JPH06274623A - Method for estimating two-dimensional data from observed data - Google Patents

Abstract

PURPOSE:To estimate a stable and accurate solution with a less arithmetic quantity by decreasing the resolution of processing in an area, where the distribution of the solution is large, and increasing the resolution in an area, where the distribution is small, by controlling the resolution from the estimated error of the solution. CONSTITUTION:An evaluated value arithmetic circuit 6 calculates an evaluated value from the observed data, variance value and estimated solution vector value. When the evaluated value is smaller than a threshold value, the evaluated value of the variance value of the solution is reduced and outputted to a resolution deciding circuit 3. When the evaluated value is not reduced even by reducing the variance value of the solution, a select signal is outputted to a solution vector output circuit 7. The circuit 7 inputs a solution vector and outputs the solution vector as the final arithmetic result through a solution vector output terminal 10 corresponding to the select signal from the circuit 6. At the time of arithmetic start, an initial vector is inputted from an initial solution vector input terminal 8 and written through a switch 9 to a solution vector memory 4. Thus, the high-accuracy solution vector is provided with the less arithmetic quantity adaptively to the local character of observation noise.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for estimating two-dimensional data from observed data, and more particularly to estimating two-dimensional data to be estimated from observed data obtained by observing two-dimensional array data such as an image. The present invention relates to a method of estimating two-dimensional data from observed data.

For example, this two-dimensional data estimation method is based on a surface shape reconstruction problem for estimating the shape of the surface of an object from a small number of observed distance data, and a two-dimensional apparent motion field from a moving image sequence. "Shape from shading" to estimate the target shape from the shaded image
All of these issues are included in this technology. This is the basic technology needed to achieve a "machine eye."

[0003]

2. Description of the Related Art Many problems of vision can be formulated as a problem of estimating original data from measured data. At this time, existence, uniqueness, stability, and accuracy of solutions are critical problems. Up to now, a method called regularization, that is, a method of introducing a further constraint into a solution to limit a possible range of the solution, etc., has been used to obtain a stable solution.

In the standard regularization theory, a vector b subjected to a linear operation A is observed from unknown data (hereinafter referred to as a vector) u, and its relation is expressed as b = Au + r (1). Here, r is a Gaussian noise vector in observation. Here, the shape of the noise distribution is known, but its variance is assumed to change temporally and spatially.
At this time, the evaluation function for obtaining the solution can be formulated as follows, and the problem of estimating u from the observation vector b can be reduced to the objective function E of the following formula as a minimization problem.

[Equation 1] Here, in the equation (2), the first term is a penalty functional representing the difference between the observed data and the solution, and the second term is the stabilizing functional indicating the constraint condition of the real world for the solution. λ is a parameter that determines the ratio of the two conditions. Also, Ω is x
-Indicates the integration region in the y-plane. The minimization of this equation is
This means finding a solution that matches the observed data as much as possible and that satisfies the constraint conditions well. When actually solving the above minimization problem, it is given in the following form in which the solution space is sampled.

[Equation 2] Can be described as Here, the vectors u _x and u _y are: u _x = (u (i + 1, j) −u ((i−1, j)) / 2 u _y = (u (i, j + 1) −u ((i, j−1)) / 2, the parameter λ is preset according to the complexity of the assumed solution, d is the sampling interval, and the minimization problem of equation (3) is the relaxation method. , I.e., the solution vector u _{i, j} ⁽ⁿ⁾ of the sample point (i, j, t) in the ^{nth step} is

[Equation 3] By repeatedly using the solution vector u _{i, j} ⁽ⁿ⁾ , υ
_{i, j} ⁽ⁿ⁾ approaches the final solution, and the estimated value is obtained.
However, here

[Equation 4] Is.

In the conventional method, the solution is estimated by the procedure as described above.

[0006]

However, as the above-mentioned conventional unsolved problems, there are problems of solution resolution and calculation amount. Generally, in the method using regularization, when the sampling interval is finer than the appropriate resolution of the solution, the solution can be stabilized, but the convergence is slow and enormous calculation is required.
On the contrary, if the sampling is rough, it will not converge to a stable solution and will be caught by a local solution. That is, the conventional method has problems that the amount of calculation becomes enormous, noise remains, and a stable solution cannot be obtained.

The present invention has been made in view of the above points, and provides a two-dimensional data estimation method from observation data that solves the above-mentioned conventional problems and estimates an accurate solution vector with an appropriate amount of calculation. With the goal.

