JP7105448B2 - Shape estimation device, shape estimation method and program - Google Patents

Description

The present invention relates to a shape estimation device, a shape estimation method and a program.

2. Description of the Related Art In recent years, attempts have been made to network a large number of small sensors with wireless functions installed in vehicles, collect data, and use them for various applications. In particular, it is desirable to assume a situation in which the sensor is inexpensive, has low power consumption, and has low functionality, and does not require the position of the vehicle (secrecy regarding the position is maintained).

Under such conditions, methods have been proposed for estimating the size and shape of an object. Non-Patent Document 1 proposes a method of estimating the overall shape of a convex polygonal object by collecting data from distance sensors mounted on many vehicles that move in a straight line and performing statistical processing. there is

H. Saito and T. Kimura, Theoretical Framework for Estimating Target-Object Shape by Using Location-Unknown Mobile Distance Sensors, ArXiv 1802.06882.

However, many actual objects include curved portions, and for such objects, the above-described prior art, which assumes a polygonal shape, cannot estimate the overall shape. Further, in the above-described prior art, statistical processing is performed on the assumption that the trajectory of a vehicle equipped with a sensor follows a specific distribution such as a uniform distribution. However, it is difficult to estimate the shape with high accuracy.

SUMMARY OF THE INVENTION The present invention has been made in view of the above points, and it is an object of the present invention to enable estimation of the overall shape of an object using a moving sensor that does not necessarily depend on a specific distribution.

Therefore, in order to solve the above problems, a shape estimating device is provided for each sensor terminal based on time-series measurement results of the distance between a fixed object and the sensor terminal, which are obtained by a plurality of moving sensor terminals. a calculation unit for calculating a partial shape of the object and a curvature function and an arc length of the object; detecting an overlapping portion between the partial shapes based on the curvature function and the arc length; and an estimating unit for estimating the overall shape of the object by connecting the .

Moving sensors, not necessarily with a particular distribution, can be used to allow estimation of the overall shape of an object.

It is a figure which shows the structural example of the shape estimation system in embodiment of this invention. It is a figure for demonstrating the problem setting given in embodiment of this invention. It is a figure which shows the hardware structural example of the shape estimation apparatus 10 in embodiment of this invention. It is a figure which shows the functional structural example of the shape estimation apparatus 10 in embodiment of this invention. 4 is a flowchart for explaining an example of a processing procedure executed by the shape estimation device 10; It is a figure which shows the geometric relationship of simulation. It is a figure which shows the result of having calculated the partial shape using Numerical formula (1) and (4). It is a figure which shows the result of having calculated the partial curvature function from Formula (2), (5), Formula (3), and (6).

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described below based on the drawings. FIG. 1 is a diagram showing a configuration example of a shape estimation system according to an embodiment of the present invention. The shape estimation system according to the present embodiment includes shape estimation device 10 and N ^~ sensor terminals from sensor terminal d1 to sensor terminal dN (hereinafter referred ^to as "sensor terminal d" when not distinguished). . The shape estimation device 10 and each sensor terminal d are connected via a wired or wireless network.

Each sensor terminal d is a distance sensor that detects an object whose shape is to be estimated (hereinafter referred to as “target object T”) existing within the monitoring target area and measures the distance to the target object T.

Each sensor terminal d is provided with a motion means such as a motor and wheels, or is mounted on or connected to a motion section which is a moving body such as another device that moves such as a vehicle. Therefore, each sensor terminal d is spatially moving. Each sensor terminal d is a distance sensor terminal having sharp directivity, and when the distance to the object T is r _max or less, the distance r (0≦r≦r _max ) to the object T is measured. (hereinafter referred to as “sensing data”), and transmits the sensing data to the shape estimation device 10 . The arrangement position of each sensor terminal d is random.

The shape estimation device 10 is one or more computers that estimate the overall shape of the target object T based on sensing data. The shape estimating device 10 receives sensing data from the sensor terminal d, and calculates the partial shape and curved surface information (curvature function, arc length) to estimate the overall shape. Equations (1)-(6) can be applied to a curvilinear object T and do not depend on the trajectory distribution of the sensor terminal d. d can be used to estimate the overall shape of the object, including curvilinear portions.

A shape estimation result is transmitted from the shape estimation device 10 to the user terminal 20 . The user terminal 20 is a terminal that displays the shape estimation result.

