1 to derive the flame speed.

  As described above, the diffusion velocity calculation device 10 generates a continuous implicit function curved surface from a discrete image group using the RBF point cloud interpolation technique, and calculates the flame velocity on the curved surface. The flame velocity component is divided into a component that propagates the flame over the combustible mixture and a component that the flame itself moves due to wind, etc., and these two components are divided into the velocity on the RBF. The flame speed is derived in correspondence with the normal direction component and the moving speed of the center of gravity of the flame in the image, and it is possible to accurately obtain the flame speed in accordance with the physical behavior.

  Hereinafter, the process performed by the diffusion speed calculation apparatus 10 will be described more specifically.

  First, the flame center-of-gravity moving speed deriving unit 1 calculates the center-of-gravity coordinates x, y of the outline of each flame using the plurality of flame image information shown in FIG. 3, and the plurality of images using the calculated coordinates x and y. A process for deriving the moving speed of the center of gravity of the flame in the information will be described.

In FIG. 3, the first image (t = 0), the second image (t = 1),..., And the nth image (t = n−1) are shown as continuous images. Has been. In this example, n−1 = 25 and 25 continuous images are used. In addition, each image used in this example is taken continuously at an interval of about 2.5 × 10 ⁻⁴ seconds.

  In this example, the center-of-gravity coordinate calculation unit 1a calculates coordinates (center-of-gravity coordinates) indicating the position of the center of gravity in each of the 1 to 25 images. When determining the position of the center of gravity, calculation is performed using all points on the contour line in the image.

As a technique for obtaining the position of the center of gravity on a curved surface, there is a technique using a known screen moment. For example, the (p + q) _-order moment m _pq of the image f (x, y) is generally given by the following equation (1), and the barycentric coordinates (x _g , y _g ) of the image at this time are It is represented by Formula (2).

  In this example, the barycentric coordinates (x, y) in the first image are (587.58125, 450.210417), and the barycentric coordinates (x, y) in the second image are (590.57852, 455.205225). The center-of-gravity coordinates (x, y) in each image are (590.566483, 457.036782), (596.538659, 459.771616), (602.164727, 462.004549), (603.249566, 463.980044), (606.67222, 467.235245), (608.811965, 470.319981). ), (608.963327,474.540404), (611.191349,477.377885), (609.860904,480.011762), (608.640138,482.199317), (609.232162,484.820546), (608.029799,487.641158), (606.96263,490.335899), (604.894983,495106318) (603.365683, 499.482303), (602.065783, 504.048939), (598.877009, 509.323098), (595.719268, 514.814209), (592.880892, 519.817609), (591.347949, 525.277569), (588.830114, 530.250697), (587.167763, 534.61135) 587.419569, 538.553522).

  Using these barycentric coordinates, the flame barycentric moving speed deriving unit 1 generates functions x (t) and y (t) obtained by interpolating each barycentric coordinate group with a spline curve by the interpolation function generating unit 1b.

  Spline interpolation is a technique for smoothly interpolating a point group using a different polynomial function for each section, and generally a cubic spline using a cubic polynomial is used. It has the feature that the first and second derivatives are continuous at the boundary of the section. FIG. 4 shows a schematic diagram of spline interpolation. In FIG. 4, the horizontal axis corresponds to the coordinate t, and the vertical axis corresponds to the coordinate x (or y). The spline interpolation is described in, for example, “Kozo Ichida, Fuji City Yoshimoto:“ Spline Function and its Application ”, Education Publishing Co., Ltd., pp. 1-59, 1979-6”.

When the above-described barycentric coordinates (x, y) are used, for example, the spline function x (t) of the first and second images shown in FIG. 3 is “−0.001216 (t-0) ³ +0.000000 (t-0). ) ² +0.421308 (t-0) +587.581250 ”and the spline function x (t) becomes“ −0.000919 (t-0) ³ +0.000000 (t-0) ² +0.591360 (t-0) +450.210417 ” .

The flame center-of-gravity moving speed deriving unit 1 takes the time differentiation of the functions x (t) and y (t) generated by the interpolation function generating unit 1b by the moving speed deriving unit 1c. The movement speed of the center of gravity of the flame is derived.

  That is, when the x-coordinate and y-coordinate of the centroid position are interpolated with the functions x (t) and y (t) using the time t as a variable as described above, the centroid velocity vector v is expressed by the following equation (3). It becomes. Here, the derived movement speed of the center of gravity is represented as (Vx2, Vy2).

  The above is the calculation of the center of gravity coordinates (x, y) of the outline of each flame using the plurality of flame image information shown in FIG. 3 by the flame center of gravity moving speed deriving unit 1, and the calculated coordinates (x, y) are used. It is description about the derivation | leading-out process of the moving speed of the gravity center of the flame in the some image information which was.

  Next, the propagation speed deriving process in which the flame spreads over the combustible mixture by the flame propagation speed deriving unit 2 will be described.

  First, by the point group interpolation by the RBF in the implicit function curved surface generation unit 2a, each continuous image (first image (t = 0), second image (t = 1)) in the continuous image shown in FIG. ..., N−1 (= 25th image)) will be described.

