JPH096969A - Contour extraction method - Google Patents

Abstract

PURPOSE: To extract an accurate contour in a short time by carrying out the 1st processing of small calculation cost and then switchin the 1st processing to the 2nd processing that can extract the accurate contour when the energy approximates to the convergence value. CONSTITUTION: An initial contour is set around an object matter by 'SNAKES' (S1). In the 1st processing, the energy E (C) is minimized by differentiation (S2). Then the energy E (C) is calculated every time the position coordinates of all control points are updated, and present energy Ej (C) is compared with the preceding energy Ej-1 (C) (S3). When the energy Ej (C) is larger than or coincident with the energy Ej-1 (C), the reduction of energy ceases and approximates to the convergence value. Therefore, the 1st processing is switched to the 2nd processing. Then the energy E (C) is minimized by the DP method in the 2nd processing (S5).

Description

Detailed Description of the Invention

[0001]

The present invention relates to an active contour model (Acti) called "SNAKES" based on the energy minimization principle.
ve Contour Model), and more particularly, to an improvement for accurately extracting a contour from an image in a short processing time.

[0002]

2. Description of the Related Art Conventionally, various methods for extracting the contour of an object from an image have been proposed as preprocessing for structuring an image necessary for recognizing shapes and characters by image processing.

<Edge Tracing Method> One of the contour extracting methods is an edge tracing method. In the edge tracing method, the density gradient of an image is binarized by an appropriate threshold value to form an edge image, and pixels in the edge image are sequentially traced to extract a contour.

However, the edge tracing method has a drawback that the contour extraction fails when the contour line does not become a closed curve. Further, there is a drawback that it is difficult to extract the contour when the contour line is branched.

<Contour Extraction Method by SNAKES> On the other hand, an active contour model based on the principle of energy minimization is called “SNAKES”, which has been proposed and used for contour extraction. Hereinafter, this will be described.

The active contour model SNAKES is defined by a polygon 1 having _n control points (vertices) CP _{1 to} CP _n as shown in FIG. That is, each control point CP _i (i =
If the position coordinates of (1 to n) are represented by (X _i , Y _i ), their set S = {(X _i , Y _i ), i = 1, 2, ..., N}
Becomes one contour model, and if the intervals between the control points of this contour model are close to some extent, a closed curve as the contour of the object can be represented.

Therefore, as shown in FIG. 5, first, an initial polygonal contour C _ini is set around the object 2 to be contour-extracted, and then the position coordinates (X _i , Y _i ) of each control point CP _i are set.
Is updated and optimized to attach the contour line C _fin to the contour of the object 2. This contour line C _ini is the extraction result.

<Evaluation function> In order to optimize the position coordinates of the control point, the energy E (C) generally given by the evaluation function of the following equation (1) is used to minimize the energy E (C). Position coordinates of the control points are updated so as to minimize.

[Equation 1] E (C) = α · E _int (C) −β · E _ext (C) (1)

In the equation (1), α and β are constants, “·” is a multiplication symbol, E _int (C) is energy (internal energy) of the geometric constraint condition of the contour model C, and E _ext (C). Represents the image energy (external energy) of the contour model C, respectively.

As a geometric constraint condition, the distance between adjacent control points and smoothness are used, and its energy E _int is used.
(C) is given by the following equation (2). The first term on the right side of the equation (2) is a component related to distance, and the second term is a component related to smoothness. Therefore, the energy E (C) becomes smaller as the distance between the control points becomes shorter and smoother.

[Equation 2] α · E _int (C) = α ₁ · Σ {(X _i −X _i-1 ) ² + (Y _i −Y _i-1 ) ² } + α ₂ · Σ {(2X _i −X _i-1 −X _{i + 1} ) ² + (2Y _i −Y _i-1 + Y _{i + 1} ) ² } Equation (2)

The average edge strength on the contour model C in the image is used as the image energy E _ext (C),
When the pixel value at each control point CP _i (X _i , Y _i ) in the differential image is G (X _i , Y _i ), it is given by the following expression (3). Therefore, the energy E (C) becomes smaller as each control point is closer to the contour of the object 2.

[Equation 3] E _ext (C) = ΣG (X _i , Y _i ) ... Formula (3)

There are the following two processing methods for minimizing the energy using the evaluation function E (C).