FIG. 2 is a diagram for explaining problem setting given in the embodiment of the present invention. Note that the problem setting described below is merely an example, and the applicable problem setting is not limited to this.

In FIG. 2, an object T is an area surrounded by a closed convex curve ∂T and is fixed within a sufficiently wide monitoring area Ω. Each point of ∂T can be represented using an arc length parameter s. The starting point s=0 of the arc length parameter is a certain point on ∂T, and the counterclockwise direction is the positive direction. Also, s is appropriately considered mod |∂T| (|∂T| is the perimeter of T). That is, s is considered as a remainder of the perimeter of ∂T. Also, the angle between the tangent vector pointing in the positive direction and the x-axis direction is a function of s and is denoted by ξ(s)ε[0,2π).

The sensor terminal d moves linearly at a constant speed v (for example, it is mounted on a vehicle that moves linearly). However, the initial position of the sensor terminal d is unknown. Also, the angle φ between the traveling direction of the sensor terminal d and the x-axis direction is unknown. The sensor number, which is the identification information of each sensor terminal d, is indicated by a subscript _i in each variable (φi, etc.), but may be omitted when discussing one sensor terminal d. The sensing area (the area (range) in which the sensor terminal d can detect the object T) is a fan-shaped area within the angle [−θ _max , θ _max ] between the radius r _max and the trajectory of the sensor terminal d (sensor trajectory). (θ _max ∈[0, π/2]), and when the object T enters the sensing area, each sensor terminal d determines the distance r(t)≦r _max to the object T at each time t. get (measure) When there is no object T within the sensing area, r(t)=Φ (empty set), and when the sensor terminal d is included in the object T, r(t)=0. In shape estimation, only sensor terminals d whose sensing data satisfy ∀t (r(t)>0 or r(t)=Φ) and ∃t (r(t)≠Φ) are used. Such a sensor terminal d will be called a valid sensor terminal d, and the corresponding sensing data will be called valid sensing data. Note that the sensing data is only information about the distance r(t) to the target object T, and the information θ(t) indicating in which direction the target object T is detected with respect to the advancing direction of the sensor terminal d is not specified. It is assumed that it is not actually included. All the sensing data {r _i (t)} _i are transmitted to the shape estimation device 10, and the shape estimation device 10 uses them to obtain the shape of ∂T based on the shape estimation method described later.

Next, important equations (1)-(6) used for shape estimation are presented. Consider the case when one valid sensor terminal d senses an object T. For simplicity, let the traveling direction of the sensor terminal d be the x-axis direction, and let the position of the sensor terminal d at time t be ^t (vt, 0). In other words, consider a -φ rotated coordinate system. Also, the moment when the sensor terminal d senses the object T for the first time (the moment when r(t)≠Φ) is assumed to be t=0. The object T is assumed to be in the area (y>0, θ>0) on the left side of the sensor terminal d in the traveling direction (if the object T is in the area on the right side in the traveling direction, the obtained shape should be horizontally reversed). should be fine.). The first and second derivatives of r(t) are denoted as r'(t) and r''(t), respectively.

With such a setting, a mathematical formula is obtained from the sensing data r(t) to determine the specific partial shape of the object T (the portion sensed by the sensor terminal d) as the envelope of the curve group. When θε(0, θ _max ), the partial shape of ∂T is given by the following equation (1) with time t as a parameter.

なお、各数式において、ｒ'は、ｒの上に・を付した記号によって表記し、ｒ''は、ｒの上に‥を付した記号によって表記する。

In each numerical formula, r' is represented by a symbol with * over r, and r'' is represented by a symbol with ... over r.

Also, the arc length parameter and curvature of the point sensed at time t are given by the following formulas (2) and (3), respectively.

但し、弧長パラメタの起点ｓ＝０としては、ｔ＝０でセンシングした点を選択した。θ∈（０、θ_ｍａｘ）が満たされているかを判定する条件は、以下の条件式（＃）で与えられる。

However, the point sensed at t=0 was selected as the starting point s=0 of the arc length parameter. A condition for determining whether θε(0, θ _max ) is satisfied is given by the following conditional expression (#).

また、θ＝θ_ｍａｘのとき、∂Ｔの部分形状は、時刻ｔをパラメタとして、以下数式（４）で与えられる。

Also, when θ=θ _max , the partial shape of ∂T is given by Equation (4) below with time t as a parameter.

