KR20190085756A - Image Segmentation Method - Google Patents

Abstract

Disclosed by the present invention is an image segmentation method. According to an embodiment of the present invention, the image segmentation method, with which an image processing device segments an image, includes: a step of segmenting an image into a plurality of areas; and a step of applying, to each point, a relative weighting function between a data fidelity function and a normalization function, which are determined based on a residual between input data and an estimated value of the input data for each of the areas. The image segmentation method is able to segment images without user interaction or prior knowledge.

Description

Image Segmentation Method [

The present invention relates to an image segmentation method and, more particularly, to a method and apparatus for segmenting an image segmented into a plurality of regions into a data fidelity function and a normalization function determined based on a residual between input data and an estimate for the input data, A method of dividing an image by applying a relative weight function between points to each point.

In general, image segmentation techniques are used in medical imaging fields such as tumor and disease detection, blood vessel volume measurement, computer assisted surgery, diagnosis, treatment planning, and anatomical structure studies, and satellite images such as roads and forests And has been widely applied to a variety of fields such as biometrics such as detection of objects, biometrics such as faces and fingerprints, forensics, scientific investigation, precision measurement, and maintenance of bridges / buildings.

On the other hand, normalization is generally imposed to reduce the allowable space of the solution in some image analysis work formulated as an inadequate inverse problem. Relevant parameters that control the strength of the regular expression are usually constant in space and iteration and are determined by grid search. In some cases, parameters are tied to data, such as in image reconstruction where noise variation is used and the stability of the estimated parameters is analyzed. Cross-validation is also used to mimic the choice of parameters with model selection. In addition, an alternative approach based on log-log plots of residuals and normalization called L-curves has been used. However, this method is unstable when the calculation cost is high and the variance of noise is small.

In conventional imaging tasks, optimization has been performed extensively based on discrete graph representation or continuous relaxation techniques. Total Variation (TV) is used as the convex form of the normalization and its optimization is performed by the primal-dual algorithm. To minimize TV, a functional lifting technique was applied to the multiple label problem. Most convex relaxation approaches to multiple label problems are based on TV normalization, but other data fidelity terms such as L ₁ norm or L ₂ norm are used.

However, the conventional multi-label model is inaccurate or redundant when using a large number of labels to force user interactions such as border boxes, outlines, graffiti or points, There was a difficulty.

Therefore, it is required to develop a technique that can divide images without user interaction or prior knowledge.

In this regard, Korean Patent Laid-open No. 10-2017-0081969, entitled " Texture Image Processing Apparatus and Method ", is available.

An object of the present invention is to provide an image segmentation method capable of dividing an image without user interaction or prior knowledge.

The technical problems of the present invention are not limited to the above-mentioned technical problems, and other technical problems which are not mentioned can be clearly understood by those skilled in the art from the following description.

According to an aspect of the present invention, there is provided an image segmentation method for an image processing apparatus, the method comprising: dividing an image into a plurality of regions; Applying a relative weight function between the data fidelity function and the normalization function to each point determined based on the residual between the data and the estimate for the input data.

)는 아래 수학식으로 산출될 수 있다. [수학식]Preferably, the residual (

) Can be calculated by the following equation. [Mathematical Expression]

는 후버손실함수, f(x)는 입력 데이터,

는 각 영역 i의 특성함수, c_i는 추정치임.here,

F (x) is the input data,

Is a characteristic function of each region i, and c _i is an estimate.

Preferably, the relative weighting function ([lambda]) may be defined by the following equation.

 [Mathematical Expression]

이고, ρ(u)는 잔차, β는 '0'보다 크고 잔차 ρ(u)의 변화와 관련된 제어 매개 변수, α는 0<α<1이고, 상대적 가중함수(λ)의 희박 정도를 제어하는 상수 매개 변수임.here,

Α is a control parameter related to the change of residual ρ (u), β is greater than 0 and α is 0 <α <1, and the degree of leaning of the relative weighting function (λ) is controlled It is a constant parameter.

)는 아래 수학식으로 정의될 수 있다. Preferably, the data fidelity function (

) Can be defined by the following equation.

