KR101117045B1 - Noise reduction system for smoothing of 3D data related to searching pieces - Google Patents

Abstract

The present invention relates to a noise removing system and a method for smoothing three-dimensional data for member retrieval, the noise removing system for receiving the image information, the ratio of the volume size and the area size with respect to the mesh of the image; A noise discriminating unit for determining whether the image is noise compared to a threshold value, and when the noise discriminating unit determines that the image is noise, the coordinates of the mesh of the image have a minimum difference between the three-dimensional volume and the two-dimensional area. The noise canceling unit is configured to remove the noise by converting in the direction of the direction, so that the noise removing efficiency of the image can be improved, and thus a good image can be displayed on the screen.

Noise, image, picture, removal, smoothing. Mesh, Area, Volume, Coordinate, 3D, 2D

Description

Noise reduction system for smoothing three-dimensional data for member search and its removal method {Noise reduction system for smoothing of 3D data related to searching pieces}

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a noise removal system for smoothing three-dimensional data for member retrieval and a method of removing the same. The present invention relates to a noise removal system for smoothing three-dimensional data for searching for a member, and to remove the noise from a screen by determining whether the image is noise compared to a threshold and a method of removing the noise.

Here, the meaning of pieces refers to a state in which things are divided into pieces.

 Data reconstructed in 3D using computer vision inevitably includes noise or errors. Meshing such data results in three-dimensional mesh data that is different from the original object due to noise or errors. This proposal proposes a method to effectively remove noise from three-dimensional mesh data reconstructed by three-dimensional reconstruction or three-dimensional mesh data obtained by a laser scanner. Since the proposed method smooths out noise using the ratio of 2 / 3-dimensional area size of the mesh, preprocessing for large-dimensional 3D mesh data is required.

Recent trends in object modeling have been to reconstruct three-dimensional data from multiple images. Object surface reconstruction from multiple images is one of the fundamental problems of computer vision. One of the common approaches to reconstructing three-dimensional data using geometric calculations is to reconstruct the three-dimensional points of the scene.

In obtaining three-dimensional data from multiple images, these studies include inevitable errors at each step-camera calibration, correspondence search, basic matrix calculation, and so on. These errors appear as peak noise or Gaussian noise in three-dimensional data.

Meshing these three-dimensional points clouds creates an object surface that is not as smooth as the original object surface. Therefore, it is important to smooth the noise on the surface while preserving the geometrical features of the object surface.

For example, if noise is added to a triangular mesh, the vertices of the mesh will be placed differently from the position of the vertices of the original mesh, and the noise and mesh vertices will need to be separated to correct the positions of the vertices. Therefore, the noise smoothing process can be seen as the same as modifying the position of the mesh. To achieve this noise smoothing, preliminary work was used on concepts based on differential geometry approaches, including the Laplacian method.

Noise smoothing based on conventional geometrical approaches makes drastic changes in the characteristics of the object. This phenomenon is shown in FIG. FIG. 15 is an exemplary screen showing a result of a noise removing method according to the prior art, in which a torus model is shown on the right side of the screen, and FIG. 15 (b) shows a model to which noise is added from the right side, and FIG. Shows the model smoothed by the Laplacian filter, and the model on the right is the model smoothed by the median filter.

Considering a mesh change process in which the positions of mesh vertices are updated, Equation 1 is obtained.

  Pnew ← Pold + λD (P)

Where D (P) is the displacement vector and λ is the step by step variable.

 In Laplacian smoothing, if the displacement vector D (P) is defined by the umbrella operator of Equation 2, the vertex position of the mesh is changed by Equation 1 above.

 Where P is the vertex of the mesh,

Equation 3 is a one-dimensional ring of mesh vertices adjacent to vertex P on the left side of FIG. The left figure of FIG. 16 shows Laplacian smoothing, which is a one-dimensional ring of mesh vertices adjacent to vertex P, and the right figure of FIG. 16 shows an edge angle α of a triangle adjacent to the vertices and edges (xi-xj). _j , β _j ).