[0008]

The present invention inputs observation data of a two-dimensional array obtained by observing two-dimensional data and observation reliability data indicating the reliability of each observation data, An evaluation value based on a first constraint condition expression describing a constraint relationship with two-dimensional data to be estimated and an evaluation value based on a second constraint condition expression describing smoothness of data to be estimated are generated, In a two-dimensional data estimation method from observation data, which estimates two-dimensional data by optimizing a total evaluation value that weights two evaluation values by iterative calculation, observation is performed from the reliability of the observation data and the reliability of the estimated data. Based on the reliability of the first constraint conditional expression calculated for each point, the solution is estimated while changing the resolution of the estimation data used for the iterative calculation.

[0009]

The present invention estimates a solution using regularization in order to estimate a highly accurate and uniquely stable two-dimensional solution vector from an observation vector without greatly increasing the calculation amount. Adaptive control is performed based on the reliability of the resolution solution. Therefore, by controlling the processing resolution based on the assumed error of the solution, the optimality of the solution is guaranteed by increasing the resolution in the region where the dispersion of the solution is large and increasing the resolution in the region where the dispersion of the solution is small. . As a result, a stable and well-controlled solution can be estimated with a small amount of calculation as compared with the method using multi-resolution.

[0010]

Embodiments of the present invention will be described below with reference to the drawings.

First, the outline of the present invention will be described. The present invention requires two methods in order to obtain a highly accurate two-dimensional solution vector that matches the accuracy of observation without increasing the amount of computation. First, the first is to evaluate the reliability of given observation data and estimation data as variance. Secondly, the resolution is controlled from the obtained reliability (dispersion) to perform highly accurate solution estimation.

The first method, that is, the observation error for each sample point,
For the method of evaluating the variance of the solution error, see “Japanese Patent Application No. 4-
7237 "2D motion field estimation system from time series images". Then, it was shown that the variance σ _r ² in regularization is given by the sum of the variance of the observed data and the variance of the solution. As a result, the evaluation value of variance not only spatially changes but also changes in the iterative process of regularization. Therefore, it is possible to optimize regularization by weighting the variance for each sample point. I showed that I can do it. The present invention provides a method for controlling the resolution of a solution.

According to the present invention, the resolution is controlled in accordance with the variance estimation value obtained for each observation sample point so that the coarse grid is used in the region where the variance is large and the fine grid is used in the region where the variance is small. Therefore, the accuracy of observation is reflected in the resolution of the estimated value. Furthermore, by controlling the variance to become gradually smaller in the iterative calculation process of regularization, solution estimation using multiresolution can be realized. The calculation amount does not become large because the calculation is performed using only the necessary sampling point data at the appropriate resolution according to the observation accuracy using the multi-resolution.

Next, as a second method, a method for obtaining the local resolution of the solution from the variance by Fourier analysis, that is, the sampling interval d of multiresolution will be described. If the solution vector u is a continuous function and the dispersion stabilizing functional is ∇ ² u, the functional to be minimized is

[Equation 5] Can be written. The sampling interval d can be determined by the sampling theorem if the frequency band of the solution u is known. Therefore, in the following, the band of the solution u will be investigated using Fourier analysis. First, by setting g = 1 / σ _r ² and taking Taylor expansion around the origin and taking up to the first-order terms and ignoring the higher-order terms, g (x, y) = g ₀ + g _x x + g _y You can write like y. Here, g ₀ is g (0,0), g _X is ∂g (0,0) / ∂x, g y is ∂g (0,0) / ∂y.

Using this g, the Euler equation of equation (6) becomes

[Equation 6] Becomes Since u is a vector of order N, N equations were obtained. Now, paying attention to the n-th equation, Fourier transform yields the following equation.

F _(n) (ω ₁ , ω ₂ ) * (2πg ₀ δ (ω ₁ , ω ₂ ) −2πg _x iδ _x (ω ₁ ) −2πg _y iδ _y (ω ₂ )) + λ (ω ₁ ² + Ω ₂ ² ) U _(n) (ω ₁ , ω ₂ ) = 0 (8) Here, F _(n) (ω ₁ , ω ₂ ) is given by ∂‖Au−b‖ ² / ∂u _(n) Fourier transform, * is a convolution operation, and δ is a Dirac delta function. Further, δ _x is the first derivative of x of the delta function, δ _y is the first derivative of _y of the delta function, and U _(n) (ω ₁ , ω ₂ ) is the Fourier transform of u _(n) . Now, assuming that the frequency space is isotropic, ω _r ² = ω
Assuming ₁ ² + ω ₂ ² , equation (8) becomes

[Equation 7] Can be written.