[Mathematical Expression]

는 상대적 가중 함수,

는 입력데이터와 추정치간의 잔차,

는 각 영역 i의 특성함수, Ci는 추정치임.here,

Is a relative weight function,

Is the residual between the input data and the estimate,

Is a characteristic function of each region i, and Ci is an estimate.

)는 아래 수학식으로 정의될 수 있다. Preferably, the normalization function (

) Can be defined by the following equation.

[Mathematical Expression]

임.here,

being.

Preferably, the step of applying the relative weight to each point may further comprise applying a Mutually Exclusive Region Constraint between the plurality of regions.

Preferably, the mutually exclusive constraint condition can be defined by the following equation.

 [Mathematical Expression]

이고,

ego,

Wherein I and j are indexes of the divided areas, and ui and uj are partition functions.

Advantageously, optimizing the energy function using the data fidelity function, normalization function, relative weighting and mutually exclusive constraints may further comprise optimizing the energy function.

Preferably, the energy function can be defined by the following equation.

 [Mathematical Expression]

Where ι is a weight parameter for mutually exclusive constraints greater than zero.

Preferably, the energy function can be simplified to an unconstrained expanded Lagrangian as shown in the equation described below.

[Mathematical Expression]

,r _i와 z_i는 최소화 될 보조 변수,

임.here,

, r _i and z _i are the auxiliary variables to be minimized,

being.

Advantageously, the final energy function simplified to Lagrangian can be optimized using a gradient-based alternating-direction number technique (ADMM).

According to the present invention, a balance between data fidelity and normalization can be dynamically determined by using a relative weight function based on residuals.

Also, images can be segmented without user interaction or prior knowledge.

The effects of the present invention are not limited to the effects mentioned above, and other effects not mentioned can be clearly understood to those of ordinary skill in the art from the following description.

1 is a flowchart illustrating a method of dividing multiple images according to an exemplary embodiment of the present invention.
2 is an exemplary diagram for explaining image segmentation according to an embodiment of the present invention.
FIG. 3 is a graph showing the results of quantitative comparison of different energy models using F-measured values (left) and residual values (right) according to an embodiment of the present invention as a function of the number of repetitions.
4 is a diagram showing a qualitative comparison result of a joint test for an increasing number of regions (5 to 7, 9 to above) according to an embodiment of the present invention.
Figure 5 is a qualitative comparative diagram showing the prejudice of the trap of a certain non-adaptive regular machine and the final solution according to an embodiment of the present invention.
Figure 6 is a graphical comparison of multiple label segmentation in a Berkeley data set using different algorithms in accordance with an embodiment of the present invention.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the invention is not intended to be limited to the particular embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. Like reference numerals are used for like elements in describing each drawing.

The terms first, second, A, B, etc. may be used to describe various elements, but the elements should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component. And / or &lt; / RTI &gt; includes any combination of a plurality of related listed items or any of a plurality of related listed items.

It is to be understood that when an element is referred to as being "connected" or "connected" to another element, it may be directly connected or connected to the other element, . On the other hand, when an element is referred to as being "directly connected" or "directly connected" to another element, it should be understood that there are no other elements in between.

The terminology used in this application is used only to describe a specific embodiment and is not intended to limit the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the contextual meaning of the related art and are to be interpreted as either ideal or overly formal in the sense of the present application Do not.

Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a flowchart illustrating a method for dividing multiple images according to an embodiment of the present invention. FIG. 2 is a diagram for explaining image division according to an exemplary embodiment of the present invention.

Referring to FIG. 1, the image processing apparatus divides an image into a plurality of regions (S110). Hereinafter, for convenience of description, a case of dividing an image into n regions will be described.

That is, the image processing apparatus can quantize an image with a preset number (the number of labels) and set it as N regions. Also, the image processing apparatus may set N regions by selecting a random number of pixels from the image.

When step S110 is performed, the image processing apparatus calculates a relative weight function between the data fidelity function and the normalization function determined based on the residual between the input data and the estimated value for the input data for each of the n regions at each point (S120).