  In the example shown in FIG. 3, 17 contour points are extracted from the first image (t = 0), and each data is stored in the HDD 28 or the like with the configuration shown in FIG.

  In this example, the contour point of the flame image is interpolated by RBF after being translated so as to cancel the movement amount of the center of gravity. For example, as described in the description of the center-of-gravity coordinates, the center-of-gravity coordinates (x, y) in the first flame image are (587.58125, 450.210417), and each contour point specified in the first flame image is The coordinate data is translated by subtracting the first barycentric coordinate (x, y) (= 587.58125, 450.210417) from the coordinate (x, y).

  For example, the value “x = 8.971536, y = −18.2042” in the first row in FIG. 5 is the actual coordinates (x = 596.552786, y = 432.006192) of each contour point specified in the first flame image. The value obtained by subtracting the center of gravity coordinates (x = 587.58125, y = 450.210417) from the first sheet. By performing this process on the coordinates of each contour point, the center of gravity of each flame image is matched with the center of gravity of the first flame image.

  In FIG. 5, “x” and “y” indicate that the center of gravity obtained from the first image is x = 0 and y = 0, and x increases as the contour point moves to the right of the center of gravity. Since y increases as it goes to the point, if the contour point is on the left or above the center of gravity, the value is negative (-).

  In FIG. 5, “t” is an image identification number (t = 0 is the first image), and “function value” indicates whether the contour point is on the contour, inside the contour, and outside the contour. “0” is on the contour, “−1” is inside the contour, and “1” is outside the contour.

  Note that the contour points are set on the contour, inside the contour, and outside the contour. When the contour point is only on the contour, the values on the right side of the simultaneous equations of Equation (6) described later are all zero (0). This is because only obvious solutions can be obtained. In this example, the number of positive contour points is the same as the number of negative contour points, and the interpolation curved surface is generated in a balanced manner, but it is not always necessary to have the same number.

  Similarly, 24 contour points are extracted from the second image (t = 1), and each data is stored in the HDD 28 or the like with the configuration shown in FIG. In FIG. 6, the second image is shown as t = 10.

  In addition, 116 contour points are extracted from the 25th image, and 1816 contour points are extracted in total from 1 to 25 images.

  Thus, each contour point has a two-dimensional coordinate (x, y), and by adding a time dimension (t) to this coordinate, it can be handled as a point (x, y, z) in a three-dimensional space. The implicit function curved surface generation unit 2a performs parallel movement so as to cancel out the movement amount of the center of gravity derived by the flame center of gravity movement speed deriving unit 1, and then each contour point (three-dimensional) of 1 to 25 flame images. An implicit function curved surface is generated by interpolating the point group) by RBF.

  Next, the process of generating an implicit function curved surface by such an implicit function curved surface generation unit 2a and the process of the velocity normal direction component deriving unit 2b in the flame propagation velocity deriving unit 2 will be described in more detail.

  The implicit curved surface generation unit 2a in the flame propagation velocity deriving unit 2 of this example uses a group point interpolation method by RBF. In this example, as described above, the contour points of the continuous image are expressed in two-dimensional coordinates ( Consider an implicit function surface f (x, y, t) = 0 that is treated as a point group in a three-dimensional space having x, y) and time (t) and interpolates these point groups.

  FIG. 3 shows an example of a continuous image, and FIG. 7 shows an example of an interpolation curved surface. FIG. 7 shows an implicit function curved surface obtained by interpolating the contour points of the flame image with RBF when the translation is not performed so as to cancel the movement amount of the center of gravity. Diffusion speed is derived for a diffusing object. In this example, the contour point of the flame image is interpolated by the RBF after the parallel movement is performed so as to cancel the movement amount of the center of gravity.

  RBF is a basis function that depends only on the distance from the origin, and there are several forms depending on the application, but in this example, a three-dimensional curved surface as shown in the following equation (4): “Triharmonic spline” is used for interpolation.

  The implicit function for interpolating the point group is determined as shown in the following equation (5) by taking a weighted sum of basis functions centered on each point.

In the above formula (5), “c _j ” represents the position vector of each point, “d _j ” represents the weight, and P (x) is a first order polynomial “p ₀ + p ₁ x + p ₂ y + p ₃ z”. The weight “d _j ” and the polynomial coefficients “p _{0 to} p ₃ ” are obtained by solving simultaneous linear equations represented by the following equation (6). The coordinates of each point are assumed to be “cj = (c ^x _j , c ^y _j , c ^z _j )”.

In the above formula (6), “φ _ij = φ (c _i −c _j )”. “H _j ” is a function value in FIGS. 5 and 6 and represents a signed distance from the curved surface. If “c _j ” is a point on the curved surface, “h _j = 0” is obtained. If it is a point, “h _j <0”, and if it is a point outside the curved surface, “h _j > 0”. As described with reference to the function values in FIGS. 5 and 6, when all the points are points (contour points) on each curved surface, the values on the right side of the simultaneous equations of the above equation (6) are all zero (0). Thus, only an obvious solution can be obtained, and here, an offset is added in the normal direction (internal and external) from the contour point.