また、時刻ｔにセンシングした箇所の弧長パラメタ、曲率は、それぞれ以下の数式（５）、数式（６）で与えられる。

Also, the arc length parameter and curvature of the point sensed at time t are given by the following equations (5) and (6), respectively.

以上に基づき対象物Ｔの形状を推定する形状推定装置１０について具体的に説明する。図３は、本発明の実施の形態における形状推定装置１０のハードウェア構成例を示す図である。図３の形状推定装置１０は、それぞれバスＢで相互に接続されているドライブ装置１００、補助記憶装置１０２、メモリ装置１０３、ＣＰＵ１０４、及びインタフェース装置１０５等を有する。

The shape estimating device 10 for estimating the shape of the object T based on the above will be specifically described. FIG. 3 is a diagram showing a hardware configuration example of the shape estimation device 10 according to the embodiment of the present invention. The shape estimation device 10 of FIG. 3 has a drive device 100, an auxiliary storage device 102, a memory device 103, a CPU 104, an interface device 105, and the like, which are connected to each other via a bus B, respectively.

A program for realizing processing in the shape estimation device 10 is provided by a recording medium 101 such as a CD-ROM. When the recording medium 101 storing the program is set in the drive device 100 , the program is installed from the recording medium 101 to the auxiliary storage device 102 via the drive device 100 . However, the program does not necessarily need to be installed from the recording medium 101, and may be downloaded from another computer via the network. The auxiliary storage device 102 stores installed programs, as well as necessary files and data.

The memory device 103 reads out and stores the program from the auxiliary storage device 102 when a program activation instruction is received. The CPU 104 executes functions related to the shape estimation device 10 according to programs stored in the memory device 103 . The interface device 105 is used as an interface for connecting to a network.

FIG. 4 is a diagram showing a functional configuration example of the shape estimation device 10 according to the embodiment of the present invention. In FIG. 4, the shape estimation device 10 has a receiver 11, a partial shape calculator 12, a partial shape connector 13, and the like. Each of these units is realized by processing that one or more programs installed in the shape estimation apparatus 10 cause the CPU 104 to execute. The shape estimation device 10 also utilizes the data storage unit 14 . The data storage unit 14 can be implemented using, for example, the auxiliary storage device 102 or a storage device that can be connected to the shape estimation device 10 via a network.

The receiving unit 11 receives sensing data from each sensor terminal d and stores the sensing data in the data storage unit 14 . The data storage unit 14 stores sensing data of each sensor terminal d in chronological order.

The partial shape calculation unit 12 calculates the partial shape of the target object T and the partial shape partial _curvilinear Calculate surface information (arc length and curvature). If the number of valid sensor terminals d is ns, then _{ns subshapes} (for each sensor terminal d) and arc lengths (for each _t ) of the time series (for each sensor terminal d), and Curvatures (for each _t ) of ns time series (for each sensor terminal d) are obtained.

The partial shape connection unit 13 appropriately connects the n _s partial shapes calculated by the partial shape calculation unit 12 to estimate the overall shape of the object T. FIG.

A processing procedure executed by the shape estimation device 10 will be described below. FIG. 5 is a flowchart for explaining an example of a processing procedure executed by the shape estimation device 10. As shown in FIG. At the start of FIG. 5, the sensing data {r _i ( _t )} _i=1 ^ns are stored in time series in the data storage unit 14 (the number of effective sensor terminals d is ns). .

In step S101, the partial shape calculator 12 substitutes 1 for the variable i. The variable i is a variable for identifying the sensor terminal d to be processed among the _ns sensor terminals d. Subsequently, the partial shape calculator 12 substitutes 0 for the variable t (S102). Variable t is a variable for identifying sensing data r _i (t) at time t among sensing data r _i of sensor terminal di.

Subsequently, the partial shape calculator 12 calculates r'/v at time t for r _i and determines whether or not the conditional expression (#) is satisfied (S103). Note that the value of v is known to the shape estimation device 10 . For example, the value of v may be stored in advance in the auxiliary storage device 102 or the like.

If the conditional expression (#) is satisfied (Yes in S103), the partial shape calculator 12 calculates the partial shape (t) (x(t) and y(t)) based on the formula (1) ( S104). Subsequently, the partial shape calculator 12 calculates the arc length s(t) based on Equation (2) (S105). Subsequently, the partial shape calculator 12 calculates the curvature κ(t) based on Equation (3) (S106). The partial shape calculator 12 stores each calculation result in the memory device 103, for example.