In general, the trade-off between data fidelity and normalization is assumed to be constant over the entire process of space (ie, the entire image area) and time (ie, typically repetitive) optimization. However, neither is desirable. Spatially adaptive regularity will be described with reference to FIG. The residual between the input image (a) and the division result (b) in which (a) is divided is displayed as (c) and the variance of the residual is displayed as (d). Looking at (c) and (d), the residuals and variances (gray levels: bigger, less dark) are not constant in space. This can be applied to other imaging problems such as motion estimation (optical flow) and image reconstruction where the local variance of the residuals is often different in space and optimization. Thus, there is a need for spatially adapted normalization beyond the static image feature as studied in the local light and dark changes. Normalization of these tasks varies with space, but deformation is constant through repetition because it is linked to image statistics. Thus, the present invention can implement spatial adaptive normalization using varying residuals during iteration.

That is, the present invention uses a normalization technique that can spatially adaptively and semiautomatically determine the weight between the data fidelity term and the normalization term. This method determines the relative weighting function without prior knowledge based on the residual between the input data and the estimated solution.

That is, the relative weight function (?) Is defined by Equation 1 described below.

[Equation 1]

이고, ρ(u)는 잔차, β는 '0'보다 크고 잔차 ρ(u)의 변화와 관련된 제어 매개 변수, α는 0<α<1이고, 상대적 가중함수(λ)의 희박 정도를 제어하는 상수 매개 변수를 의미할 수 있다. 상대적 가중 함수(λ)는 데이터 충실도와 정규화 간의 균형을 결정한다. 예를 들어, λ가 커지면 데이터 충실도가 더 중요한 것으로 간주되어 경계가 명확하게 유지되고, λ가 작아짐에 따라 정규화가 더 많이 부과되어 오버 스무딩 효과가 발생한다. here,

Α is a control parameter related to the change of residual ρ (u), β is greater than 0 and α is 0 <α <1, and the degree of leaning of the relative weighting function (λ) is controlled It can mean a constant parameter. The relative weight function (λ) determines the balance between data fidelity and normalization. For example, if λ is large, the data fidelity is regarded as more important, the boundary is clearly maintained, and as λ becomes smaller, more normalization is imposed, resulting in an over-smoothing effect.

가 작을 때 정규화가 강하며, 잔차가 작을 때 약하고 등가 적으로

가 큰 경우 에너지 최적화 프로세스 중에 설계되도록 설계된다. The relative weight function (lambda) between data fidelity and normalization is applied adaptively at each point x according to the residual? (U (x)) determined by the local fitness of the data for the model. The adaptive rule based on the relative weighting function (λ) is more robust and equiva- lent when the residual is large

Is small, the normalization is strong, and when the residual is small,

Is designed to be designed during the energy optimization process.

의 범위는 가중치 1-λ를 [α, 1) 정규화가 모든 곳에 부과되도록 데이터 충실도 ρ(u)와 정규화

의 정의에서 임계 파라미터 μ> 0을 갖는 강력한 후버 손실 함수(

)를 사용한다.Having a positive Lagrange multiplier &lt; RTI ID = 0.0 &gt;

(U) and normalization (i) such that the weighting 1 - [lambda], [1, 1)

A strong Hoover loss function with critical parameter μ> 0 (

) Is used.

The Hober loss function can be defined by Equation (2) below.

&Quot; (2) &quot;

Compared with the L ₂ norm, the use of the Hoover loss function has the advantage of having a continuous derivative, unlike the non-differentiating L ₁ norm leading to stair artifacts, while maintaining geometric features such as edges better. Huber loss also enables efficient convex optimization due to the equivalence of the L ₁ norm to the proximal operator.

이고

이면

이다. 분할은 라벨링 함수

로 표현되고,

는

인 레이블 집합을 나타낸다. 라벨링 함수 l(x)는

가 되도록 각 점 x∈Ω에 라벨을 할당한다.On the other hand, the multiple image segmentation aims at dividing the image domain (?) Into n number of pairs of separated areas (? I). here,

ego

If

to be. Split is a labeling function

Lt; / RTI &gt;

The

Lt; / RTI &gt; label set. The labeling function l (x)

Lt; / RTI &gt; to each point x &lt; RTI ID = 0.0 &gt;

)은 특성 함수(

)에 의해 표시되고,

일 수 있다. Each divided area (

) Is the characteristic function (

), &Lt; / RTI &gt;

Lt; / RTI &gt;

)는 아래 기재된 수학식 3으로 정의될 수 있다. Characteristic function (

) Can be defined by the following equation (3).