Here, “φ (c _i −c _j )” is the cube of the length of the vector, as shown in the above equation (4). Therefore, “φ _ij ” is “i-th”. Is the cube of the distance between the point and the j-th point ”.

For example, in the above equation (6), the component in the first row and the second column is “φ ₁₂ = φ (c ₁ −c ₂ ) ³ = (the cube of the distance between the first point and the second point” And the component in the first row and third column is “φ ₁₃ = φ (c ₁ −c ₃ ) ³ = (the cube of the distance between the first point and the third point”).

  In the matrix determined by the point cloud data shown in FIGS. 5, 6, etc., for example, the first row is “0, 63985.12 79952.23 35056.78 10.3544 61675.83 71839.82 28682 ・ ・ ・ 116136.6 ・ ・ ・ 44312.81 ・ ・ ・ 592041.7 ・ ・ ・246172.8 ... 1959455 ... 762641.4 ... 1149980 565262.1 499082.3 482887.9 "etc., and this and the function value h form the first line of the simultaneous linear equations of the above equation (6). In this example, The simultaneous linear equation 6) consists of 1816 lines.

By solving the simultaneous linear equations, each weight “d _j ” and polynomial coefficients “p _{0 to} p ₃ ” in each row of 1816 rows are calculated.

By applying each weight “d _j ” and polynomial coefficients “p _{0 to} p ₃ ” calculated in this way to the above equation (5), the equation of the curved surface is determined.

That is, the function of Expression (5) has a form in which 1816 terms are added, and in this example, “f (x) = d ₁ φ (x−c ₁ ) + d ₂ φ (x−c ₂ )”. + D ₃ φ (x−c ₃ ) +... + D ₁₈₁₆ φ (x−c ₁₈₁₆ ) + p ₀ + p ₁ x + p ₂ y + p ₃ z ”.

  In this example, the velocity normal direction component deriving unit 2b derives the differential value of the function shown in the equation (5) to derive the velocity normal direction component at each contour point on the implicit function curved surface.

  Hereinafter, derivation of the normal direction component of the velocity at each contour point on such an implicit function curved surface will be described. As for the derivation of the normal direction component of the velocity at each contour point on this implicit function curved surface, the technique described in “3. NORMAL VELOCITY” of Stam's paper in Non-Patent Document 2 described above can be used. A detailed description will not be given here.

  As described above, consider a curved surface represented by a time-dependent implicit function f (x, y, z) = 0.

  Taking the total derivative of the function f with respect to time, the following equation (7) is obtained.

  At points on the curved surface, this differential value is zero (0). That is, it can be expressed as the following formula (8). Thereby, only the normal direction component of the speed is determined.

  Here, on condition that the velocity direction is the normal direction of the contour line, the following equation (9) is used to calculate the velocity of the normal component of the RBF as the propagation velocity.

  From the above equations (8) and (9), the following equation (10) is obtained, and this equation (10) becomes the normal component of the velocity.

The normal direction component of the speed of each contour point is calculated using the above equation (10). In this example, the function of Expression (5), that is, “f (x) = d ₁ φ (x−c ₁ ) + d ₂ φ (x−c ₂ ) + d ₃ φ (x−c ₃ ) +. + D ₁₈₁₆ φ (x−c ₁₈₁₆ ) + p ₀ + p ₁ x + p ₂ y + p ₃ z ”is obtained, the sum of 1816 is obtained, thereby obtaining an expression representing the speed. For example,“ When “x = 10.773644”, “y = −18.675817” and “z = 0” are substituted, “Vx1 = −3.998188” and “Vy2 = −3.873554” are normal direction components of the velocity of the contour point, that is, flame propagation Obtained as a speed value.

  As described above, in the image, x increases as it goes to the right, and y increases as it goes down, so that the vector consisting of “Vx1 = −3.9998188” and “Vy2 = −3.8873554” 3.998188 means that the vector is 3.873554 on the upper side.

  The moving velocity deriving unit 1c in the above-described flame center-of-gravity moving velocity deriving unit 1 derived from the normal component (vector) of the velocity of each contour point as the flame propagation velocity thus obtained and the flame image. The sum of the moving speed (vector) of the center of gravity is the flame speed of each contour point.

  FIG. 8 shows the result when the speed derivation processing is performed by the above-described diffusion speed calculation device 10 for each flame image shown in FIG. It is a flame image, and the straight line portion represents the speed. Here, the flame speed is visually represented by connecting the coordinates of the contour point from which the speed is derived to the coordinates of the velocity vector derived by the diffusion speed calculation device 10 with a straight line.

  In addition, FIG. 9 shows an example in which the velocity is calculated by the diffusion velocity calculation device 10 for a circle whose diameter increases while being translated, and FIG. 10 is the same as the case of FIG. The result of calculating the velocity only from the RBF curved surface without considering the movement of the center of gravity is shown.

  Also from FIG. 9, it can be seen that the diffusion speed calculation device 10 of this example can cope with a movement in which parallel movement and deformation are combined.