Further, from the property of the Dirac delta function, the equation (9) is expressed as 2πg ₀ F _(n) (ω _r ) −2πig _r F _{r (n)} (ω _r ) + λω _r ² U _(n) (ω _r ) = 0 (10)

When the above U _{(n) is} arranged,

[Equation 8] Is obtained. Where g ₀ is the value of the origin of 1 / σ _r ² and g
_r is the gradient in the r direction at the origin of 1 / σ _r ² . F
_{Since (n)} (ω _r ) is band limited, F
_The band of _{r (n)} (ω _r ) is similarly limited. From equation (11), the spectrum is

[Equation 9]

However, H ₀ (ω _r ) = 2πg ₀ / λω _r ² and H _r (ω _r ) =-2πig _r / λω _r ² . This equation (12) H ₀ in _{ω r = 0 (ω r)} , H
_r (ω _r ) seems to diverge, but in fact F
_{Since (n)} (ω _r ) and F _{r (n)} (ω _r ) have finite energy, they do not diverge. Now, F _(n) (ω _r ) and F _{r (n)} (ω
_It is assumed that the band of _r ) is wider than H ₀ (ω _r ) and H _r (ω _r ). Since F _(n) (ω _r ) and F _{r (n)} (ω _r ) are obtained from the error between the estimated value and the observed value, it is generally considered that the band is wide. Therefore, this process is often established, and the main factors that determine the band of | U _(n) (ω _r ) | can be regarded as H ₀ (ω _r ) and H _r (ω _r ).

Equation (12) states the following facts. That is, where the observation noise does not change spatially, only g ₀ contributes to the determination of the resolution of U _(n) (ω _r ), and where the observation noise changes spatially greatly, g ₀ and g _r Both terms of contribute to the resolution of U _(n) (ω _r ). In other words, the band of U _(n) (ω _r ) becomes narrower where the value of variance is large and where the spatial variation of variance is large,
It has a wide band where the dispersion is small.

In the above discussion, F _(n) (ω _r ), F _{r (n)} (ω
_r ) is not a major factor in determining the bandwidth, so U
_(n) (ω _r ) can have the same band for any n.

A concrete method for determining the sampling interval is as follows.
become. First, the estimated variance σ_r ²To g₀, G_rTo
calculate. Next, determine an arbitrary decimal β,₀(Ω_r) | <Β and | H_r(Ω_r) | <Β frequency ω_maxTo calculate. This frequency ω_maxIs the solution u
Is the band. Therefore, the sampling frequency ω_sIs nai
To satisfy the Kist theorem ω_s= 2ω_max Given by. The corresponding grid spacing d is d = 1
/ Ω_sGiven in.

As a result of the above, the resolution of the solution becomes high where the observation accuracy is good, and an accurate solution is obtained.
Since the band is narrowed where the observation accuracy is poor, a stable solution that satisfies the required smoothness can be obtained.

FIG. 1 shows a flowchart for estimating a solution according to an embodiment of the present invention. A procedure for obtaining the sampling interval d from the variance σ _r ² and applying it to the regularization to estimate the solution will be described with reference to FIG.

Step 1: First, the initial value of the solution is determined, and the variance σ _u ² of the solution is calculated from the difference between the initial value and the expected range of the target solution.

Step 2: Input the reliability (dispersion) σ _b ² of the observation data and the observation noise.

Step 3: Evaluate the variance σ _r ² in the equation (3) from the variance A σ _u ^{2 of the} solution and the variance σ _b ² of the observation noise.

Step 4: Select the grid spacing d of resolution according to the variance value. The grid interval is variably set for each observation point.

Step 5: Regularize the observation points of the obtained grid and obtain a solution by interpolation.

Step 6: When the regularization process converges to a steady value, the evaluation value of the dispersion of the solution is re-evaluated (decreased), and the process proceeds to step 3. Even if the evaluation value σ _u ² of the solution variance is reduced, the process ends when the solution does not change.

The above procedure is equally applicable to many vision problems including motion field estimation in the gradient method.

The method described above has the following features. (1) An accurate solution matching the observation accuracy can be obtained. Optimality is guaranteed without excess or deficiency of smoothing. (2) The uniqueness and stability of the solution are guaranteed. (3) Since the pixels to be calculated are thinned out by the introduction of the multi-resolution, the amount of calculation is small and the convergence is fast.