&Quot; (3) &quot;

은 도메인

를 갖는 실측 이미지라 하자. 영상(f(x))의 분할은 일련의 특성 함수 집합(

)에 대해 에너지 함수를 최소화하는 영역

을 찾음으로써 얻어진다.

Domain

. The partitioning of the image (f (x)) involves a set of characteristic functions (

) For minimizing the energy function

&Lt; / RTI &gt;

In general, the energy function is defined using a data fidelity function and a normalization function. That is, the energy function is defined by Equation 4 described below.

&Quot; (4) &quot;

Data fidelity measures how well an estimate describes the given data, and normalization can mean a measure of the discontinuity of the estimated domain boundary.

를 가지는

를 사용할 수 있다. 여기서,

는 중심이 가우시안 분포를 따르고 꼬리가 후버 손실 함수(

)에 이르는 라플라스 분포를 따르는 이항 분포를 따른다고 가정한다.For data fidelity, we use a simple piecewise constant image model with an additional noise process. In other words,

Having

Can be used. here,

The center follows the Gaussian distribution and the tail follows the Hoover loss function (

), Which follows the Laplace distribution.

)는 아래 기재된 수학식 5와 같이 정의될 수 있다. Then, the data fidelity function (

) Can be defined as shown in Equation (5) below.

&Quot; (5) &quot;

는 상대적 가중 함수로, 레이블(i)에 대한 상대 가중 함수

는 수학식 1에서 정의된 잔여

에 기반하여 결정된다.

는 각 영역 i의 특성함수, Ci는 추정치를 의미할 수 있다.

는 입력데이터와 추정치간의 잔차로, 아래 기재된 수학식 6으로 정의될 수 있다. here,

Is a relative weight function, and the relative weight function for label ( i)

Lt; RTI ID = 0.0 &gt; 1 &lt; / RTI &

.

Is a characteristic function of each region i, and Ci can be an estimate.

Is the residual between the input data and the estimate, and can be defined by Equation 6 below.

&Quot; (6) &quot;

A standard length penalty is used for each region (Ω _i ) for normalization.

)는 아래 기재된 수학식 7로 정의될 수 있다.Then, the normalization function (

) Can be defined by Equation (7) described below.

&Quot; (7) &quot;

는 아래 기재된 수학식 8로 정의될 수 있다. here,

Can be defined by the following equation (8).

&Quot; (8) &quot;

은

이고, Huber 함수(

)에 대한 임계값을 의미한다. here,

silver

, And the Huber function (

). &Lt; / RTI &gt;

)의 수학식 4에서의 에너지 함수는 그것의 정수 제약

로 인해 볼록하지 않다. 이에, 고전적인 convex relaxation 방법을 사용하여 에너지 함수의 convex 형태를 도출할 수 있다. 즉,

는 바운드된 변이(bounded variation)의 연속 함수

로 대체하고, 정수 제약

는 볼록 집합

로 완화될 수 있다. Characteristic function (

) &Lt; / RTI &gt; of Equation (4)

So it is not convex. The convex shape of the energy function can be derived using the classic convex relaxation method. In other words,

Is a continuous function of the bounded variation

, And an integer constraint

A convex set

Lt; / RTI &gt;

This can be expressed by the following equation (9).

&Quot; (9) &quot;

은 스무스한(smooth) 함수이고, 데이터 피델리티

와 정규화

는 아래 기재된 수학식 10과 수학식 11로 정의된다.here

Is a smooth function, and the data fidelity

And normalization

Is defined by the following equations (10) and (11).

&Quot; (10) &quot;

&Quot; (11) &quot;

는 수학식 1에서 정의된 잔차

를 기반으로 결정되어 모델과 관측사이의 불일치가 발생하는 분할 함수에 더 높은 정규화를 부과한다. 대조적으로, 국부(로컬) 관측이 모델에 맞는 영역에 대해서는 보다 낮은 정규화가 부과된다.Weight function

Lt; RTI ID = 0.0 &gt; 1 &lt; / RTI &

And imposes a higher normalization on the partition function where the mismatch between the model and the observation occurs. In contrast, a lower normalization is imposed for regions where local (local) observations fit the model.