The bidirectional Laplacian filter is a method of replacing a negative component with two scale components having opposite signs by a large magnitude change by the Laplacian method. This smoothing suppresses the high frequency components of the umbrella operator. The vertex update formula for this filter is:

 Where μ> λ> 0, U2 is the square of the umbrella operator.

 The mean curvature filter is a robust discontinuous approximation of the mean curvature vector. The differential definition of the curvature normal is used as a discontinuous equation, such as equations (5) and (6).

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In Equations 5 and 6, H is an average curvature and n is a normal vector at vertex xi. A is the area of the adjacent area around xi, and ▽ is the derivative for xi. {Fig. 17 (b)}

The average curvature normal is used to define the quasi-laplacian for smoothing the inner and boundary vertices in the local domain. Vertices move along the normal direction to the appropriate size to maintain shape and smooth the mesh well. Applying a limited weighted average curvature normal to only those vertices that are adjacent to one vertex effectively preserves the original mesh features.

On the other hand, when considering the original triangle mesh in the median filter method, let T be a triangle mesh, n (T) is the unit normal, A (T) is the area of T, and C (T) is the center of T. N (T) denotes the set of all triangular meshes that share the edges or vertices that form the triangular mesh T. Considering all face normals in the mesh, the position of each mesh vertex P is changed by equations (7) and (8).

의 투영이다. 도 17(a)는 지역적인 N(T)에서 중심 삼각형 T와 이웃하는 삼각형들을 나타낸 것으로서, n(T)는 원래의 면 법선이고, m(T)는 필터링된 법선이며, 도 17(b)는 수학식 8의 가시적인 표현인 도형이다.Where the sum is for all triangular meshes adjacent to point P, and v (T) in FIG. 17 (b) is a vector in the direction of m (T)

Is the projection of. Figure 17 (a) shows the triangles adjacent to the center triangle T at the local N (T), where n (T) is the original face normal, m (T) is the filtered normal, and Figure 17 (b) Is a figure that is a visual representation of equation (8).

However, noise smoothing based on differential geometry approaches, including Laplacian method, has a problem that the displayed image is not natural because it changes the geometrical features in general.

Meanwhile, in image processing, a method of removing noise using a median filter among nonlinear filters having characteristics of preserving the characteristics of an image has also been recently introduced. However, although the median filter generally removes peak noise well, there is a problem in that it does not effectively remove Gaussian noise or meshes of different sizes from three-dimensional data.

Recently, three-dimensional filters using surface normal vectors of three-dimensional meshes have been used to smooth these noises. However, even the filters using the surface normal vector do not satisfactorily remove the peak noise included in the reconstructed three-dimensional data from the image.

In order to solve the above problems, an object of the present invention is to detect peak noise and Gaussian noise present in three-dimensional mesh data by using a ratio of three-dimensional area and two-dimensional area of a mesh, and smooth them according to the characteristics of the noise. In addition, the present invention provides a noise removal system for smoothing three-dimensional data for member searching and a method of removing the same.

In order to achieve the above object, a noise removing system for smoothing three-dimensional data for searching for a member according to the present invention includes an image receiving unit for receiving image information, and a ratio of a volume size and an area size with respect to a mesh of an image. A noise judging unit for judging whether the image is noise by comparison, and a direction in which the difference between the three-dimensional volume and the two-dimensional area is minimized in the coordinates of the mesh of the image when the noise judging unit determines that the image is noise. It characterized in that it consists of a noise removing unit for removing the noise by converting to.

On the other hand, the noise removal method for smoothing the three-dimensional data for the member search according to the present invention is the image receiving step for receiving the image information, and comparing the ratio of the volume size and the area size with respect to the mesh of the image with a threshold value A noise discrimination step of determining whether the image is noise, and when the noise discriminating unit determines that the image is noise, the coordinates of the mesh of the image are converted into a direction in which the difference between the three-dimensional volume and the two-dimensional area is minimized. Characterized in that the noise removal step of removing the noise.

In the noise removing system and the noise removing method, the noise discriminating unit discriminates the image as noise when the value on the left side of the inequality sign is larger than the value on the right side of the inequality code according to the following equation (1).

