JP2017156286A - Shape estimation device, shape estimation method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique that uses a distance sensor and can accurately estimate the size and outer circumferential length of an object which is not necessarily convex, and estimate whether the object is convex.SOLUTION: A shape estimation device estimates the shape of an object on the basis of measurement results received from a plurality of sensor terminals 201 for measuring distance from the object in a sensing area. The shape estimation device comprises: a communication unit 301 for receiving the measurement results from the sensor terminals 201; and a processing unit for calculating a statistic on deviation from a measurement result of a first characteristic estimation result by a first characteristic estimation expression suitable if the object is convex, and for determining that the object is not convex if the statistic is equal to or more than a threshold value.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a technique for estimating the size and shape of an object based on a measurement result obtained by a randomly wound distance sensor.

  In recent years, attempts have been made to distribute small sensors with wireless functions in a target area, network them, and use them for various applications. Since it is considered that a large number of sensors are used, it is desirable that the position of each sensor can be used without designing or registering.

  In addition, it is considered that positioning functions such as GPS are not installed in low-cost sensor nodes in terms of price and power consumption. Consider detecting an object having a two-dimensional or three-dimensional spread under such circumstances.

  On the other hand, Patent Document 1 discloses an invention that estimates the area and outer circumference length of an object from information of a sensor (binary sensor) that detects only whether or not the object is detected. An invention for estimating the shape of an object from a binary sensor is disclosed. Further, Patent Document 3 discloses an invention for estimating the angle of an object and the number of objects from a combined binary sensor.

  In the above prior art, while shape estimation is performed using binary sensors or a combination thereof, Patent Document 4 discloses an invention that uses multiple classes of distance sensors to estimate the size and outer circumference of an object. It is disclosed.

Japanese Patent No. 5084771 JP 2011-69637 A Japanese Patent No. 5300797 Japanese Patent No. 5371907

  The method of combining binary sensors results in a large structure and is not easy to deploy. As described above, an invention for estimating the size and outer circumference length of an object using a binary sensor or a distance sensor has been made, but the expression used in the invention is valid for an object whose estimation equation is convex. Therefore, there is a problem that the estimation accuracy is reduced for an object that is not convex.

  The present invention has been made in view of the above points, and uses a distance sensor to estimate the size and outer peripheral length of an object with high accuracy for an object that is not necessarily convex, and to estimate the convexity. It is an object to provide a technology that makes it possible to perform the above.

According to an embodiment of the present invention, a shape estimation device that estimates the shape of an object based on measurement results received from a plurality of sensor terminals that measure the distance to the object in a sensing area,
A receiving unit for receiving the measurement results from the plurality of sensor terminals;
Calculate a statistic related to the deviation from the measurement result of the first characteristic estimation result according to the first characteristic estimation formula suitable for the case where the object is convex, and if the value of the statistic is equal to or greater than a threshold value, And a processing unit that determines that the object is not convex.

Further, according to the embodiment of the present invention, the shape estimation device that estimates the shape of the object based on the measurement results received from the plurality of sensor terminals that measure the distance to the object in the sensing area is executed. A shape estimation method for
A receiving step of receiving the measurement results from the plurality of sensor terminals;
Calculate a statistic related to the deviation from the measurement result of the first characteristic estimation result according to the first characteristic estimation formula suitable for the case where the object is convex, and if the value of the statistic is equal to or greater than a threshold value, And a processing step of determining that the object is not convex.

  According to the embodiment of the present invention, it is possible to estimate the size and outer circumference length of an object with high accuracy and to estimate the convexity for an object that is not necessarily convex using a distance sensor. It becomes possible to provide the technology.

It is a block diagram of the shape estimation system in this Embodiment. It is a flowchart which shows the process sequence in this Embodiment. It is a figure which shows the example of the target object approximated by the polygon. It is a figure which shows the target object used by simulation.

  Hereinafter, embodiments of the present invention (hereinafter referred to as the present embodiment) will be described with reference to the drawings. The embodiment described below is merely an example, and the form to which the present invention can be applied is not limited to the following embodiment.