은 특히 많은 수의 레이블을 가지고 이 제약 조건을 적용하는데 비효율적이다. Through the above process, the image is divided into n regions, but the condition of Equation (20)

Is particularly inefficient in applying this constraint with a large number of labels.

Accordingly, the image processing apparatus applies Mutually Exclusive Region Constraint between the n regions (S130).

가 모든

에 대해 최소화되도록 영역

에서 각 쌍의 조합의 공통 영역을 페널티하는 새로운 제약 조건을 도입한다. 영역

에서 각 쌍의 조합의 공통 영역을 페널티하는 상호 배타적 제약 조건(Mutually Exclusive Region Constraint)을 수학식 9의 에너지 함수에 적용하면, 아래 기재된 수학식 12와 같이 정의될 수 있다. That is, the image processing apparatus

All

Lt; RTI ID = 0.0 &gt;

Introduces a new constraint that penalizes the common area of each pair combination. domain

(Mutually Exclusive Region Constraint) that penalizes the common region of each pair combination in the energy function of Equation (9) can be defined as Equation (12) described below.

&Quot; (12) &quot;

Where ι is ι> 0 and is a weight parameter for mutually exclusive constraints.

The desired partitioning result is obtained by the optimal set of partitioning functions u _i . That is, the division result can be defined by Equation (13) described below.

&Quot; (13) &quot;

If the energy function is defined through the above process, the image processing apparatus optimizes the energy function (S140).

The energy function for the partitioning control of equation (12) is minimized for the set of partition function {u _i } and intensity estimate {c _i } in an expectation maximization (EM) framework. Applying the u _i = v _i dividing variable to the energy function of equation (12) can be simplified to unconstrained enlarged Lagrangian as shown in equation (14) below.

&Quot; (14) &quot;

을 간단한 제약 조건

과

로 분해할 수 있는 등가 제약 조건 u_i = v_i에 대한 이중 변수이다. 수학식 10의 데이터 충실도 ρ(u_i, c_i)와 수학식 11의 정규화

는 비 - 평활 함수

의 Moreau-Yosida 정규화에 의해 효율적으로 최적화 될 수있다. 즉, 데이터 충실도 ρ(u_i, c_i)와 정규화

는 정규화된 형식 ρ(u_i, c_i, r_i)와

로 대체된다. Where θ is a scalar magnification factor with θ> 0. w _i is the original constraint u _i ∈ [0, 1]

To a simple constraint

and

Is the double variable for the equality constraint u _i = v _i that can be decomposed into. The data fidelity ρ (u _i , c _i ) of (10) and the normalization of

Is a non-smoothing function

Can be efficiently optimized by the Moreau-Yosida normalization of That is, the data fidelity ρ (u _i , c _i )

(U _i , c _i , r _i ) and the normalized form ρ

.

Then, Equation (10) is defined as Equation (15) described below, and Equation (11) is defined as Equation (16) described below.

&Quot; (15) &quot;

&Quot; (16) &quot;

Here, r _i and z _i are auxiliary variables to be minimized.

The constraint condition for u _i and v _i in Equation (14) can be represented by a display function 隆_A (x) of the set A defined by Equation (17) below.

&Quot; (17) &quot;

는

인 δ_A(u_i)로 주어지며 제약 조건

은

인

로 주어진다. 데이터 충실도와 정규화의 정규화 된 형식과 제약 조건에 대한 지시자 함수는 레이블 i에 대해 아래 기재된 수학식 18과 같은 제한되지 않은 확장된 Lagrangian (

)을 유도한다. Constraint

The

Lt; _{RTI ID =} 0.0 &gt; _A &_lt; / _RTI &gt; (u _i )

silver

sign

. The indicator function for the normalized form and constraint of data fidelity and normalization is the unlimited extended Lagrangian (&lt; RTI ID = 0.0 &gt;

).