  When solving simultaneous equations such as the above equation (6) using a general CPU, the calculation time becomes very long as the matrix size increases. Therefore, processing speed can be increased by processing matrix operations in parallel using a GPU (Graphics Processing Unit).

  Next, the diffusion rate calculation processing by the diffusion rate calculation device 10 of this example will be described using FIG. Each step shown in FIG. 11 indicates processing contents based on a program stored in a storage device such as the HDD 28 of the CPU 22 in FIG.

  In step 100, the center-of-gravity coordinates (x, y) in each successive flame image (flame contour) are calculated by the same processing as the center-of-gravity coordinate calculation unit 1a in FIG. 1, and in step 102, the interpolation function in FIG. The interpolation functions x (t) and y (t) are generated by the same processing as the generation unit 1b. In step 104, the movement speed of the center of gravity of each flame image is obtained by the same processing as the movement speed deriving unit 1c in FIG. Is calculated.

  Further, in step 106, an implicit function curved surface is generated by the same processing as the implicit function curved surface generating unit 2a in FIG. 1, and in step 108, by the same processing as the velocity normal direction component deriving unit 2b in FIG. The normal direction component of the velocity at each contour point is calculated.

  In step 110, the flame speed is calculated by the same process as the flame speed deriving unit 3 in FIG. 1, and in step 112, the calculation result is output.

  Note that the flame speed is the rotation speed when the flame rotates together with the moving speed of the center of gravity (the moving speed of the flame itself) and the normal speed (the propagation speed at which the flame spreads over the combustible mixture). Speed is considered.

  A basic technique for determining the rotational speed of such a flame will be described below.

  When generating a curved surface from continuous images, the inclination of the principal axis of inertia of the shape in each image can be obtained, and the rotation of the shape can be grasped from the change in the inclination of the axis between images. The inclination of the principal axis of inertia can be obtained from the moment of the image.

The moment M _pq around the center of gravity is given by the following equation (11).

  The inclination θ of the inertial main axis at this time is expressed by the following equation (12).

  Now consider the speed of the rotating object. Considering an ellipse that rotates around a point, it is natural that the direction of velocity at each point is perpendicular to the line segment connecting the center of rotation and the point. Further, when the distance from the rotation center is r and the rotation angle is θ, the speed magnitude | v | is expressed by the following equation (13).

  Therefore, the speed of the rotating object can be obtained from the rotation center of the shape (which may be the center of gravity) and the rotation angle (inclination of the principal axis of inertia).

  Hereinafter, a diffusion speed calculation device that calculates the flame speed including the rotation speed of the flame will be described with reference to FIGS. 12 and 13.

  FIG. 12 shows the configuration of the diffusion rate calculation device 10a that performs such processing. Similarly to the diffusion rate calculation device 10 shown in FIG. 1, the diffusion rate calculation device 10a has the configuration of the computer shown in FIG.

  In addition to the configuration of the diffusion rate calculation device 10 shown in FIG. 1, the diffusion rate calculation device 10 a includes a flame inclination calculation unit 5 a that calculates the inclination of each inertia principal axis of a plurality of flame images, and the obtained inclination of the inertia main axis. A flame rotation speed deriving unit 5 including a rotation speed deriving unit 5b for deriving the rotation speed of the flame image is provided.

  Note that the flame center-of-gravity moving speed calculation unit 1 in FIG. 12 performs the same processing as the flame center-of-gravity moving speed calculation unit 1 in FIG. 1, and includes a barycentric coordinate calculation unit 1a, an interpolation function generation unit 1b, and a moving speed. The deriving unit 1c will not be described here.

  In this example, the flame propagation speed deriving unit 2c is translated in the implicit function curved surface generation unit 2a ′ so as to cancel the movement amounts of the center-of-gravity coordinates x and y, and the flame inclination calculating unit of the flame rotation speed deriving unit 5 After canceling the inclination of the principal axis of inertia between the flame images obtained in 5a, each contour point is interpolated by RBF to generate a continuous implicit function curved surface, which is generated by the velocity normal direction generation unit 2b ′. The velocity in the normal direction at each contour point of the flame image on the implicit function curved surface is derived as the flame propagation velocity.

  Then, the flame velocity deriving unit 3a has a normal direction velocity at each contour point as a flame propagation velocity derived by the flame propagation velocity deriving unit 2c, and a gravity center moving velocity derived by the flame gravity center moving velocity deriving unit 1. The flame speed is derived by adding the three rotation speeds of the flame image derived by the flame rotation speed deriving unit 5.

  The diffusion rate calculation process by the diffusion rate calculation device 10a of this example will be described with reference to FIG. Each step shown in FIG. 13 shows the processing contents based on a program stored in a storage device such as the HDD 28 of the CPU 22 in FIG. 2 as in the case of FIG.