(System configuration)
FIG. 1 is a configuration diagram of a shape estimation system in the present embodiment. As shown in FIG. 1, the shape estimation system according to the present embodiment includes a center server 401 and m sensor terminals 201-1 to 201 as sensor terminals that detect an object and measure the distance to the object. 201-m, and shape information of the object is estimated. Here, the shape information is information relating to the shape of the object, such as the area (size, size) of the object, the length of the outer periphery of the object, and the unevenness of the object. Hereinafter, an object in the shape estimation system is referred to as an object T, an area thereof is represented as an area S, and an outer circumference length is represented as a circumferential length L.

  Each of the m sensor terminals 201-1 to 201-m includes a measurement unit 101, a communication unit 102, and a power supply unit 103. It is assumed that each sensor terminal does not have a positioning function and the geographical location where it is deployed is not designed in detail.

The measuring unit 101 is a sensor that detects an object in the sensing area of the sensor terminal and measures the distance between the terminal and the object. More specifically, the measuring unit 101 is a distance sensor having sharp directivity, and when the distance to the object is equal to or less than r _max , the distance r to the object r (0 <= r <= r _max ) Is obtained as a measurement result. The communication unit 102 transmits information indicating a measurement result by the measurement unit 101 (hereinafter, measurement result information) to the center server 401. The power supply unit 103 supplies power.

  Hereinafter, the m sensor terminals 201-1 to 201-m are also collectively referred to as sensor terminals.

  The center server 401 is a computer terminal that includes a communication unit 301, a data processing unit 302, a storage unit 303, an input / output unit 304, and a power supply unit 305.

  The communication unit 301 performs communication processing for receiving measurement result information transmitted from the sensor terminals 201-1 to 201-m. The communication unit 301 stores the received measurement result information in the storage unit 303.

  The data processing unit 302 calculates an estimated value of the shape information of the object T based on the measurement result information received by the communication unit 301.

  The data processing unit 302 first calculates the size (area) S and the circumference L of the object based on the formula stored in the storage unit 303. Further, T convexity determination is performed. If the object is not convex, the estimated value of the circumference L is corrected. These processes will be described in detail later. The processing result is output from the input / output unit 304.

The storage unit 303 stores parameters used in calculation formulas such as calculation formulas and sensing distances r _{max of} sensor terminals, the area S _A of the monitoring target area A, and the number m of sensor terminals. The storage unit 303 also stores calculation results during the calculation process.

  The center server 401 according to the present embodiment can be realized by causing a computer to execute a program describing the processing contents described in the present embodiment. That is, the functions of the center server 401 can be realized by executing a program corresponding to the processing executed by the center server 401 using hardware resources such as a CPU and a memory built in the computer. It is. The program is, for example, a program including processing of each mathematical formula described in the present embodiment and a processing procedure using the mathematical formula.

  The above-mentioned program can be recorded on a computer-readable recording medium (portable memory or the like), stored, or distributed. It is also possible to provide the program through a network such as the Internet or electronic mail.

(Details of shape estimation processing)
Hereinafter, the shape estimation process of the target T executed by the shape estimation system in the present embodiment will be described along the procedure shown in the flowchart of FIG.

  First, the sensor terminals 201-1 to 201-m are randomly arranged in a predetermined monitoring target area A (step S101). The sensor terminal measures the distance to the object T at regular intervals, transmits the measurement result (sensing result) to the center server 401, and the center server 401 acquires the measurement result (step S102). Note that the measurement time interval does not necessarily have to be constant. Further, the position of the sensor terminal may move.

  The object T in the present embodiment does not change in size or shape, is in the monitoring target area A, and is moving. The object T is not necessarily moved, but will be described below as being moved. The object T can be approximated by a polygon.

The center server 401 applies the total n _s measurement results sent from the sensor terminals 201-1 to 201-m to the calculation formula stored in the storage unit 303, and calculates an estimated value and the like (steps S103 to S103). S113). At this time, the n _s measurement results may be a single measurement result from m sensor terminals (in this case, n _s = m), or a plurality of measurement results may be used together. Good. In theory, since it is assumed that each measurement result is independent, the estimation accuracy may be reduced if the measurement interval is excessively short relative to the moving speed of the object T. .

  More specifically, the processing in the data processing unit 302 is executed as follows. Hereinafter, the processing procedure using each formula will be described, and the theoretical background of each formula will be described after the description of the processing procedure.