------------ (1)

------------ (One)

는 부피크기와 면적 크기에 대한 평균 비율, σ는 상기 평균 비율(

)에 관한 표준 편차임 Where Vi is the volume size for the mesh of the image, Si is the area size for the mesh of the image,

Is the average ratio of the volume size and the area size, and σ is the average ratio (

Is the standard deviation for

According to the noise removal system for smoothing three-dimensional data for the member search and the method for removing the same according to the present invention, in particular, the ratio of the volume size and the area size with respect to the mesh of the image is compared with a threshold to determine whether the image is noise. The noise can be precisely removed by discriminating and removing the noise from the screen. Therefore, a cleaner and more natural image can be displayed on the video screen.

As shown in Fig. 1, the image receiving unit 2 for receiving image information is a means capable of acquiring a camera or other image information installed in a digital camera or a mobile phone.

The noise discriminating unit 4 is a microprocessor connected to the image receiving unit 2 so as to determine whether the corresponding image is noise by comparing the ratio between the volume size and the area size with respect to the mesh of the image with a threshold value.

When the noise discriminating unit 4 determines that the image is noise, the noise removing unit 6 converts the coordinates of the mesh of the image to a direction in which the difference between the three-dimensional volume and the two-dimensional area is minimized. A microprocessor that removes noise from the user's field of view by smoothing the height of the mesh vertices by lowering the height of the (high dot).

The display unit 8 is a screen connected to the noise removing unit 6 to receive a display signal from the noise removing unit 6 and to display an image from which the noise is removed, for example, a display screen of a digital camera and a display of a mobile phone. Screen or monitor.

The noise discriminating unit 4 uses the following equation (1) to calculate the data required for the expression and the associated operation so as to discriminate the image as noise when the value on the left side of the inequality sign for the mesh vertex of the image is larger than the value on the right side of the inequality sign. It is connected to the stored memory 10.

------------------ (1)

------------------ (One)

는 부피크기와 면적 크기에 대한 평균 비율, σ는 상기 평균 비율(

)에 관한 표준 편차임. 여기서 부피의 의미는 메쉬 정점과 메쉬 바닥면인 육각형이 이루는 4면체의 실제 부피를 의미하는 것이 아니고, 상기 사면체의 표면적의 총합을 의미하며, 이하 동일하게, '부피'는 사면체 표면적의 합을 의미하는 것으로 사용된다. Where Vi is the volume size for the mesh of the image, Si is the area size for the mesh of the image,

Is the average ratio of the volume size and the area size, and σ is the average ratio (

Is the standard deviation for. Here, the volume does not mean the actual volume of the tetrahedron formed by the hexagon of the mesh vertex and the mesh bottom surface, but means the sum of the surface areas of the tetrahedron, and equally, the 'volume' means the sum of the tetrahedral surface areas. Used to.

The control unit 12 is the image receiving unit 2, the noise discriminating unit 4, the noise removing unit 6, the display unit 8 and the memory 10 performs the smoothing operation of the mesh vertices of the image to remove the noise as a whole The controlling microprocessor.

The control unit 12, the noise discriminating unit 4, and the noise removing unit 6 may be configured as separate microprocessors as in the present embodiment, or may have respective regions in one microprocessor. It may be configured.

Hereinafter, a method of controlling a noise removing system for three-dimensional data according to an embodiment of the present invention in connection with a noise removing system for three-dimensional data according to an embodiment of the present invention configured as described above will be described with reference to FIG. 2. do.

First, the image receiving unit 2 recognizes an image of an arbitrary object (including a person) (S1).

Next, in step S2, an image signal is transmitted from the image receiving section 2 to the noise discriminating section 4. The noise discriminating unit 4 then converts the image signal into mesh data consisting of a plurality of squares. Next, the vertices of each mesh are calculated.