  First, in step 200, the center-of-gravity coordinates (x, y) in each successive flame image (flame contour) are calculated by the same processing as the center-of-gravity coordinate calculation unit 1a in FIG. 12, that is, in FIG. The interpolation functions x (t) and y (t) are generated by the same processing as that of the interpolation function generation unit 1b in FIG. 12, that is, FIG. 1, and in step 204, the same as the movement speed deriving unit 1c in FIG. By processing, the moving speed of the center of gravity of each flame image is calculated.

  Next, in step 202a, the inclination of the principal axis of inertia in each successive flame image (flame contour) is calculated by the same processing as the flame inclination calculation unit 5a in FIG. 12, and in step 204a, the rotational speed in FIG. The rotational speed of the flame image is derived by the same processing as the deriving unit 5b.

  In step 206a, a continuous implicit function curved surface is generated by the same processing as the implicit function curved surface generating unit 2a ′ in FIG. 12, and in step 208a, the velocity normal direction component deriving unit 2b ′ in FIG. The normal direction component of the velocity at each contour point is calculated as the flame propagation velocity by the same processing as.

  In step 210a, the flame speed is derived by the same process as the flame speed deriving unit 3a in FIG. 12, and in step 212a, the calculation result is output.

  As described above with reference to FIGS. 1 to 11, in the diffusion speed calculation device 10 of this example, a plurality of flame images obtained by continuously photographing the state of propagation / diffusion of a flame as a diffusing object are obtained. Based on the change over time, the flame center-of-gravity movement speed deriving unit 1 for deriving the center-of-gravity movement speed of the flame image, and each flame image are translated in parallel so that the centers of gravity of the plurality of flame images are aligned. A flame propagation speed deriving unit 2 for generating a continuous implicit function curved surface by interpolation with a radial basis function, and deriving a velocity in the normal direction at each contour of the flame image on the generated implicit function curved surface as a propagation speed; A flame speed deriving unit 3 for deriving a flame diffusion speed based on the propagation speed derived by the flame propagation speed deriving unit 2 and the center of gravity moving speed derived by the flame center of gravity moving speed deriving unit 1; Yes.

  The flame center-of-gravity moving speed deriving unit 1 interpolates between the center-of-gravity coordinates of the flame images calculated by the center-of-gravity coordinate calculation unit 1a and the center-of-gravity coordinate calculation unit 1a of the plurality of flame images. An interpolating function generating unit 1b that generates a function, and a moving speed deriving unit 1c that derives the moving speed of the center of gravity by differentiating the interpolating function generated by the interpolating function generating unit 1b. After each flame image is translated so that the center-of-gravity coordinates of each of the plurality of flame images coincide, a plurality of contour points set along each contour of the plurality of flame images are interpolated by a radial basis function. The implicit function curved surface generation unit 2a that generates a continuous implicit function curved surface and the implicit function curved surface generated by the implicit function curved surface generation unit 2a are time-differentiated to obtain the normal direction of each contour point of the plurality of flame images. Deriving velocity as propagation velocity A velocity normal direction component deriving unit 2b, and the flame velocity deriving unit 3 means includes a propagation velocity derived by the velocity normal direction component deriving unit 2b and a gravity center moving velocity derived by the moving velocity deriving unit 1c. To derive the speed at which the flame propagates and diffuses.

  As described above, the diffusion velocity calculation device 10 generates a continuous implicit function curved surface from a discrete image group using the RBF point cloud interpolation technique, and calculates the flame velocity on the curved surface. The flame velocity component is divided into a component that propagates the flame over the combustible mixture and a component that the flame itself moves due to wind, etc., and these two components are divided into the velocity on the RBF. The flame speed is derived in correspondence with the normal direction component and the moving speed of the center of gravity of the flame in the image, and it is possible to accurately obtain the flame speed in accordance with the physical behavior.

  On the other hand, in the diffusion speed calculation device 10a described with reference to FIGS. 12 and 13, based on temporal changes of a plurality of flame images obtained by continuously photographing the propagation / diffusion state of a flame as a diffusing object, A flame center-of-gravity moving speed deriving unit 1 for deriving the center-of-gravity moving speed of the flame image, a flame rotation speed deriving unit 5 for deriving the rotation speed of the flame image based on the temporal change of the flame image, and each of the plurality of flame images Each flame image is translated to match the center of gravity, and each flame image is rotated to match the inclination of the principal axis of inertia of each flame image, and then the contour of each flame image is interpolated by a radial basis function to continuously A simple implicit function curved surface, and a flame propagation velocity deriving unit 2c for deriving the velocity in the normal direction at each contour of the flame image as a propagation velocity on the generated implicit function curved surface, and a flame propagation velocity deriving unit 2c Flame speed derivation for deriving the speed at which the flame propagates and diffuses based on the measured propagation speed, the center of gravity movement speed derived by the flame center-of-gravity movement speed deriving section 1 and the rotation speed derived by the flame rotation speed deriving section 5 Part 3a.