On the other hand, if the conditional expression (#) is not satisfied (No in S103), the partial shape calculator 12 calculates the partial shape (t) (x(t) and y(t)) based on the formula (4). (S107). Subsequently, the partial shape calculator 12 calculates the arc length s(t) based on Equation (5) (S108). Subsequently, the partial shape calculator 12 calculates the curvature κ(t) based on Equation (6) (S109). The partial shape calculator 12 stores each calculation result in the memory device 103, for example.

Following step S106 or S109, the partial shape calculator 12 adds 1 to t (S110). Subsequently, the partial shape calculator 12 determines whether r _i (t) is Φ (S111). That is, it is determined whether r _i (t) is invalid sensing data. If r _i (t) is not Φ, that is, if r _i (t) is valid sensing data (No in S111), the partial shape calculator 12 repeats step S103 and subsequent steps. The result is a time series of subshape(t), arc length s(t) and curvature κ(t) for sensor terminal di. The partial shape calculation unit 12 obtains the partial shape of _∂T based on the valid sensing data ri by connecting the time series of the partial shape (t).

On the other hand, if r _i (t) is Φ, that is, if r _i (t) is invalid sensing data (Yes in S111), the partial shape calculator 12 adds 1 to i (S112). . Subsequently, the partial shape calculator 12 determines whether the value of i is less than or equal to ns ( _S113 ). If the value of i is less than or equal to ns (No in _S113 ), the partial shape calculator 12 repeats step S103 and subsequent steps.

On the other hand, if the value of i exceeds ns (Yes in _S113 ), step S114 and subsequent steps are executed. At this point, there are _ns partial shapes (for each sensor terminal d), ns arc lengths (for each _t ) of the time series (for each sensor terminal d), and _ns (for each sensor terminal d The curvature of the time series (for each t) is obtained.

After step S114, the partial shape connecting unit 13 executes processing for estimating the overall shape of the target object T by connecting the partial shapes. Here, it is possible to find overlapping portions of partial shapes and connect them. difficult to find. Therefore, it is preferable to use the curvature function κ(s) obtained by converting the curvature κ(t) obtained using the equations (3) and (6) into an arc length parameter representation. The curvature function κ(s) can be easily obtained from Equations (2), (3), (5) and (6). Since the curvature function κ(s) is a function unique to the partial shape and does not depend on the rotation angle φ of the coordinates, it is easy to find overlapping portions of the curves indicated by the curvature function κ(s). Hereinafter, the curvature function κ(s) obtained for each sensor terminal d will be referred to as a “partial curvature function”, emphasizing that it is a partial curvature of the object T.

In step S114, the partial shape connecting unit 13 converts the _ns partial shapes into _ns partial curvature functions. Subsequently, the partial shape connecting unit 13 detects at least a partial overlapping portion between the curve indicated by each partial curvature function and the curve indicated by another partial curvature function (S115). Note that the overlapping portion does not have to be an overlapping (common) portion among all the partial curvature functions. Each overlapping portion may be detected between at least two partial curvature functions. Subsequently, the partial shape connecting unit 13 constructs an overall image of the curvature functions for each of the plurality of combinations of the partial curvature functions (S116). For example, when there are five sensor terminals d, five partial curvature functions are obtained. Combinations are generated and an overview is constructed for each combination. The same partial curvature function may belong to multiple combinations.

Subsequently, the partial shape connecting unit 13 determines whether or not a consistent overall image has been constructed in combinations equal to or greater than the threshold (S117). Consistent overview refers to the same overview. Also, the threshold may be a value indicating a ratio to the total number of combinations, or a value indicating the number of combinations.

If a consistent overall image can be constructed in combinations equal to or greater than the threshold value (Yes in S117), the partial shape connecting unit 13 connects each of the combinations related to any of the combinations that can construct a consistent overall image. The partial shapes corresponding to the partial curvature functions are connected so as to overlap at locations corresponding to the overlapping portions detected in step S115 to generate an estimated value of the overall shape of the object T(∂T) (S118).

Next, an example of a method for detecting overlapping portions between partial curvature functions in step S115 will be described. However, the detection method applicable to this embodiment is not limited to the following examples.