<First processing: Energy minimization by differentiation
Method> Normally, each control point CP_i(X_i, Y_i) With energy
Differential value Δv of E (C)_i= (ΔX_i, ΔY_i),
Control point CP based on this differential value_iPosition coordinates of
(X _i, Y_i) To (X_i′, Y_i′) ＝ (X_i+ ΔX
_i, Y_i+ ΔY_i), The energy E
Contour line C that minimizes (C)_finAsk for. This technique
This is referred to as process No. 1. Differentiate and position at the control point in the following equation (4)
The formula for updating coordinates is shown below.

[0014]

(Equation 4)

<Second Process: Energy Minimization Method by DP Method> As another method, DP method (Dynamic Program
g: Dynamic programming) has been proposed to minimize energy. This method is called the second processing and will be described below.

[0016] The formula (1) and looking at the equation (2), the energy of the i-th control point CP _i can, i-1-th control point CP _i-1
Position coordinates (X _i-1 , Y _i-1 ) and the i + 1th control point C
It is a function of the position coordinates of P _{i + 1} (X _{i + 1} , Y _{i + 1} ). Therefore, the energy of the i-th control point CP _i is set to E _i
Is expressed by the following equation (5).

[Equation 5] E _i = α ₁ · {(X _i −X _i-1 ) ² + (Y _i −Y _i-1 ) ² } + α ₂ · {(2X _i −X _i-1 −X _{i + 1 ^{) 2 + + (2Y i -Y}} i-1 -Y i + 1) 2} -β · G (X i, Y i) ... (5)

However, G (X _i , Y _i ) is a pixel value at position coordinates (X _i , Y _i ) of the image obtained by differentiating the original image.

Next, assuming that the position coordinates of the 1st to i−2nd control points have already been determined, the procedure for updating the position coordinates of the i−1th control point will be described. .

First, as shown in FIG. 6, a table 3 having 9 rows and 9 columns is created. In this table 3, when calculating the energy of the i−1th control point, the i−1th control point is moved to the position coordinates (X _i−1 , Y) before updating as shown in FIG. 7A.
_i-1 ) moved in the vicinity of 8 and the i-th control point is shown in FIG.
As shown in (B), by moving the position coordinates (X _i , Y _i ) before updating 8 neighborhoods, the energy value of the i−1th control point calculated for all the combinations is entered. There is. Here, each position in the 8 neighborhoods of the i-i-th control point is represented by p (1 ≦ p ≦ 9), and each position in the 8 neighborhoods of the i-th control point is represented by q (1 ≦ q ≦ 9). Let each energy value of the corresponding position (p, q) of 3 be T [p] [q].

Subsequently, as shown in FIG. 8, a similar table 4 having 9 rows and 9 columns is created. However, in this table 4, the i-th control point is moved in the vicinity of the position coordinates (X _i , Y _i ) before update as shown in FIG. 9A, and the i + 1-th control point is moved to the position shown in FIG. As shown in B), by moving the position coordinates (X _{i + 1} , Y _{i + 1} ) before updating 8 neighborhoods, the energy value of the i-th control point calculated for all combinations is entered. ing. Here, each position in the 8 vicinity of the i-th control point is represented by q (1 ≦ q ≦ 9), and each position in the 8 vicinity of the i + 1-th control point is represented by r (1 ≦ r ≦ 9). For convenience, each energy value at the corresponding position (q, r) is T _n [q] [r].

Next, the energy value T [p] of Table 3
The sum T [p] [r] + T _n [q] [r] of [q] and the energy value T _n [q] [r] of the table 4 is calculated for all combinations of the eight neighboring positions p, q, r. The position p in the vicinity of the i−1th control point in the smallest combination is calculated as the position coordinate of the new i−1th control point.

Paying attention to the i-th control point again, two tables are sequentially created from the 8-neighbor movement of the i + 1th control point and the 8-neighbor movement of the i + 2nd control point, and the same procedure is repeated to repeat i. The position coordinates of the th control point are determined and this is done for all control points.

Such updating of the position coordinates of the control point is repeated until the energy E (C) reaches the minimum value.