&Quot; (18) &quot;

)를 유도한다. Equation (18) is the final energy function &lt; RTI ID = 0.0 &gt;

).

&Quot; (19) &quot;

을 최소화함으로써 최적의 분할 함수 세트가 얻어진다. 에너지 함수를 최적화하기 위해서 그래디언트에 기반한 교대 방향 수 기법(ADMM) 알고리즘을 이용할 수 있다. Energy function

The optimal set of partition functions is obtained. To optimize the energy function, we can use a gradient-based alternate-direction-counting (ADMM) algorithm.

The ADDM algorithm is shown in Table 1.

[Table 1]

에 대한 증가된 라그랑지안을 최소화하도록 진행한다. 획득된 중간 솔루션 u_i 및 v_i는 각각 A와 B에 반영된다. ADDM 알고리즘은 레이블링 함수 l(x)에 대한 주어진 초기화로부터의 수렴(convergence)까지 반복된다. According to the ADDM algorithm shown in Table 1,

Lt; / RTI &gt; to minimize the increased &lt; RTI ID = 0.0 &gt; Lagrangian &lt; / RTI & The obtained intermediate solutions u _i and v _i are reflected in A and B, respectively. The ADDM algorithm is repeated until convergence from a given initialization for the labeling function l (x).

Hereinafter, robustness and effect of the dynamic normalization method for image segmentation according to the present invention will be described using experimental results. In the experiment, we used an image of the Berkeley partitioned data set and a simple but exemplary composite image. We also used random initialization for the initial labeling function for all algorithms throughout the experiment.

FIG. 3 is a graph showing the results of quantitative comparison of different energy models using F-measured values (left) and residual values (right) according to an embodiment of the present invention as a function of the number of repetitions. The TV-L ₁ and TV-L ₂ approaches are compared to the Huber-Huber (H2) model of the present invention. In order to effectively demonstrate the robustness of the Huber-Huber model as compared to TV-L1 and TV-L2, we consider the dual-partition image model ignoring the effect of constraints on the common area of the nu- Apply the primal-dual algorithm to TV-L1 and TV-L2 models for optimization. It can be seen that the H2 model converges more precisely and faster for the problem of the partitioning of nutrients in the image suitable for the binary image model.

4 is a diagram showing a qualitative comparison result of a joint test for an increasing number of regions (5 to 7, 9 to above) according to an embodiment of the present invention. Qualified results are compared qualitatively with a different number of labels in a classical cross-point test. The number of labels is then fixed to less than one. The region number algorithm of the input image is forced to "inpaint" the central disc with labels in the surrounding area. As shown in (a), the input joint image has 5 (upper), 7 (middle) and 9 (lower) regions in the subdivision results of the intersection prototype images having different areas. (f) H2 model without mutual exclusive constraints and (g) all H2 models with constraints for the following algorithm. (d) Douglas-Rachford (VTV) [59] based on Total Variation using primitive-dual (TV) [58] (E) paired calibration (PC) [7]. This experiment was designed specifically to demonstrate the need for constraints of mutual exclusiveness, so that the input image is made to fit the correct piecewise constant model, making the base image model of the compared algorithm fit. It can be seen that the exemplary results shown in FIG. 4 show that the algorithm according to the present invention produces consistently better results, while the majority of algorithms are degraded as the number of regions increases (from top to bottom).

Figure 5 is a qualitative comparative diagram showing the prejudice of the trap of a certain non-adaptive regular machine and the final solution according to an embodiment of the present invention. Image (a) has three regions with sharp edges / edges and various spatial variabilities. Using a small normalization (d) (large λ), the boundaries are made clear but separated by three irregular regions (red, green, and blue), with different labels distributed in the center and right rectangles. Using a large normalization weight (e) (small λ) creates a homogeneous region, but the boundary is blurred and the edges round in the left region (red). The method (b) according to the present invention causes the justification device (right area, rounding boundary), which is driven by data (left area, sharp boundary) and data is more uncertain, to be metered. (a) empirically demonstrates the effect of the proposed adaptive normalization using an exemplary composite image with four regions representing spatial statistics of different variances. Artificial noise is added on a white background. A red rectangle on the left, a green rectangle in the middle, and a blue rectangle on the right. To maintain a sharp boundary, you must manually select a small normalization. However, if the intensity difference of some data is large, irregular boundaries are created between the regions, and the red and blue scattered throughout the middle and right rectangle (d) appear, but the edges are sharp. On the other hand, in order to ensure homogeneity of regions, large-scale regularization is required, and also in the case of the final solution (e) where the edges are rounded, and the regions that allow fine boundary crystals (red). However, our approach to adaptive normalization (b) allows the data term to find a well-defined solution to support it (red) and apply the weight to the solution when the data is more uncertain (blue). In order to emphasize the geometric properties of the solution around the edges, image enlargements for the areas indicated in (b) and (e) are shown in (c) and (f), respectively.