FIG. 2 shows the configuration when an embodiment of the present invention is applied to an estimation device. In the figure, the estimation device holds an observation vector input terminal 1 for inputting an observation vector b, a variance value input terminal 2 for inputting a variance value, a resolution determination circuit 3 for executing the equation (2), and a solution vector u. Solution vector memory 4, observation vector input from observation vector input terminal 1 and resolution determined by resolution determination circuit 3, solution vector operation circuit 5 that corrects the solution vector using solution vector from solution vector memory 4, variance value Evaluation value calculation circuit 6 for calculating an evaluation value using the variance value input from the input terminal 2, the observation vector input from the observation vector input terminal 1, and the solution vector input from the solution vector calculation circuit 5, and the solution vector calculation A solution vector output circuit 7 for outputting a solution vector according to the solution vector obtained by the circuit 5 and a selection signal from the evaluation value calculation circuit 6, a solution vector And outputs the solution vector output terminal 10, the initial solution vector input terminal 8 for inputting a first initial solution vector arithmetic, and the switch 9.

First, observation data is input from the input terminal 1 to the solution vector calculation circuit 5 and the evaluation value calculation circuit 6. The variance value associated with the observation data is input from the variance input terminal 2 to the resolution determination circuit 3, the solution vector calculation circuit 5, and the evaluation value calculation circuit 6.

The resolution determination circuit 3 calculates the variance σ _r ² from the variance value input from the variance input terminal 2 and the variance value of the solution input from the evaluation value calculation circuit 6, and then the equation (12) The resolution is determined based on. The grid spacing d thus determined is output to the solution vector calculation circuit 5.

The solution vector calculation circuit 5 corrects the solution vector based on the observation data, the variance value, and the uncorrected solution vector input from the solution vector memory 4, using the data of the given grid interval d. . The solution vector of the sample point that is not calculated because the grid interval is large is calculated by interpolation. The solution vector operation circuit 5 is described in Japanese Patent Application No.
As described in -7237, the obtained solution vector correction value realized only by the addition, subtraction, multiplication and division operation is input to the solution vector memory via the evaluation value operation circuit 6, the solution output circuit 7, and the switch 9. .

The evaluation value calculation circuit 6 calculates the evaluation value shown in the equation (3) using the observation data, the variance value, and the estimated solution vector value. The evaluation value calculation circuit 6 is composed of a multiplier and an accumulator. This evaluation value is compared with a predetermined threshold value, and when the evaluation value becomes smaller than the threshold value, the evaluation value of the dispersion value of the solution is reduced and output to the resolution determination circuit 3. If the evaluation value does not decrease even if the variance value of the solution is reduced, the repetitive calculation is stopped and the selection signal is output to the solution output circuit 7.

The solution output circuit 7 inputs the solution vector and outputs the solution vector as the final operation result via the output terminal 10 in response to the selection signal from the evaluation value operation circuit 6. At the start of calculation, the initial solution vector is input from the initial solution vector input terminal, and the switch 9 is input to the solution vector memory 4.
Written through. The initial value may be selected to be within the range of the expected solution. After inputting the initial solution vector, the switch is turned to the output side of the solution vector calculation circuit 5.

With the above-mentioned configuration, it is possible to obtain a highly accurate solution vector with a small amount of calculation by adapting to the local property of observation noise. INDUSTRIAL APPLICABILITY The present invention can be applied to various vision system problems such as speed detection of an object in robot vision.

[0040]

As described above, according to the present invention, the resolution of processing is controlled based on the assumed error of the solution, so that the resolution is low in the area where the dispersion of the solution is large and the resolution is small in the area where the dispersion is small. By increasing the value, a stable and accurate solution can be estimated with a small amount of calculation.

[Brief description of drawings]

FIG. 1 is a flow chart showing a method realized by the present invention.

FIG. 2 is a block diagram showing an embodiment of the present invention.

[Explanation of symbols]

 1 Observation vector input terminal 2 Variance value input terminal 3 Resolution determination circuit 4 Solution vector memory 5 Solution vector operation circuit 6 Evaluation value operation circuit 7 Solution vector output circuit 8 Initial solution vector terminal 9 Switch 10 Solution vector output terminal

Claims (1)

[Claims] 1. The observation data of a two-dimensional array obtained by observing the two-dimensional data and the observation reliability data indicating the reliability of each observation data are input to estimate the observation data.
The evaluation value based on the first constraint condition expression describing the constraint relationship with the dimensional data and the evaluation value based on the second constraint condition expression describing the smoothness of the data to be estimated are generated, and two evaluation values are generated. In a two-dimensional data estimation method from observation data, which estimates two-dimensional data by optimizing the total evaluation value weighted by the iterative calculation, the reliability of the observation data and the reliability of the estimated data are calculated for each observation point A two-dimensional data estimation method from observation data, characterized in that a solution is estimated while changing a resolution of estimation data used for iterative calculation based on the reliability of the first constraint condition expression.