KR101021173B1 - Apparatus and method for creating mosaic image based on amdamento - Google Patents

Abstract

An andmento based mosaic image generating apparatus and method are disclosed. The image input unit receives an original image for generating a mosaic image, and the reference point arranging unit randomly arranges a predetermined number of reference points for the original image. The first vector determiner determines, for each reference point, a first vector toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum. The second vector determiner determines the second vector based on a sum of a plurality of vectors generated in a direction opposite to a vector toward another reference point adjacent to the reference point and whose magnitude is inversely proportional to the distance to another reference point adjacent to the reference point. The third vector determiner determines the third vector based on a component perpendicular to the reference flow line in the sum of a plurality of vectors from the reference flow line crossing the reference point to the auxiliary reference point positioned adjacent to the reference point along the reference flow line. . The final vector determiner multiplies the first vector to the third vector by a predetermined weight and adds the final vector to calculate the final vector for each reference point. The tile placement unit generates a Voronoi diagram for the reference points repositioned according to the final vector, and generates a mosaic image by placing a tile in each Voronoi cell. According to the present invention, the intended andamento can be accurately represented to generate a mosaic image close to the classic mosaic.

Description

Apparatus and method for creating mosaic image based on amdamento}

The present invention relates to an apparatus and method for generating mosaic images based on andamento, and more particularly, to an apparatus and method for implementing mosaic images capable of expressing various andamentos by computer graphics.

Mosaic, one of the topics under study in the field of non-realistic rendering, is a decorative art technique that collects various small tiles and expresses specific images and patterns. Mosaics have been widely used in ancient times, mainly for floor and wall decoration, and until recently, various studies have been attempted by graphics researchers according to the nature and arrangement of the tiles constituting the mosaic.

Batiato et al. Define mosaics as examples of discrete primitive-based images, and largely multi-picture mosaics and tile mosaics depending on whether the tiles used in the mosaic are images or not. Divided into. Multi picture mosaic is a method of composing an original image using many images stored in a database as tiles, and includes a photo mosaic and a puzzle image cape. Tile mosaics are also reproductions of the mosaic as a classical decorative art, which includes an antique mosaic and a crystallization mosaic.

The general method of making a tile mosaic is as follows. First determine the layout and design of the mosaic, and then sketch the main areas of the determined design and the guidelines to stick along the tiles on the plane to which the tiles will be tiled. Next, cut the tiles to fit the shape of the area and stick them along the guidelines. Finally, fill the grout in the gap between the tiles to complete the mosaic.

The layout or design of the mosaic that is determined first in the process of making such a mosaic is called Andamento. Andamento is a Latin word representing the flow or movement of tile arrangement, and is classified as follows according to the shape and arrangement of the tile. In addition, Figure 1 is a view for explaining a variety of andmento.

(1) Opus Tesselatum: Tiles arranged in a straight line like a brick.

(2) Opus Classicum: A form in which the background except the object area is arranged according to Opus Tesselatum.

(3) Opus Vermiculatum: Tiles arranged along the boundary between the object area and the background.

(4) Opus Musivum: In the Opus Vermiculatum technique, the tile arrangement on the boundary extends to the entire area of the background.

(5) Opus Palladianum: irregularly arranged tiles.

(6) Opus Sectile: A mosaic in which tiles are shaped to match the shape of the object area.

 2A to 2E are diagrams showing examples of mosaics having andamentos of Opus Tesselatum, Opus Classicum, Opus Musivum, Opus Palladianum, and Opus Sectile, respectively. Such andamentos can be easily found in ancient tile mosaic works, and are also used to determine the layout of works in the current mosaic production process.

Many researches have been conducted on the technique of simulating tile mosaics using computer graphics, but mainly for only one andamento. 3A-3E illustrate examples of mosaics implemented in computer graphics by conventional methods. Referring to FIG. 3A, the shapes of the tiles constituting the mosaic image are all uniform and thus do not appear in the actual mosaic work. In addition, the mosaic shown in Figure 3b is implemented using a given tile, which is different from the traditional mosaic technique. The mosaic shown in Figure 3c shows the Opus Musivum among the Andamento, the tile shape is constant. The mosaic shown in FIG. 3D represents Opus Musivum and Opus Classicum simultaneously, and the tile shape is different from the shape of the tile shown in the actual mosaic work. Finally, the mosaic of FIG. 3E represents Opus Palladianum, but has a disadvantage in that the shape of the tiles is unnatural.

Therefore, it is necessary to develop the technique to realize the mosaic similar to the actual mosaic works by grasping the characteristics of each andamento and applying it to all the andamento.