  The flame center-of-gravity moving speed deriving unit 1 interpolates between the center-of-gravity coordinates of the flame images calculated by the center-of-gravity coordinate calculation unit 1a and the center-of-gravity coordinate calculation unit 1a of the plurality of flame images. An interpolation function generation unit 1b that generates a function, and a movement speed deriving unit 1c that derives the center of gravity movement speed by differentiating the interpolation function generated by the interpolation function generation unit 1b with respect to time. Each of the plurality of flame images calculated by the flame inclination calculation unit 5a for determining the inclination of each inertia main axis of the plurality of flame images, and the inclination of the inertia main axis obtained by the flame inclination calculation unit 5a and the barycentric coordinate calculation unit 1a And a rotation speed deriving unit 5b for deriving the rotation speed of the flame image based on the center of gravity coordinates of each of the flame images, and the flame propagation speed deriving unit 2c includes each flame so that the center of gravity coordinates of the plurality of flame images coincide with each other. Translate the image In each case, after rotating each flame image so that the inclination of each principal axis of inertia of each of the plurality of flame images matches, a plurality of contour points set along each contour of the plurality of flame images are interpolated by a radial basis function. And the implicit function curved surface generation unit 2a ′ for generating a continuous implicit function curved surface and the implicit function curved surface generated by the implicit function curved surface generation unit 2a ′ are time-differentiated to obtain normal lines at respective contour points of a plurality of flame images. A velocity normal direction component deriving unit 2b ′ for deriving the velocity in the direction as a propagation velocity, and the flame velocity deriving unit 3a is a propagation velocity and movement velocity deriving unit derived by the velocity normal direction component deriving unit 2b ′. The speed at which the flame propagates and diffuses is derived by synthesizing the center-of-gravity moving speed derived in 1c and the rotational speed derived in the rotational speed deriving unit 5b.

  As described above, in the diffusion rate calculation device 10a shown in FIG. 12, in addition to the configuration of the diffusion rate calculation device 10 shown in FIG. 1, a flame inclination calculation unit 5a for obtaining inclinations of the respective principal axes of the plurality of flame images; The flame rotation speed deriving section 5 comprises a rotation speed deriving section 5b for deriving the rotation speed of the flame image from the obtained inclination of the principal axis of inertia, and the flame propagation speed deriving section 2c cancels the movement amount of the centroid coordinates x and y. In parallel, and after canceling out the inclination of the principal axis of inertia between the flame images obtained by the flame inclination calculating section 5a of the flame rotation speed deriving section 5, each contour point is continuously interpolated by RBF. An implicit function curved surface is generated, and the flame speed deriving unit 3a calculates the normal direction velocity at each contour point derived by the flame propagation speed deriving unit 2c to the center of gravity coordinates x and y by the flame center of gravity moving speed deriving unit 1. With travel The center of gravity moving speed of the flame issued by adding the rotational speed of the flame which is derived by the flame speed deriving unit 5 derives the speed of the flame. Thereby, the speed of the flame image including rotation can be obtained with high accuracy.

  The interpolation function generation unit 1b generates interpolation functions x (t) and y (t) by interpolating the gravity center coordinates x and y of the plurality of flame images calculated by the gravity center coordinate calculation unit 1a with a spline curve.

  The contour point is either on the contour line of the flame image, inside the contour line, or outside the contour line, and the number of contour points inside the contour line is the same as the number of contour points outside the contour line. By doing so, the implicit function curved surface is generated in a balanced manner.

  In addition, this invention is not limited to the example mentioned above, A various deformation | transformation and application are possible within the range which does not deviate from the summary of this invention.

  For example, in this example, the flame speed has been described as an object, but it can also be applied to other diffusing objects, such as obtaining the diffusion speed of oil diffusing on the water surface. It is possible to ask.

In this example, spline interpolation is used as a technique for generating a curve by interpolating the barycentric coordinates, but it is also possible to use Lagrange interpolation or Newton interpolation. However, in this Lagrangian interpolation, n points are interpolated with a curve of an n−1 degree equation. For example, if there are three points, a quadratic equation “x (t) = at ² + bt + c”. This Lagrange interpolation is very simple to implement, but if the number of points increases, the curve may vibrate unnaturally.

  In the computer configuration shown in FIG. 2, a program for realizing the function of each processing unit according to the present invention is recorded on a computer-readable recording medium, and the program recorded on the recording medium is stored in a computer system. By reading and executing, the processing by each configuration may be executed, or the program may be read by using a communication function not shown.

  The computer-readable recording medium refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, and a CD-ROM, and a storage device such as a hard disk built in the computer system.

  The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.

  The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, what is called a difference file (difference program) may be sufficient.

  Moreover, the flame center-of-gravity moving speed deriving unit 1, the flame propagation speed deriving unit 2, and the flame speed deriving unit 3 in the diffusion speed calculating apparatus 10 according to the present embodiment are configured by a computer capable of executing each function by a program. However, a hardware configuration including a logic element circuit may be used.

  As described above, the embodiment for carrying out the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and the scope of the present invention is not deviated. Design etc. are also included.