As the measurement result, n _s number of results are obtained, of which the number is N ₀ amino measurements r = 0 is a thing, 0 <measurements <= r number of _max is a thing are K, measurement results Suppose that no detection was K ₀ .

  When each case detection is independent, if T is convex, the maximum likelihood estimators of L and S are given by the following equations (1) and (2).

そこで、まず、凸であることを仮定して、記憶部３０３に保持された式（１）、（２）を計算する（ステップＳ１０３、Ｓ１０４）。Sについては、凸でなくとも式（２）による推定量が妥当であることから、式（２）による結果を入出力部３０４から出力する（ステップＳ１０４）。つまり、この時点で、Sの推定値が決まり、出力される。

Therefore, first, assuming that it is convex, the equations (1) and (2) held in the storage unit 303 are calculated (steps S103 and S104). For S, the estimated amount according to the equation (2) is appropriate even if it is not convex, so the result according to the equation (2) is output from the input / output unit 304 (step S104). That is, at this point, the estimated value of S is determined and output.

  If T is not convex, using equation (1) as an estimated amount of L results in an underestimation of L. Therefore, the following equation (3) held in the storage unit 303 is calculated as an estimated value of L. (Step S105).

式（３）において、N(s)は、測定結果n_s個のうち、測定結果<=sであったものの数を表す。また、s₁, s₂は、適切に設定すべきパラメータであるが、経験的には、s₂は、Tの凹を構成する辺の長さ程度、s₁はs₂の数分の１程度が目安である。ただ、Tの辺の長さが未知であることから、例えば、式（１）において、n_sとしてn_s/10を代入し、Kとしてn_s/10個のうち測定結果<=r_maxであった測定結果数を代入して求めたL^の1/10、すなわちL^/10をs₂の値とする。n_s/10を使用するのは、サンプルとして全測定結果のうちの1/10を使用することを意味し、L^/10は、Tが凸の場合に、凸を構成する辺の長さが外周長の1/10程度と推定されることを意味する。なお、本明細書のテキストにおいては、記載の便宜上、例えばL^のように、推定値を表すハット＾を、変数の頭ではなく、変数の前に置いている。

In Expression (3), N (s) represents the number of measurement results <= s among the n _s measurement results. In addition, s ₁ and s ₂ are parameters that should be set appropriately, but empirically, s ₂ is about the length of the side that constitutes the recess of T, and s ₁ is a fraction of s ₂ The degree is a guide. However, since the length of the side T is unknown, for example, in the formula (1), by substituting n _s / 10 as n _s, n _s / 10 pieces of measurement result as K in <= r _max there measurement result number L ^ 1/10 found by replacing the, i.e. the L ^ / 10 and the value of s _2. Using n _s / 10 means that 1/10 of all measurement results is used as a sample, and L ^ / 10 is the length of the edges that make up the convex when T is convex Is estimated to be about 1/10 of the perimeter. In the text of this specification, for convenience of description, a hat ^ representing an estimated value is placed in front of a variable instead of the head of the variable, for example, L ^.

  Actually, since it is not known whether T is convex, it is effective if this can be determined. In addition, since there may be an object that is characterized by being concave, it is important to estimate convexity. Therefore, the data processing unit 302 performs the following convexity estimation.

  When T is convex, the probability that the measurement result s of the sensor is r or less is given by the following equation (4).

式（４）中のLとSを式（１）、（２）の推定値に置き換えることにより、この確率の推定値は下記の式（５）で与えられる。

By replacing L and S in Equation (4) with the estimated values of Equations (1) and (2), the estimated value of this probability is given by Equation (5) below.

この確率の推定値とこの確率の観測値N(r)/n_sの乖離が、この推定値の標準偏差σの一定数倍以下なら、Tが凸、そうでなければ、Tが凹と判定する。標準偏差σは、下記の式（６）を計算することで近似的に与えられる。

Determining an estimate of the probability and deviation of observations N (r) / n _s of this probability, if below a certain number times the standard deviation σ of the estimated value, T is convex, otherwise, T is concave To do. The standard deviation σ is approximately given by calculating the following equation (6).