[0024]

In the first process, that is, the energy minimization method by differentiation, the energy of the i-th control point depends on the positions of the (i-1) th control point and the (i + 1) th control point. However, since the energy is minimized while fixing these two points, the convergence is poor and the energy oscillates. for that reason,
The contour extraction result is poor. Experimental results are shown in FIGS. The ellipse 5 in FIG. 10 is the object to be extracted, and
The closed curve C _ini outside 1 is the initial contour, and the closed curve C _fin inside 1 is the extraction result.

The second process, that is, the energy minimization method by the DP method solves the drawback of the first process and obtains a good extraction result as a closed curve C _fin shown in FIG. However, in the second processing, the amount of calculation is very large, and it takes a very long time to converge. Incidentally, the calculation cost when the number of control points is n is proportional to n in the first processing,
In the second processing, it is proportional to the cube of n.

Therefore, an object of the present invention is to provide a method capable of extracting the contour of an object from an image in a processing time shorter than that of the second processing and more accurately than the first processing.

[0027]

The contour extraction method of the present invention which solves the above-mentioned problems uses an active contour model consisting of a plurality of control points, and the energy given as a function of the position coordinates of the control points is minimized. In the contour extraction method for extracting the contour of the object from the image by updating the position coordinates of the control points as described above, (1) the differential value of energy is calculated at each control point, and the position of each control point is calculated based on the differential value. Performing the first process of updating the coordinates until the energy approaches the convergence value,
(2) After the energy approaches the convergence value in the first process,
It is characterized by performing a second process of determining the position coordinates of the control point where the energy becomes a minimum by the dynamic programming method.

Alternatively, in addition to the above, the contour extraction method of the present invention repeats the first process to determine that the energy has approached the convergent value when the current energy is higher than the previous energy, and The process of 2 is characterized by starting after returning the position coordinates of the control point to the state immediately before the energy increase, or by repeating the first process, the energy converges when the current energy matches the previous energy. It is characterized in that it is determined that the value has approached, and the second process is immediately started, or the first process is repeated, and when the energy gradient exceeds a predetermined threshold value, the energy reaches a convergent value. It is characterized in that it is determined to be approaching, or the threshold value is a negative value near zero.

[0029]

The first process is the energy minimization method by differentiation, and as described above, the calculation cost is small, but when the energy approaches the minimum value, it vibrates and the convergence is poor and the contour extraction result is not good. On the other hand, the second processing is the energy minimization method by the DP method, and as described above, the contour extraction result is accurate, but the calculation cost is high.

Therefore, in the present invention, when the contour is extracted by SNAKES, the position coordinate of the control point is updated by the energy minimization method by differentiation until the energy approaches the convergence value, and then the energy minimization by the DP method is performed. Switch. As a result, the contour can be accurately extracted with a relatively small calculation cost, that is, a short processing time as a whole.

The method of determining whether or not the energy has approached the convergent value may be basically arbitrary, but the current energy obtained each time when the first process is repeated is compared with the previous energy, and the current energy is compared. A simple method is to determine that the energy is close to the converged value when the energy increases from the previous energy or when the current energy matches the previous energy. However, when the energy of this time is larger than that of the previous time, if the position coordinates of the control point are returned to the state immediately before the energy increase and then the second process is started, the calculation cost becomes further shorter.

Alternatively, since the energy is normally directed to decrease, noting that the sign of the slope is negative, when the slope of the energy exceeds a certain threshold value,
The method of determining that the energy is close to the convergence value may be simple. In this case, the threshold value may be either positive or negative or zero, but if the value is a negative value near zero, the calculation cost becomes further shorter.

[0033]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below with reference to the drawings with reference to the accompanying drawings.

<First Embodiment> A contour extracting method according to a first embodiment of the present invention will be described with reference to FIG. In FIG. 1, an initial contour is set around the target object by "SNAKES" (step S1). First, as the first processing,
Energy minimization is performed by differentiation (step S2).

In the energy minimization by the differentiation, as described above, the internal energy E _int (C) given by the equation (1) is used.
Using the energy E (C) consisting of the external energy E _ext (C) and the differential value of the energy E (C) calculated at each control point for all control points as shown in equation (4). The position coordinates of the same control point are updated based on the value.

Basically, such positional coordinate updating of all control points is repeatedly performed.

However, the energy E (C) is calculated each time the position coordinates of all control points are updated, and the magnitude relationship between the current energy and the previous energy is determined (step S3).