An object of the present invention is to provide an apparatus and method for mosaic image generation based on an Andamento capable of generating a mosaic image accurately expressing characteristics of an intended Andamento from an original image.

Another technical problem to be solved by the present invention is to read a computer program for executing an Andamento-based mosaic image generation method capable of generating a mosaic image accurately expressing the characteristics of the intended Andamento from the original image. To provide a recording medium that can be.

Andamento based mosaic generating apparatus according to the present invention for achieving the above technical problem, an image input unit for receiving an original image for generating a mosaic image; A reference point arranging unit which randomly arranges a predetermined number of reference points with respect to the original image; A first vector determiner configured to determine a first vector toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum with respect to each reference point; A second vector is determined for each reference point based on the sum of a plurality of vectors generated in a direction opposite to a vector toward another reference point adjacent to the reference point and whose magnitude is inversely proportional to the distance to another reference point adjacent to the reference point. A second vector determiner; For each reference point, a reference flow line intersecting the reference point is determined among a plurality of flow lines constituting a tangent flow field extracted from the original image, and adjacent to the reference point along the reference flow line from the reference flow line. A third vector determiner configured to determine a third vector based on a component perpendicular to the reference flow line from a sum of a plurality of vectors directed to an auxiliary reference point located; A final vector determiner configured to multiply the first vector, the second vector, and the third vector by a predetermined weight, and add the multiplied weights to calculate a final vector for each reference point; And generating a Voronoi diagram for the reference points rearranged according to the final vector calculated for each reference point, and arranging a tile in each Voronoi cell constituting the Voronoi diagram to generate the mosaic image. It includes a tile arrangement unit.

Andamento based mosaic generation method according to the present invention for achieving the above another technical problem, an image input step of receiving an original image for generating a mosaic image; A reference point arranging step of randomly arranging a predetermined number of reference points with respect to the original image; A first vector determining step of determining a first vector for each reference point toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum; A second vector is determined for each reference point based on the sum of a plurality of vectors generated in a direction opposite to a vector toward another reference point adjacent to the reference point and whose magnitude is inversely proportional to the distance to another reference point adjacent to the reference point. Determining a second vector; For each reference point, a reference flow line intersecting the reference point is determined among a plurality of flow lines constituting a tangent flow field extracted from the original image, and adjacent to the reference point along the reference flow line from the reference flow line. A third vector determining step of determining a third vector based on a component perpendicular to the reference flow line from a sum of a plurality of vectors heading to an auxiliary reference point positioned at a predetermined distance; A final vector determination step of multiplying the first vector, the second vector, and the third vector by a predetermined weight, and then adding them to calculate a final vector for each reference point; And generating a Voronoi diagram for the reference points rearranged according to the final vector calculated for each reference point, and arranging a tile in each Voronoi cell constituting the Voronoi diagram to generate the mosaic image. Tile arrangement step;

According to the Andamento-based mosaic image generating apparatus and method according to the present invention, after placing the reference point irrespective of the andamento of the mosaic image to be generated, the characteristics such as color, size and alignment of the tiles constituting the mosaic image Accordingly, by differently setting the weights assigned to the first to third vectors for repositioning the reference point, the intended andamento can be accurately represented to generate a mosaic image close to the classic mosaic.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the andamento-based mosaic image generating apparatus and method according to the present invention.

4 is a block diagram showing the configuration of a preferred embodiment of the mosaic image generating apparatus according to the present invention.

Referring to FIG. 4, the mosaic image generating apparatus according to the present invention includes an image input unit 410, a reference point arranging unit 420, a first vector determiner 430, a second vector determiner 440, and a third vector determiner. A unit 450, a final vector determining unit 460, and a tile arrangement unit 470 are provided.

The image input unit 410 receives an original image for generating a mosaic image. The original image is an image in which the tile effect that appears in the mosaic image does not appear. The mosaic image is generated by arranging tiles having the same color as the corresponding area in the divided regions of the original image.

The reference point arranging unit 420 randomly arranges a predetermined number of reference points with respect to the original image. In this case, the reference point may be disposed on the original image to generate a new mosaic image therefrom, or the reference point may be arranged on the canvas by generating a canvas having the same size as the original image.

Each reference point corresponds to a point at which tiles for generating a mosaic image are arranged, and a reference point equal to the number of tiles arranged is disposed. The plurality of reference points are not necessarily arranged according to a predetermined rule, and are randomly arranged on the original image, and then have a layout that is suitable for the user's intended andamento by the relocation process described later.