DESCRIPTION OF SYMBOLS 1 Flame center-of-gravity moving speed deriving part 1a Center-of-gravity coordinate calculating part 1b Interpolation function generating part 1c Moving speed deriving part 2, 2c Flame propagation speed deriving part 2a, 2a 'Implicit function curved surface generating part 2b, 2b' Speed normal direction direction component deriving part 3, 3a Flame speed deriving section 4 Storage section 10, 10a Diffusion speed computing device 5 Flame rotation speed deriving section 5a Flame inclination calculating section 5b Rotational speed deriving section 14 Keyboard 16 Mouse 18 Display 20 Interface section (IF)
22 CPU
24 RAM
26 ROM
28 Hard disk (HDD)

Claims (13)

Centroid movement speed deriving means for deriving the centroid movement speed of the object image based on temporal changes of the object image representing the plurality of objects obtained by continuously photographing the state of diffusion of the diffusing object;
After each object image is translated so that the centroids of the plurality of object images are aligned, the contour of each object image is interpolated with a radial basis function to generate a continuous implicit function curved surface. A propagation velocity deriving means for deriving the velocity in the normal direction at each contour of the object image as a propagation velocity;
Speed deriving means for deriving a speed at which the object diffuses based on the propagation speed derived by the propagation speed deriving means and the gravity center moving speed derived by the gravity center moving speed deriving means;
A diffusion speed calculation device. The center-of-gravity moving speed deriving unit generates a center-of-gravity coordinate calculating unit that calculates the center-of-gravity coordinates of each of the plurality of object images, and an interpolation function that interpolates between the center-of-gravity coordinates of each object image calculated by the center-of-gravity coordinate calculating unit. Interpolating function generating means, and movement speed deriving means for deriving the barycentric moving speed by differentiating the interpolation function generated by the interpolation function generating means with respect to time,
The propagation speed deriving means translates each object image so that the barycentric coordinates of each of the plurality of object images coincide with each other, and then sets a plurality of contour points set along the contours of the plurality of object images. And an implicit function curved surface generating means for generating a continuous implicit function curved surface by interpolating with a radial basis function, and an implicit function curved surface generated by the implicit function curved surface generating means by time differentiation, A velocity normal direction component deriving unit for deriving a velocity in the normal direction at each contour point as the propagation velocity,
The velocity deriving unit derives a velocity at which the object diffuses by combining the propagation velocity derived by the velocity normal direction component deriving unit and the gravity center moving velocity derived by the moving velocity deriving unit.
The diffusion speed calculation device according to claim 1. Centroid movement speed deriving means for deriving the centroid movement speed of the object image based on temporal changes of the object image representing the plurality of objects obtained by continuously photographing the state of diffusion of the diffusing object;
Object rotation speed deriving means for deriving the rotation speed of the object image based on a time change of the object image representing the object;
Each object image is translated so as to match the center of gravity of each of the plurality of object images, and each object image is rotated so as to match the inclination of the principal axis of inertia of each of the plurality of object images. Propagation speed deriving means for generating a continuous implicit function curved surface by interpolation with a radial basis function, and deriving the velocity in the normal direction of each contour of the object image as the propagation speed on the generated implicit function curved surface,
The object diffuses based on the propagation speed derived by the propagation speed deriving means, the gravity center moving speed derived by the gravity center moving speed deriving means, and the rotation speed derived by the object rotation speed deriving means. Speed deriving means for deriving a speed to perform,
A diffusion speed calculation device. The center-of-gravity moving speed deriving unit generates a center-of-gravity coordinate calculating unit that calculates the center-of-gravity coordinates of each of the plurality of object images, and an interpolation function that interpolates between the center-of-gravity coordinates of each object image calculated by the center-of-gravity coordinate calculating unit. Interpolating function generating means, and movement speed deriving means for deriving the barycentric moving speed by differentiating the interpolation function generated by the interpolation function generating means with respect to time,
The object rotation speed deriving means is calculated by an inclination calculating means for calculating an inclination of an inertia main axis of each of the plurality of object images, and an inclination of the inertia main axis obtained by the inclination calculating means and the barycentric coordinate calculating means. Rotation speed deriving means for deriving the rotation speed of the object image based on the barycentric coordinates of each of the plurality of object images,
The propagation velocity deriving means translates each object image so that the center-of-gravity coordinates of each of the plurality of object images coincide with each other, and converts each object image to match the inclination of each principal axis of inertia of the plurality of object images. After the rotation, an implicit function curved surface generating means for generating a continuous implicit function curved surface by interpolating a plurality of contour points set along the respective contours of the plurality of object images with a radial basis function; A velocity normal direction component deriving unit for deriving the velocity in the normal direction at each contour point of the plurality of object images as the propagation velocity by differentiating the implicit function curved surface generated by the function curved surface generation unit with respect to time. ,
The speed deriving means calculates the propagation speed derived by the speed normal direction component deriving means, the gravity center moving speed derived by the moving speed deriving means, and the rotational speed derived by the rotational speed deriving means. Combining to derive the speed at which the object diffuses,