Here, this time is the j-th position coordinate update, and the updated energy value is E _j (C), and the previous time is the j-th position.
This is the first position coordinate update, and the updated energy value is E
_{If j-1} (C), the process is as follows. (1) When E _j (C) <E _j-1 (C), that is, when the current energy E _j (C) is smaller than the previous energy E _j-1 (C), the energy decreases. Therefore, the process returns to step S2, and energy minimization by differentiation is repeated. (2) When E _j (C)> E _j-1 (C), that is, when the current energy E _j (C) is larger than the previous energy E _j-1 (C), the decrease in energy is Since the value has stopped and has approached the convergence value, the process moves from the first process to the second process of step S5.
However, before starting the second process, the position coordinates of each control point are returned to the state before updating, that is, the state of the j-1th position coordinate updating (step S4). (3) When E _j (C) = E _j-1 (C), that is, when the current energy E _j (C) matches the previous energy E _j-1 (C), the energy reduction stops. Since it has approached the convergent value, the first process is switched to the second process. In this case, the second process may be started after returning the position coordinates of each control point to the state before updating, but since the energy has not changed, the second process is performed after updating for simplification of the process. State, that is, the state of the j-th position coordinate update, the second step of step S5 is performed.
Move on to processing.

In step S5, DP is set as the second process.
Energy minimization by the method. In the energy minimization by the DP method, as described above, the energy E _i for each control point given by the equation (5) is used, and in the case of the i-th control point, the vicinity of 8 undetermined control points before and after is determined. The process of determining the position coordinates of the i-th control point that minimizes the energy E _i from the movement and the 8-neighbor movement of the i-th control point is performed for all control points, and the position coordinates of all control points are updated. .

The updating of the position coordinates of all the control points is repeated until the energy E (C) given by the equation (1) reaches the minimum value.

In this embodiment, the energy E (C) is calculated each time the position coordinate is updated, the current energy is compared with the previous energy, and it is determined that the minimum value is reached when they coincide (step). S6).

That is, the position coordinate update in the first processing is
Including, this time is the kth position coordinate update, and after that update
Energy value of E_k(C), the last time is the (k-1) th
The position coordinate is updated, and the energy value after the update is E_k-1
(C), E_k(C) = E _k-1When it becomes (C), the second
Finish processing and outline the shape made by all control points at this point
As the extraction result of.

FIG. 2 shows the experimental result of this embodiment. In FIG. 2, 5 is an ellipse as a target object, C _ini is an initial contour, and C _fin is a contour extraction result. Comparing FIG. 2 and FIG. 11, it can be seen that the extraction result according to the present embodiment is extremely good as compared with the case where only the first processing (energy minimization method by differentiation) is used.

Further, Table 1 shows the calculation time (calculation cost) required in the experiment of this embodiment together with the calculation time in the case of FIG. 12 using only the second processing (energy minimization method by the DP method). . As can be seen from Table 1, the calculation time of this embodiment is extremely short. The number of control points is the same.

[0045]

[Table 1]

<Second Embodiment> A contour extracting method according to a second embodiment of the present invention will be described with reference to FIG. In FIG. 3, the initial contour is set around the target object by "SNAKES" also in this embodiment (step S11), and first, the first contour is set.
The energy minimization by differentiation is performed as the processing of (step S12).

In the energy minimization by this differentiation, the first
Similar to the embodiment, the internal energy E given by equation (1)
Energy E consisting of _int (C) and external energy E _ext (C)
(C) is used to calculate the differential value of energy E (C) at each control point for all control points as shown in equation (4), and the position coordinates of the control point are updated based on the obtained differential value. To do. Basically, such positional coordinate updating of all control points is repeatedly performed.

However, every time the position coordinates of all control points are updated, energy is saved.
Energy gradient G from Rugi E (C) _iCalculate the threshold
Value G_thIs determined (steps S13 and S1).
4).

Here, this time is the j-th position coordinate update, the updated energy value is E _j (C), and the previous time is the j-th position.
This is the first position coordinate update, and the updated energy value is E
_{If j-1} (C) and the current gradient is G _j , the following equation (6)
Calculate.

G _j = E _j (C) −E _j-1 (C) Equation (6)

The threshold value G _th is set to a negative value near zero, and processing is performed as follows. (1) When G _j ≦ G _th , that is, when the energy gradient G _i is less than or equal to the threshold value, the energy is significantly reduced by a certain amount or more, and thus the process returns to step S12 and the energy minimum by the DP method is minimized. Repeat (2) When G _j > G _th , that is, when the energy gradient G _j exceeds the threshold value G _th , the energy almost does not decrease and approaches the converged value. Therefore, from the first process to step S15. To the second processing of.