式（６）において、N(>r)=K+N₀−N(r)である。具体的には、データ処理部３０２は、記憶部３０３に保持された式（５）を計算し、その値をN(r)/n_sから引き、その結果をe(r)とおく（ステップＳ１０６）。すなわち、下記のとおりである。

In the formula (6), N (> r) = K + N ₀ −N (r). Specifically, the data processing unit 302, a stored in the storage unit 303 (5) calculated, subtract it from the N (r) / n _s, put the result with e (r) (step S106). That is, it is as follows.

そして、記憶部３０３に保持された式（６）を計算し、標準偏差σを得る（ステップＳ１０７）。得た標準偏差σでe(r)を割り算する。rの値は、経験的にはr_max/2などがよいが、0以上r_max以下の任意の値を用いてもよい（ステップＳ１０８）。ステップＳ１０８での結果が、予め定めた閾値以上であれば（ステップＳ１０９のＹｅｓ）、凸ではないと推定して、その結果を入出力部３０４から出力し（ステップＳ１１０）、閾値以下であれば（ステップＳ１０９のＮｏ）、凸であると推定して、その結果を入出力部３０４から出力する（ステップＳ１１１）。

Then, the equation (6) held in the storage unit 303 is calculated to obtain the standard deviation σ (step S107). Divide e (r) by the obtained standard deviation σ. The value of r is empirically preferably r _max / 2, but any value between 0 and r _max may be used (step S108). If the result in step S108 is equal to or greater than a predetermined threshold value (Yes in step S109), it is estimated that it is not convex, and the result is output from the input / output unit 304 (step S110). (No in step S109), it is estimated to be convex, and the result is output from the input / output unit 304 (step S111).

  When it is estimated that (i) it is not convex, the data processing unit 302 outputs the calculation result of Expression (3) from the input / output unit 304 (step S112), and (ii) it is estimated that it is convex. In this case, the calculation result of Expression (1) is output from the input / output unit 304 (step S113).

  From the above, based on the measurement result of the center terminal, the estimation result of the convexity of the target T (whether it is convex or not), the estimated value of the area S of the target T, the outer peripheral length L of the target T Are estimated and are output from the center server 401. Note that it is not essential to output all of these. For example, when it is desired to know only the convexity of the target object T, only the convexity estimation result may be output.

(Theoretical background)
For convex objects, equation (4) is derived from equation (6.48) of the document "LA Santalo, Integral Geometry and Geometric Probability, Second edition. Cambridge University Press, Cambridge, 2004." Then, since the sensing result is a random sample from the distribution having this probability, the likelihood is given by the following equation (7).

式（１）、（２）は、その尤度を最大化するLとSとして得られる。式（５）は、式（４）におけるLとSを、式（１）、（２）で与えられるその推定値で置き換えることで得られる。更に、式（５）で与えられる推定量の期待値は、N(r)/n_sの期待値に等しいことに注意して、「N(r)/ n_s−式（５）で与えられる推定量」の標準偏差σを計算する。センシング結果が0であるか、r以下であるか、rより大きいかは、多項分布に従い、その標本値は、N₀、N(r)−N₀、N(>r)であることから、
（１）N(>r)]の分散は、

Equations (1) and (2) are obtained as L and S that maximize the likelihood. Equation (5) is obtained by replacing L and S in equation (4) with their estimated values given in equations (1) and (2). Furthermore, the expected value of the estimator is given by equation (5) is to note that equal to the expected value of N (r) / n _s, "N (r) / n _s - is given by Equation (5) The standard deviation σ of “estimated amount” is calculated. Whether the sensing result is 0, less than r, or larger than r follows a multinomial distribution, and the sample values are N ₀ , N (r) −N ₀ , N (> r),
(1) The variance of N (> r)] is

で与えられ、これは、N(>r)(n_s−N(>r))/n_sで近似できる。

Given, this is, N (> r) (n s -N (> r)) can be approximated by / n _s.

Also, (2) N (r) −N ₀ variance is

で与えられ、これは、(N(r)−N₀)(n_s−N(r)+N₀)/n_sで近似できる。

Which can be approximated by (N (r) −N ₀ ) (n _s −N (r) + N ₀ ) / n _s .