[(A) Focusing on the feature points of the curvature function]
The curvature function may have a non-differentiable point, a plane curve vertex (dκ/ds=0), and an inflection point (a point where the sign of d ² κ/ds ² changes before and after). Since these are characteristic points on the closed curve, they are extremely strong candidates for overlapping portions. In particular, for smooth curves, the theorem "Four Vertex Theorem for Convex Curves: There are at least four vertices in a C ³ class convex curve" is known. A non-smooth curve has non-differentiable points and higher-order non-differentiable points. In other words, it can be considered that any object T has some kind of feature point.

[(B) Calculate arc length between feature points]
If it is an overlapping part, the arc lengths between the feature points found in (A) should also be equal. By listing the arc lengths between the feature points for each partial curvature function, it is easy to determine overlapping portions.

[(C) Count the number of feature points]
When there are multiple vertices with the same curvature value, such as an ellipse, or when there are multiple non-differentiable points with similar shapes, such as a rectangle, it becomes troublesome to determine the connection, but follow the steps below. By doing so, the number can be obtained, which can be used for estimating the overall shape and detecting overlapping portions. However, since it is assumed here that the trajectory of the sensor terminal d follows a uniform distribution as in Non-Patent Document 1, the method described here is not used if this assumption is not satisfied.

First, the number of partial curvature functions (i.e., the sensor corresponding to the partial curvature function Count the number of terminals d (including invalid sensor terminals d), and let this be _nc . Next, the expected value n _e of the number of sensor terminals d sensing the one point is obtained according to the following formula (7).

数式（７）は、非特許文献１に従い容易に導出できる。最後にｎ_ｃ／ｎ_ｅを計算することで、∂Ｔ上の当該点の個数を求められる。

Equation (7) can be easily derived according to Non-Patent Document 1. Finally, calculating n _c /n _e gives the number of points on ∂T.

As described above, if there are enough sensor terminals d to sense all parts of the object, it is possible to estimate the overall shape. Not assumed (except when using (C)). Further, by obtaining the partial shape according to the formulas (1) and (4), the shape can be estimated even if the object is curved, and it is not necessary to assume a polygonal shape.

[Theoretical Background]
The derivation of Equation (1), Equation (2), and Equation (3) will be described below. When the sensed point of the object T is smooth, the sensing direction of the sensor terminal d and the tangent line at the sensed point of the object T are orthogonal. That is, ξ−θ=3π/2 holds. Since this relationship holds at each time t, the boundary ∂T of the object T keeps contacting the circle with the center ^t (vt, 0) and the radius r(t). This means that ∂T is the envelope of the family of curves f(x,y,t)=(x−vt) ² +y ² −r(t) ² =0 parameterized by t. The envelope can be obtained by solving for x and y the following formula (8) in which f=0 and ∂f/∂t=0.

数式（８）を、ｘ，ｙについて解いた結果が数式（１）である。

Equation (1) is the result of solving Equation (8) for x and y.

Equation (2) is based on Equation (1), and the following formula

を用いて容易に導出できる。

can be easily derived using

Equation (3) is obtained by variable conversion of θ(t) to θ(s) using s obtained in Equation (2) and differentiating it with respect to s.

Next, the derivation of equations (4), (5), and (6) will be described. Equation (4) can be easily derived by elementary geometric calculations. Equation (5) is based on Equation (4) and can be easily derived using the above formula. Equation (6) is obtained by differentiating ξ by s using s obtained by Equation (5).

As described above, according to the present embodiment, it is possible to estimate the overall shape of an object including curved portions by using the moving (moving) sensor terminal d without necessarily depending on a specific distribution. can.

Subsequently, using the present embodiment, the results of a simulation performed when an elliptical object T is used will be described.

FIG. 6 is a diagram showing the geometric relationship of the simulation. As shown in FIG. 6, an elliptical object T having a major axis of 20 and a minor axis of 10 is arranged at the center of a disk Ω (monitoring target area) having a radius of 100. As shown in FIG. 500 sensor terminals d are moved with velocity v=1 (known). Each sensor terminal d sets r _max =100, θ _max =π/2, and acquires sensing data r(t) at intervals of Δt=0.05.