+ σ)보다 큰가를 판별하여, 상기 메쉬의 3차원 면적의 합과 메쉬의 2차원 면적의 비율(Rn)이 문턱값(

+ σ)보다 클 경우에, 단계S4에서 해당 화상의 메쉬 정점을 노이즈로 판별한다.Next, in step S3, the noise discriminating unit 4 determines that the ratio (Rn) of the sum of the three-dimensional areas of the mesh and the two-dimensional area of the mesh is represented by the equation (1).

is determined to be greater than + sigma, and the ratio Rn of the sum of the three-dimensional areas of the mesh and the two-dimensional area of the mesh

If larger than + sigma), the mesh vertices of the image are discriminated as noise in step S4.

Next, in step S5, an image signal and a discrimination result signal are transmitted from the noise discriminating section 4 to the noise removing section 6. The noise removing unit 6 then calculates a correction height D corresponding to a correction amount for correcting the height P _old of the vertex of the image determined as noise according to the following equation (2).

-------------- (2)

-------------- (2)

는 부피크기와 면적 크기에 대한 평균 비율, σ는 상기 평균 비율(

)에 관한 표준 편차임Vi is the volume size for the mesh of the image, Si is the area size for the mesh of the image,

Is the average ratio of the volume size and the area size, and σ is the average ratio (

Is the standard deviation for

Next, the noise removing unit 6 moves the coordinates of the mesh vertices of the image corresponding to each noise based on the correction height D calculated based on the above expression (2) according to the following equation (3). Lower the height of the mesh vertices (P _old ) to have the height of the new mesh vertices (P _new ).

P _new = P _old + D ----------- (3)

That is, the newly updated point P _new in 3D (three-dimensional) is placed in the opposite direction of the normal vector N _P of the point P _old as shown in the figure on the right of Figure 9 smoothes the mesh vertices. Therefore, peak noises are effectively removed.

Next, from the noise removing unit 6 to the display unit 8, a mesh vertex is smoothed and an image signal from which noise is removed is output. Subsequently, the display unit 8 outputs a smooth and natural screen from which noise is removed.

<Description of Mathematical and Geometric Basis of Noise Reduction System for Smoothing 3D Data for Member Retrieval and Its Removal Method According to the Present Invention>

 When the 3D data reconstructed by the scanner or the 3D reconstruction method is meshed, the meshes adjacent to the point P are shown in FIG. 4. Fig. 4 is a hexagonal shape showing six triangular meshes sharing a point P in a mesh smoothing method through a general noise analysis. The area (volume) of a three-dimensional mesh adjacent to the point P to detect and smooth the peak noise. And the area of the projected two-dimensional mesh.

The projected two-dimensional mesh is created as follows. After calculating the normal vector Ni of the meshes sharing the point P in FIG. 5, the normal vector NP of the point P is obtained as an average of the normal vectors of adjacent meshes as shown in Equation (9). FIG. 5 is a diagram illustrating a normal vector of a point P, N is a normal vector of a triangle P, and N is a triangle vector neighboring a point P. Where n is the number of meshes adjacent to point P. Project point P in the direction opposite to normal vector NP.

Through the above process, as shown in FIG. 6, two-dimensional mesh data in which the three-dimensional mesh data and the point P are projected can be obtained. 6 is a two-dimensional form (right) of the mesh projected perpendicular to the normal vector NP and the configuration of the meshes (left) in three-dimensional space.

 The areas of the three-dimensional and two-dimensional meshes thus obtained are calculated. First, the process of calculating the area (volume) of the 3D mesh is described and the process of calculating the area of the 2D mesh is described.

 The area of the three-dimensional mesh is obtained as follows. Here, the area of the three-dimensional mesh is also referred to as 'volume'. The basic area calculation unit of a three-dimensional mesh is tetrahedrons. Each vertex and origin of the triangular mesh are connected to form a tetrahedron. Each tetrahedron is calculated with a sign area. The magnitude of the calculated value is the area of the tetrahedron, and the sign checks whether the origin is in the same or opposite direction as the triangle normal. In Figure 7, triangle ABC has a normal NABC. The volume of the tetrahedral OABC is shown in Equation 10.

 The sign of the tetrahedral OABC is positive in the opposite direction of NABC. The three-dimensional area of the mesh is shown in equations (11) and (12).