The diffusion speed calculation device according to claim 4. 5. The diffusion speed calculation according to claim 2, wherein the interpolation function generation unit generates the interpolation function by interpolating between the barycentric coordinates of the plurality of object images calculated by the barycentric coordinate calculation unit with a spline curve. apparatus. The speed at which the flame is diffused is derived from a plurality of flame images obtained by continuously photographing the state in which the flame is diffused. The diffusion rate calculation device described in 1. The contour point is one of the contour line of the object image, the inner side of the contour line, and the outer side of the contour line, and the number of contour points inside the contour line and the number of contour points outside the contour line The diffusion rate calculation device according to any one of claims 2, 4 to 6. A centroid movement speed deriving step for deriving a centroid movement speed of the object image based on a temporal change of the object image representing the plurality of objects obtained by continuously photographing the state of diffusion of the diffusing object;
After each object image is translated so that the centroids of the plurality of object images are aligned, the contour of each object image is interpolated with a radial basis function to generate a continuous implicit function curved surface. And a propagation velocity deriving step for deriving the velocity in the normal direction in each contour of the object image as the propagation velocity;
A speed deriving step of deriving a speed at which the object diffuses based on the propagation speed derived in the propagation speed deriving step and the gravity center moving speed derived in the gravity center moving speed deriving step;
A diffusion rate calculation method including The center-of-gravity moving speed deriving step generates a center-of-gravity coordinate calculating step for calculating the center-of-gravity coordinates of each of the plurality of object images and an interpolation function for interpolating between the center-of-gravity coordinates of each object image calculated in the center-of-gravity coordinate calculating step. An interpolation function generating step, and a moving speed deriving step of deriving the center of gravity moving speed by differentiating the interpolation function generated in the interpolation function generating step with respect to time,
In the propagation speed deriving step, the plurality of contour points set along the respective contours of the plurality of object images are obtained by translating each object image so that the barycentric coordinates of the plurality of object images coincide with each other. The implicit function curved surface generation step for generating a continuous implicit function curved surface by interpolating with the radial basis function, and the implicit function curved surface generated in the implicit function curved surface generation step with time differentiation, A velocity normal direction component deriving step for deriving a velocity in the normal direction at each contour point as the propagation velocity,
The velocity deriving step derives a velocity at which the object diffuses by synthesizing the propagation velocity derived in the velocity normal direction component deriving step and the gravity center moving velocity derived in the moving velocity deriving step.
The diffusion rate calculation method according to claim 8. A centroid movement speed deriving step for deriving a centroid movement speed of the object image based on a temporal change of the object image representing the plurality of objects obtained by continuously photographing the state of diffusion of the diffusing object;
An object rotation speed deriving step for deriving a rotation speed of the object image based on a time change of the object image representing the object;
Each object image is translated so as to match the center of gravity of each of the plurality of object images, and each object image is rotated so as to match the inclination of the principal axis of inertia of each of the plurality of object images. A propagation velocity deriving step for generating a continuous implicit function curved surface by interpolation with a radial basis function, and deriving a velocity in the normal direction at each contour of the object image on the generated implicit function curved surface as a propagation velocity;
The object diffuses based on the propagation speed derived in the propagation speed deriving step, the gravity center moving speed derived in the gravity center moving speed deriving step, and the rotation speed derived in the object rotation speed deriving step. A speed deriving step for deriving a speed to perform,
A diffusion rate calculation method including The center-of-gravity moving speed deriving step generates a center-of-gravity coordinate calculating step for calculating the center-of-gravity coordinates of each of the plurality of object images and an interpolation function for interpolating between the center-of-gravity coordinates of each object image calculated in the center-of-gravity coordinate calculating step. An interpolation function generating step, and a moving speed deriving step of deriving the center of gravity moving speed by differentiating the interpolation function generated in the interpolation function generating step with respect to time,
The object rotation speed deriving step is calculated by an inclination calculating step for obtaining an inclination of an inertia main axis of each of the plurality of object images, an inclination of the inertia main axis obtained in the inclination calculating step, and the barycentric coordinate calculating step. A rotational speed deriving step for deriving the rotational speed of the object image based on the barycentric coordinates of each of the plurality of object images,
The propagation speed deriving step translates each object image so that the center-of-gravity coordinates of each of the plurality of object images coincide with each other, and converts each object image to match the inclination of each principal axis of inertia of the plurality of object images. After the rotation, an implicit function curved surface generating step for generating a continuous implicit function curved surface by interpolating a plurality of contour points set along each contour of the plurality of object images by a radial basis function; A velocity normal direction component deriving step for differentiating the implicit function curved surface generated in the function curved surface generation step with respect to time and deriving a normal direction velocity at each contour point of the plurality of object images as the propagation velocity. ,
In the speed deriving step, the propagation speed derived in the speed normal direction component deriving step, the gravity center moving speed derived in the moving speed deriving step, and the rotational speed derived in the rotational speed deriving step are calculated. Combining to derive the speed at which the object diffuses,
The diffusion speed calculation method according to claim 10. The speed at which the flame is diffused is derived from a plurality of flame images obtained by continuously photographing the state in which the flame is diffused. The diffusion rate calculation method described in 1.   A program for causing a computer to function as each unit of the diffusion rate calculation device according to any one of claims 1 to 7.

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