In step S15, as the second processing, D
The energy is minimized by the P method. In the energy minimization by the DP method, as in the first embodiment, the energy E _i for each control point given by the equation (5) is used, and if it is the i-th control point, the undetermined control points before and after it are used. The process of determining the position coordinates of the i-th control point that minimizes the energy E _i is performed for all control points from the 8-neighbor movement of 8 and the i-th control point's 8-neighbor movement. To update. Such position coordinate updating of all control points is performed by the equation (1).
Repeat until the energy E (C) given by reaches the minimum value.

Also in this embodiment, the position seat is the same as in the first embodiment.
The energy E (C) is calculated each time the target is updated, and the energy
And the previous energy are compared, and when they match, the minimum value is reached.
It is determined that it has been done (step S16). That is,
This is the k-th time, including the update of the position coordinates in the processing of 1.
Is the position coordinate update of E and the energy value after the update is E _k
(C), and the last time was the k-1th position coordinate update.
The energy value after the update of E_k-1(C), E
_k(C) = E_k-1When it becomes (C), the second process is finished and
The shape formed by all control points at
You.

[0053]

According to the present invention, as described above with reference to the embodiments, when the contour of an object is extracted from an image by "SNAKES", first, the first processing with a small calculation cost is performed to converge the energy. When the value approaches the value, the process is switched to the second process that can extract an accurate contour, so that the contour can be accurately extracted as a whole in a shorter time than conventional.

[Brief description of drawings]

FIG. 1 is a diagram showing a procedure of a contour extracting method according to a first embodiment of the present invention.

FIG. 2 is a diagram showing an experimental result of the first embodiment.

FIG. 3 is a diagram showing a procedure of a contour extracting method according to a second embodiment of the present invention.

FIG. 4 is a diagram showing the definition of SNAKES.

FIG. 5 is a diagram showing a relationship between a target object, an initial contour, and an extraction result.

FIG. 6 is a diagram showing an example of a table used to calculate the energy of the i−1th control point in the DP method.

FIG. 7 is a diagram showing an 8-neighbor movement of the i−1th control point and an 8-neighbor movement of the i-th control point for creating the table of FIG. 6;

FIG. 8 is a diagram showing an example of a table used for calculating energy of an i-th control point in the DP method.

9A and 9B are diagrams showing the 8-neighbor movement of the i-th control point and the 8-neighbor movement of the i + 1-th control point for creating the table of FIG.

FIG. 10 is a diagram showing an example of a target object in an experiment.

FIG. 11 is a diagram showing an experimental result of a contour extraction method using only the conventional first processing.

FIG. 12 is a diagram showing an experimental result of a contour extraction method using only conventional second processing.

[Explanation of symbols]

C _ini Initial contour C _fin Extraction result 1 Polygon 2 Object 3,4 Table 5 Ellipse (target object)

Claims (5)

[Claims] 1. An active contour model including a plurality of control points is used, and the position coordinates of the control points are updated so that the energy given as a function of the position coordinates of the control points is minimized. In the contour extraction method for extracting, (1) a first process of calculating a differential value of energy at each control point and updating the position coordinates of each control point based on the differential value,
Do it until the energy approaches the convergent value. (2) After the energy approaches the convergent value in the first process,
A contour extracting method characterized by performing a second process of determining a position coordinate of a control point having a minimum energy by a dynamic programming method. 2. The first process is repeatedly performed, and when the energy of this time is larger than the energy of the last time, it is determined that the energy is close to the converged value, and the second process increases the energy of the position coordinate of the control point. The contour extracting method according to claim 1, wherein the method is started after returning to the immediately preceding state. 3. The first process is repeatedly performed, and when the current energy matches the previous energy, it is determined that the energy is close to the converged value, and the second process is immediately started. The contour extraction method according to item 1. 4. The contour extracting method according to claim 1, wherein the first process is repeated to determine that the energy is close to a converged value when the energy gradient exceeds a predetermined threshold value. . 5. The contour extraction method according to claim 4, wherein the threshold value is a negative value near zero.