 Here, i means triangle or basic tetrahedron. Coordinates of the vertices of (xi1, yi1, zi1), (xi2, yi2, zi2) and (xi3, yi3, zi3) triangles i. Since the area of the three-dimensional mesh as shown in Fig. 7 is always positive, the final result is obtained by taking the absolute value of Vtotal. As shown in FIG. The three-dimensional mesh area calculates the area of each triangle and calculates the sum of the area of each triangle.

The two-dimensional area of the mesh is obtained as follows. Two-dimensional meshes are polygons that are polygonal contours. Assume a two-dimensional mesh of lines in FIG. 8. Create a set of triangles connecting the origin and vertices of the polygon. 8 is a diagram showing the area of polygons (polygons) of the 2D mesh. Each edge and origin forms a basic triangle. When the triangle OA'B 'is made in FIG. 9, the area of the triangle OA'B' is calculated as in Equation 13.

Next, the area of each triangle is calculated as shown in equation (14).

|

|

과

는 시점과 끝점의 좌표이다. 메쉬의 2차원 면적은 수학식 15와 같이, 모든 면적의 합으로 계산된다. Where i is the index of all edges or fundamental triangles,

and

Is the coordinates of the start and end points. The two-dimensional area of the mesh is calculated as the sum of all areas, as shown in equation (15).

은 수학식 16으로부터 얻어진다.Using the above results, we can calculate the ratio of the three-dimensional and two-dimensional projected areas, | Vtotal | / | Stotal |, of adjacent meshes at each vertex of the mesh data. Average of area ratio

Is obtained from equation (16).

, n은 메쉬의 갯수

, n is the number of meshes

In the case of peak noise, this point is regarded as peak noise if the area ratio of 2D and 3D is larger than the sum of the average area ratio and the standard deviation as shown in Equation 17.

Points detected as peak noise by Equation 17 have information on the sum of the areas of adjacent meshes of each point P in 3D and the area sum of the meshes projected in 2D. Therefore, as shown in FIG. 9, the distance D at which the difference between the two-dimensional area and the three-dimensional volume becomes the minimum at the point P _old regarded as peak noise is calculated as in Equation 18. FIG. 9 is a diagram illustrating that coordinates are transformed by a distance D as a point recognized as peak noise, and the figure on the left shows a point P _old regarded as peak noise, and the figure on the right of FIG. Represents a point (P _new ) whose coordinates have been corrected.

The newly updated point P _new in 3D lies in the opposite direction of the normal vector N _P of point P _old as in the figure on the right in FIG. 9. In this way, the peak noise is effectively removed by the equation (19).

P _new = P _old + D

<Experiment Result>

(Example 1 Experiment)

Next, the results of experiments on the method of the present invention will be described.

The performance of the proposed study was tested with three-dimensional data obtained by various methods. The experiment was performed by adding noise to 3D data obtained from a laser scanner, 3D data generated by a computer, and 3D data obtained using a computer (stereo) vision. The area of the mesh close to the peak noise has a larger surface area than the other meshes constituting the object. Using the characteristic of the peak noise, it is possible to detect the peak noise as shown in Figure 10 (a) by the ratio of the area of the adjacent 3D mesh and the projected 2D area in the 3D data. If a limit for reducing the area of the meshes adjacent to the peak noise point is applied according to the 2D / 3D mesh area ratio, the peak noise is effectively smoothed as shown in FIG. 10 (b). 10 (c) and 10 (d) show an enlarged image of peak noise of a specific portion and an image of which peak noise is smoothed in that portion, respectively. FIG. 10 is an image obtained by removing noise by using a noise and 2D / 3D mesh area ratio in data obtained by a 3D laser scanner, (a) indicates noise detection, (b) indicates noise smoothing result, and (c) illustrates FIG. An enlarged image of (a), (d) is an enlarged image of Figure 10 (b).

11 is a graph representing the area ratio of 3D data with respect to the above (ceramic ware) image by the proposed peak noise detection method. That is, FIG. 11 is a graph showing the 2D / 3D area ratio of the mesh at each vertex. The threshold value of the area ratio recognized as peak noise is 2.43258.