Also, (3) N (> r), N (r) -N ₀ covariance is

で与えられ、これは、−N(>r)(N(r)−N₀)/ n_sで近似できるので、標準偏差σは、式（６）で与えられる。

Given, this is because it approximated by -N (> r) (N ( r) -N 0) / n s, the standard deviation sigma, given by equation (6).

  On the other hand, Expression (3) is derived by assuming that the object is approximated by a polygon. When the vertices at both ends of one side are convex, for example, as shown in FIG. 3A, the sensing area of the sensor outside the object is not blocked by the other side. On the other hand, when it has a concave vertex, for example, as shown in FIG. 3B, sensing is interrupted by another side. For this reason, distortion occurs in the obtained N (r). That is, the statistic related to N (r) is not what was expected. Specifically, the distribution of N (r) increases when r is small and decreases when it is large. This strain varies with the value of r. It is necessary to correct this distortion.

The internal angle of the i-th vertex that is concave is φ _i , and one of the lengths of the sides constituting the vertex is h. φ _i > π. If the interior angle of the vertex and both sides of the vertex satisfy {3π / 2 <φ _i <2π, r <h | sinφ _i |} or {π <φ _i <3π / 2, r <h} The quantity can be derived relatively easily by geometric calculation. As a result, the probability that the measurement result s of the sensor is r or less is obtained by the following equation (8).

s₁、s₂が{3π/2<φ_i <2π, s₁,s₂< h|sinφ_i|}または{π<φ_i <3π/2, s₁,s₂<h }の場合、式（８）でr= s₁,s₂とした２つの式について、当該式の左辺は、N(s₁)/n_s, N(s₂)/n_sで近似できることから、LとSについて解いて、LとSの推定量を式（２）、（３）として得る。

If s ₁ and s ₂ are {3π / 2 <φ _i <2π, s ₁ , s ₂ <h | sinφ _i |} or {π <φ _i <3π / 2, s ₁ , s ₂ <h}, For the two equations where r = s ₁ , s _{2 in} equation (8), the left side of the equation can be approximated by N (s ₁ ) / n _s , N (s ₂ ) / n _s , so L and S To obtain the estimated amounts of L and S as equations (2) and (3).

(Effects of the embodiment)
Hereinafter, the results of the simulation using (a) a sports car (a convex object) and (b) a tank (a non-convex object) shown in FIG. 4 as objects will be described.

In FIG. 4, the unit of the number indicating the length of the side of the object is meter. Here, it is assumed that the object moves straight at a speed of 10 m per second on the center line of a straight road having a width of 50 m. The sensors were distributed on the road at a density of 1 [/ square meter], the sensors were to sense at a measurement interval of 1 second, and each sensor measured 1000 times in total. R _max = 20 m. Ten simulations were performed for each object.

  Concerning convexity determination, there is a determination error once for each sports car and tank, and the correct answer rate is 90%. The average relative error of the outer peripheral length is not determined by the unevenness, but the expression (1) is different from that of the sports car by the method according to S112 and S113 of the present invention which uses the expressions (1) and (3) according to the unevenness determination. Tanks improved from 0.137% and 10.5% to 0.0654% and 2.60%.

  As described above, with the technology according to the present embodiment, it is possible to estimate the convexity of an object and the outer circumference of an object that is not convex, using the sensing results of a sensor whose position is randomly deployed. It became.

(Summary of embodiment)
As described above, according to the present embodiment, a shape estimation device that estimates the shape of an object based on measurement results received from a plurality of sensor terminals that measure distances from the object in the sensing area. A reception unit that receives the measurement results from the plurality of sensor terminals, and a statistic relating to a divergence from the measurement result of an estimation result of the first characteristic according to a first characteristic estimation formula suitable when the object is convex. A shape estimation device is provided that includes a processing unit that calculates a quantity and determines that the object is not convex if the value of the statistic is equal to or greater than a threshold value.

  The center server 401 illustrated in FIG. 1 is an example of a shape estimation apparatus, and the communication unit 301 is an example of a reception unit. The data processing unit 302 and the storage unit 303 are examples of processing units.