FIG. 7 is a result of selecting 5 effective sensing data from 500 sensing data and calculating the partial shape using the formulas (1) and (4). In FIG. 7, axes are meaningful as scales, but absolute values are meaningless. Also, FIG. 8 shows partial curvature functions calculated from formulas (2), (5), formulas (3), and (6). In FIG. 8, s is the horizontal axis and κ(s) is the vertical axis.

Based on these, the overall shape is estimated by the methods (A), (B), and (C) described in the partial shape connection step below.

First, regarding (A), it can be seen that there are two types of vertices in FIG. 8, a minimum value of 0.025 (marked with x) and a maximum value of 0.2 (marked with ●). Furthermore, regarding (B), the arc length between the point giving the maximum value and the point giving the minimum value is indicated by an arrow in the figure, and the length is the same at sensor terminal d3 and sensor terminal d5. . Considering that the shape around the apex is symmetrical and that similar trends can be seen in sensing data other than those shown here, for example, sensor terminal d3→sensor terminal d5→sensor terminal d4→sensor It can be seen that the entire image of κ(s) is likely to be obtained if the terminals are connected in the order of terminal d3. In fact, vertices corresponding to the curvature graph are also written in the partial shape of FIG. By sequentially connecting the partial shapes corresponding to these sensor terminals d, the elliptical shape of the object T can be reconstructed with high accuracy.

Note that if the trajectory of the sensor terminal d follows the same distribution as in Non-Patent Document 1, (C) can be used to derive information about the number of vertices, further supporting the above conclusion. There are only two types of vertices in the partial curvature function (minimum value 0.025, maximum value 0.2). It should exist. Therefore, when counting the number of sensor terminals d that observed two types of vertices in 500 sensing data generated according to the distribution of Non-Patent Document 1, _nc (minimum) = 201, _nc (maximum) =223. On the other hand, when the formula (7) is calculated in this problem setting, n _e ≈102. Therefore, it can be seen that there are two vertices of each of the two types. This information is useful in connecting sub-shapes and is in fact consistent with the conclusions obtained above.

In addition, in the present embodiment, the partial shape calculator 12 is an example of a calculator. The partial shape connecting unit 13 is an example of an estimating unit.

Although the embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications can be made within the scope of the gist of the present invention described in the claims. Transformation and change are possible.

10 shape estimation device 11 reception unit 12 partial shape calculation unit 13 partial shape connection unit 14 data storage unit 20 user terminal 100 drive device 101 recording medium 102 auxiliary storage device 103 memory device 104 CPU
105 interface device B bus d sensor terminal

Claims (7)

Based on time-series measurements of the distance between a fixed object and the sensor terminal by a plurality of sensor terminals each moving, a partial shape of the object, a curvature function of the object, and a curvature function of the object for each of the sensor terminals. a calculator for calculating arc length ;
an estimating unit that detects overlapping portions between the partial shapes based on the curvature function and the arc length , connects the partial shapes at the overlapping portions, and estimates the overall shape of the object;
A shape estimation device characterized by comprising: The calculation unit calculates the partial shape as an envelope of a curve group calculated from the measurement result.
The shape estimation device according to claim 1, characterized in that: The estimating unit determines the feature points of the curvature function that are non-differentiable points, vertices, or inflection points of the curvature function of the object, the arc length between the feature points of the curvature function, or the number of feature points of the curvature function. detecting the overlap based on
3. The shape estimation device according to claim 1 or 2, characterized in that: Based on time-series measurements of the distance between a fixed object and the sensor terminal by a plurality of sensor terminals each moving, a partial shape of the object, a curvature function of the object, and a curvature function of the object for each of the sensor terminals. a computational procedure for calculating the arc length ;
an estimation step of detecting overlapping portions between the partial shapes based on the curvature function and the arc length , connecting the partial shapes at the overlapping portions, and estimating the overall shape of the object;
A shape estimation method characterized in that the computer executes The calculation procedure calculates the partial shape as an envelope of a family of curves calculated from the measurement results.
5. The shape estimation method according to claim 4, wherein: The estimation procedure is based on the feature points of the curvature function that are non-differentiable points, vertices, or inflection points of the curvature function of the object, the arc length between the feature points of the curvature function, or the number of feature points of the curvature function. detecting the overlap based on
6. The shape estimation method according to claim 4 or 5, characterized in that: A program for causing a computer to execute the shape estimation method according to any one of claims 4 to 6.

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