The number of vertices of the 3D data for the above-mentioned magnetic ware image is 10,764 and the number of vertices detected by the peak noise is 113. Most of the 107 peak noises added to the 3D data were detected and smoothed. Table 1 shows quantitative values of the change in area and the difference in average distance. The area is the area of the triangular mesh that each vertex forms, and the average distance is the average of the distances between the original coordinates of the vertices determined as noise and the coordinates changed by the noise effect. It can be seen that the peak noise is effectively removed by the noise smoothing method using the 2D / 3D area ratio.

Changes in area and average distance error when noise is added and removed from 3D data Area of mesh data Average distance error 3D data 8085.29779 (100%) - Add noise 8622.98630 (106.65%) 0.326997 Noise reduction 8238.51752 (101.89%) 0.108264

(Example 2 Experiment)

Next, we compare the performance of the proposed algorithm with computer-generated window-shaped 3D data. When the peak noise and the Gaussian noise are added to the left image of FIG. 12A, many changes occur at the edge and the boundary portion as shown in the right image of FIG. 12A. Images of the result of removing noise by applying the method using the median filter and the 2D / 3D area ratio to the deformed data are shown on the left and right sides of Fig. 12B, respectively. FIG. 12 shows experimental results of computer-generated image data, in which 3D data (left side of FIG. 12A), noise-added image (right side of FIG. 12A), and a result of smoothing noise with a median filter (left side of FIG. 12B) 12B is an image of the noise smoothing result of the smoothing method according to the present invention. Conventional median smoothing method does not effectively remove the noise at the edge or boundary portion of the object, it can be seen that there is still a lot of noise existing inside the object. The smoothing method of the present invention removes noise at edges or boundary portions of an object differently from the conventional median smoothing method, and also shows better performance in removing noise inside the object.

FIG. 13 is a graph showing a 2D / 3D area ratio of a mesh formed by each vertex in the above window data. It can be seen that the peak noise can be effectively removed by the noise smoothing method using the 2D / 3D area ratio. The threshold value of the area ratio recognized as peak noise is 2.43258.

14 is a graph showing a comparison of the error between the conventional method (Laplacian, the median) and the method according to the present invention according to the number of times of noise detection repetition. That is, FIG. 14 is a graph comparing the performance of the conventional method and the method of the present invention by averaging the sum of the distances between the coordinates according to the conventional method and the modified coordinates at each vertex determined as the noise according to the number of repetitions. In the smoothing method of the mesh vertices according to the present invention, as in other conventional methods, as the repetitive processing is performed, the error is greatly reduced. As shown in FIG. 14, the number of repetitions was confirmed to be 20 or less through experiments. There was no change in the error even after noise smoothing was repeated 20 times or more. As shown in FIG. 14, the proposed noise smoothing method can be seen that the error remains constant after 10 iterations.

1 is a control block diagram of a noise reduction system of three-dimensional data according to an embodiment of the present invention;

2 is a flowchart of a method for removing noise of 3D data according to an embodiment of the present invention;

3 is a flowchart schematically illustrating a process of processing an image signal according to the present invention;

4 is a hexagonal shape figure showing six triangular meshes sharing a point P in a mesh smoothing method through a general noise analysis;

FIG. 5 is a diagram illustrating a normal vector of triangle meshes in which NP is a point P and N is a triangular mesh sharing point P in a general method, with neighboring triangle meshes as point P. FIG.

6 is a diagram showing the configuration of the meshes in the three-dimensional space (left) and the two-dimensional shape (right) of the mesh projected perpendicular to the normal vector NP in a general method,

7 is a diagram illustrating a method of calculating a three-dimensional mesh area according to the present invention;

8 is a diagram illustrating a method of calculating the area of a polygon according to the present invention;

9 is a process in which coordinates are transformed by a distance D as a point recognized as peak noise according to the present invention.