  In addition, the expression (5) in the embodiment corresponds to the first characteristic estimation expression, and the calculation result obtained by dividing e (r) by the standard deviation σ in the embodiment corresponds to the statistic.

  For example, when the value of the statistic is equal to or greater than a threshold value, the processing unit calculates a second characteristic estimation formula suitable for the case where the object is not convex based on the measurement result, An estimated value is obtained, and when the value of the statistic is not equal to or greater than a threshold, a third characteristic estimation formula suitable for a case where the object is convex is calculated based on the measurement result, and an estimated value of the characteristic X Ask for.

  Formula (1) of the embodiment corresponds to the third characteristic estimation formula, and formula (3) of the embodiment corresponds to the second characteristic estimation formula.

  The first characteristic estimation formula is an expression for estimating, as the first characteristic, a probability that the measurement results received from the plurality of center terminals are equal to or less than a certain value, and the statistic regarding the deviation is based on the measurement results. The calculation result obtained by subtracting the estimation result by the first characteristic estimation formula from the calculated probability may be a calculation result obtained by dividing the calculation result by the standard deviation of the calculation result. The characteristic X is, for example, the outer peripheral length of the object.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims.

DESCRIPTION OF SYMBOLS 101 Measurement part 102 Communication part 103 Power supply part 201-1 to 201-m Sensor terminal 301 Communication part 302 Data processing part 303 Storage part 304 Input / output part 305 Power supply part 401 Center server

Claims (8)

A shape estimation device that estimates the shape of an object based on measurement results received from a plurality of sensor terminals that measure the distance to the object in a sensing area,
A receiving unit for receiving the measurement results from the plurality of sensor terminals;
Calculate a statistic related to the deviation from the measurement result of the first characteristic estimation result according to the first characteristic estimation formula suitable for the case where the object is convex, and if the value of the statistic is equal to or greater than a threshold value, And a processing unit that determines that the object is not convex. The processor is
When the value of the statistic is equal to or greater than a threshold, a second characteristic estimation formula suitable for a case where the object is not convex is calculated based on the measurement result to obtain an estimated value of the characteristic X,
When the value of the statistic is not greater than or equal to a threshold value, a third characteristic estimation formula suitable for a case where the object is convex is calculated based on the measurement result to obtain an estimated value of the characteristic X. The shape estimation apparatus according to claim 1. The first characteristic estimation formula is an expression for estimating a probability that the measurement result received from the plurality of center terminals is a certain value or less as the first characteristic,
The statistic relating to the deviation is a calculation result obtained by dividing a calculation result obtained by subtracting an estimation result based on the first characteristic estimation formula from the probability calculated based on the measurement result by a standard deviation of the calculation result. The shape estimation apparatus according to claim 1 or 2. The shape estimation apparatus according to claim 2, wherein the characteristic X is an outer peripheral length of the object. A shape estimation method executed by a shape estimation device that estimates the shape of an object based on measurement results received from a plurality of sensor terminals that measure the distance to the object in a sensing area,
A receiving step of receiving the measurement results from the plurality of sensor terminals;
Calculate a statistic related to the deviation from the measurement result of the first characteristic estimation result according to the first characteristic estimation formula suitable for the case where the object is convex, and if the value of the statistic is equal to or greater than a threshold value, And a processing step for determining that the object is not convex. In the processing step, the shape estimation device includes:
When the value of the statistic is equal to or greater than a threshold, a second characteristic estimation formula suitable for a case where the object is not convex is calculated based on the measurement result to obtain an estimated value of the characteristic X,
When the value of the statistic is not greater than or equal to a threshold value, a third characteristic estimation formula suitable for a case where the object is convex is calculated based on the measurement result to obtain an estimated value of the characteristic X. The shape estimation method according to claim 5. The first characteristic estimation formula is an expression for estimating a probability that the measurement result received from the plurality of center terminals is a certain value or less as the first characteristic,
The statistic relating to the deviation is a calculation result obtained by dividing a calculation result obtained by subtracting an estimation result based on the first characteristic estimation formula from the probability calculated based on the measurement result by a standard deviation of the calculation result. The shape estimation method according to claim 5 or 6.   The program for functioning a computer as each part in the said shape estimation apparatus of any one of Claims 1 thru | or 4.

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