Figure 6 is a graphical comparison of multiple label segmentation in a Berkeley data set using different algorithms in accordance with an embodiment of the present invention. The algorithms according to the present invention are compared with existing state-of-the-art techniques (FL [57], TV [58], VTV [59], PC [7]) which assume a constant image of a statue for a fair comparison of the base model. The input image is shown in (a) and the segmentation results provide the qualitative evaluation of Figure 6 shown in (b) - (f) where the same number of labels are applied to all algorithms. The parameters of the algorithm are optimized with respect to accuracy. 0.5,? = 0.5,? = 0.01,? = 10,? = 0.5,? = 1. While the method according to the present invention yields a better label than the other, , It may appear to be generally incomplete due to limitations of the underlying image model. Quantitative comparisons are reported in Table 2 with precision and recovery using a variable number of labels.

[Table 2]

Table 3 shows the costs (eg, image pyramid) calculated as the baseline for 481_321_3 color images without special hardware (eg, multicore GPU / CPU) and image processing technology.

[Table 3]

The present invention has been described with reference to the preferred embodiments. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the present invention is defined by the appended claims rather than by the foregoing description, and all differences within the scope of equivalents thereof should be construed as being included in the present invention.

Claims (11)

A method for an image processing apparatus to divide an image,
Dividing the image into a plurality of regions; And
Applying to each point a relative weight function between a data fidelity function and a normalization function determined based on a residual between input data and an estimate for the input data for each of the plurality of regions;
And an image segmentation method. The method according to claim 1,
The residual (

) Is calculated by the following equation
[Mathematical Expression]

here,

F (x) is the input data,

Is a characteristic function of each region i, and c _i is an estimate. 3. The method of claim 2,
Wherein the relative weighting function (?) Is defined by the following equation
[Mathematical Expression]

here,

Α is a control parameter related to the change of residual ρ (u), β is greater than 0 and α is 0 <α <1, and the degree of leaning of the relative weighting function (λ) is controlled It is a constant parameter. The method of claim 3,
The data fidelity function (

) Is defined by the following equation:
[Mathematical Expression]

here,

Is a relative weight function,

Is the residual between the input data and the estimate,

Is a characteristic function of each region i, and Ci is an estimate. 5. The method of claim 4,
The normalization function (

) Is defined by the following equation:
[Mathematical Expression]

here,

being. The method according to claim 1,
After applying the relative weight to each point,
Further comprising applying a mutually exclusive region constraint between the plurality of regions. The method according to claim 6,
Wherein the mutually exclusive constraint condition is defined by the following equation:
[Mathematical Expression]

ego,
I, j is an index of a partitioned area, and ui and uj are partition functions. 8. The method of claim 7,
Further comprising optimizing an energy function using the data fidelity function, the normalization function, the relative weight, and the mutually exclusive constraint. 9. The method of claim 8,
Wherein the energy function is defined by the following equation:
[Mathematical Expression]

Where ι is a weight parameter for mutually exclusive constraints greater than zero. 10. The method of claim 9,
Wherein the energy function is simplified to an unconstrained enlarged Lagrangian as shown in the following equation:
[Mathematical Expression]

here,

, r _i and z _i are the auxiliary variables to be minimized,

being. 11. The method of claim 10,
Wherein the final energy function simplified to Lagrangian is optimized using a gradient-based alternating-direction-number technique (ADMM).

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