9 (a) is a diagram showing a point P _old regarded as peak noise,

9 (b) is a diagram showing a point P _new whose coordinates are corrected by D,

10 is an experimental result of the present invention, the image showing the image change before and after the noise is removed,

11 is a 2D / 3D area ratio of the mesh at each vertex,

FIG. 12 is a computer generated data as another experimental result of the present invention, showing an image change before and after noise is removed.

12 (a) shows an image represented as initial data in three dimensions (3D) and an image added with noise;

12 (b) is an image showing the result of smoothing the noise with the median filter, an image of the window showing the result of noise smoothing according to the noise removing method of the present invention,

FIG. 13 is a graph showing a 2D / 3D area ratio at the vertices of each mesh in relation to FIG. 12;

14 is a correlation graph of the vertex of the mesh and the image representation repetition frequency comparing the existing methods {(Laplacian method, median method)} with the noise removing method according to the present invention.

FIG. 15 is an exemplary screen showing a result of a noise removing method according to the prior art, in which a torus model is shown on the right side of the screen, and FIG. 15 (b) shows a model to which noise is added from the right side, and FIG. Shows the model smoothed with the Laplacian filter, the fourth from the right is the model smoothed with the median filter,

FIG. 16 is a geometrical representation of the vertex p of the mesh according to the prior art, in which the left figure is a one-dimensional ring of mesh vertices adjacent to vertex P, and the right figure is a triangle adjacent to vertices and edges (xi-xj). Edge angles (αj, βj),

FIG. 17 is a diagram illustrating a triangular mesh representation in a median filter method according to the prior art, in which a figure on the left shows triangles adjacent to a center triangle T at a local N (T), and a figure on the right is a visual representation of Equation 8 A shape that is an expression.

Explanation of symbols on the main parts of the drawings

2: image receiving unit 4: noise discriminating unit

6: noise removing unit 8: display unit

12: control unit D: correction height

Claims (4)

delete delete delete An image receiving step (a) of receiving image information, A noise discrimination step (b) of comparing the ratio between the volume size and the area size with respect to the mesh of the image with a threshold to determine whether the image is noise; In the noise discrimination step, when the image is determined to be noise, a noise removing step (c) is performed to convert the coordinates of the mesh of the image to a direction in which the difference between the three-dimensional volume and the two-dimensional area is minimized to remove the noise. In the noise removal method for smoothing three-dimensional data for the member search, The noise determination step (b), The image is discriminated as noise when the value on the left side of the inequality sign is larger than the value on the right side of the inequality sign, executed by the following equation (1);

------- (One) Where Vi is the volume size for the mesh of the image, Si is the area size for the mesh of the image,

Is the average ratio of the volume size and the area size, and σ is the average ratio (

Is the standard deviation for. The noise removing step (c), Calculating a correction height D corresponding to a correction amount for correcting the height P _old of the vertex of the image determined as noise according to the following equation (2);

------ (2) Where Vi is the volume size for the mesh of the image, Si is the area size for the mesh of the image,

Is the average ratio of volume size to area size, and σ is the average ratio (

Is the standard deviation for. Based on the correction height D, the coordinates of the mesh vertices of the image corresponding to each noise are moved according to the following equation (3), the height of the mesh vertices P _old is lowered, and the height of the new mesh vertices P (c-1) to have _new ); P _new = P _old + D ---- (3) Size volume (V _i) of the mesh of the associated picture, According to the following equations (10) to (12), the area of the tetrahedron (OABC) connecting each vertex and the origin of the triangular mesh is obtained, and then the sum of the areas of the tetrahedrons is obtained.

--- (10)

---- (11)

---- (12)  Where i denotes a triangle or a basic tetrahedron, and is the coordinates of the vertices of (xi1, yi1, zi1), (xi2, yi2, zi2) and (xi3, yi3, zi3) triangles i. A two-dimensional area of the mesh size (S _i) is According to the following equations (13) to (15), the area of a triangle connecting the origin and the vertex of the polygon that is the polygonal contour is obtained, and then the area of each triangle is summed to obtain the three-dimensional data for the member search. Noise removal method for smoothing.

--- (13)

------ (14)

----- (15) Where i is the index of all edges or fundamental triangles,

and

Is the coordinate of start and end point.

Images