In the present invention, the andamento of the mosaic image may be represented as an energy function representing the characteristics of each tile constituting the mosaic image. The characteristics of the Andamento are the accuracy of how accurately each tile reflects the original image, the uniformity of whether the shape and size are consistent between each tile constituting the mosaic image, and the center of gravity of each tile where the tile is positioned in the original image. An arrangement indicating whether or not the flow in the region to be arranged, that is, arranged along the flow line, is also defined by the type of the flow line. Among them, accuracy, uniformity and alignment are included in each term of the energy function. The characteristics of each andamento described above are shown in Table 1 below. However, since Opus Vermiculatum has the same characteristics as Opus Musivum and Opus Classicum has both the characteristics of Opus Vermiculatum and Opus Tessellatum, it is omitted.

accuracy Uniformity Alignment Type of flow line Opus tesselatum usually height height Straight Opus mustivum usually height height Object outside Opus palladianum lowness lowness lowness none Opus skeleton height lowness lowness none

Referring to Table 1, Opus Sectile, which cuts and pastes tiles to match the shape and color of the objects in the original image, is more accurate, while Opus Palladianum, which has a random shape and color of tiles, has a large difference between the mosaic image and the original image. Because of the low accuracy. Also, Opus Tesselatum and Opus Musivum have high uniformity because the background of mosaic image is filled with tiles with uniform shape and size. Opus Sectile and Opus Palladianum with irregular shape and size of tiles have low uniformity. Finally, in the case of alignment, Opus Mussivum has a high degree of alignment because the tiles are placed along a flow line that spreads at regular intervals from the outside of the object in the original image.

The energy function created based on the above Andamento's characteristics is shown in Equation 1 below.

Where E is the value of the energy function, E _d is the accuracy, E _r is the uniformity, E _a is the degree of alignment, w _d is the weight given to the accuracy, w _r is the weight given to the uniformity, and w _a is the degree of alignment The weight given. In addition, all three weights given according to the characteristics of the Andamento have a value between -1 and 1, and the sum of the three weights is 1.

The accuracy value E _d is calculated based on the color difference between the original image and the mosaic image at the position of the tile placed on the reference point by Equation 2 below.

는 모자이크 이미지를 구성하는 타일에서 (x,y) 위치를 가지는 화소의 색상값, C(x,y)는 원본 이미지에서 동일한 위치를 가지는 화소의 색상값, 그리고 k는 정규화 변수로서 본 발명에서는 2로 설정된다.Here, E _d is the accuracy, N is the number of tiles constituting the mosaic image, that is, the number of reference points disposed on the original image, n is the number of pixels included in one tile, (x, y) is the i-th tile the position of the pixel in the region corresponding to t _i ,

Is the color value of the pixel having the (x, y) position in the tile constituting the mosaic image, C (x, y) is the color value of the pixel having the same position in the original image, and k is a normalization variable. Is set to.

5 is a diagram illustrating a color difference between an original image and a mosaic image. Referring to FIG. 5, tiles of a single color are arranged in divided regions of an original image to form a mosaic image. It can be seen that the difference between the color values of the original image and the mosaic image is large in the area where the color gradient of the original image appears. As the size of the tiles constituting the mosaic image increases, the difference in color values becomes larger.

Next, the uniformity value E _r is defined by the uniformity value of the tile size and the uniformity value of the tile shape, and is calculated by the following equation (3).

Where E _r is the uniformity, w _size and w _shape are the weights given to the tile size and the uniformity of the shape, E _size is the uniformity of the tile size, and E _shape is the uniformity of the tile shape.

In Equation 3, the uniformity E _size of the tile size is a value defined by the average of the difference between the tile size average and the size of each tile, and is calculated by the following Equation 4.

는 모자이크 이미지 T를 구성하는 전체 타일의 크기의 평균, 그리고 S_t는 모자이크 이미지 T에서 t번째 타일의 크기이다.Where E _size is the uniformity of the tile sizes, N is the number of tiles constituting the mosaic image T,

Is the average of the size of the entire tile constituting the mosaic image T, and S _t is the size of the t-th tile in the mosaic image T.

Next, the uniformity E _shape of the tile _shape in Equation 3 may be obtained as in Equation 5 by calculating the similarity between two selected tiles among the tiles constituting the mosaic image using the tangent function of the edge of the tile. .

Where E _shape is the uniformity of the tile shape, N is the number of tiles constituting the mosaic image T, t _i is the i-th tile, t _j is the j-th tile, T () is the tangent function, and θ ₀ is the adjacent tile. The angle of rotation of the tiles to minimize the difference in edge angle.

6 is a view for explaining a process of obtaining the uniformity of the tile shape. Referring to FIG. 6, a graph of a tangent function for edges of two tiles for which similarity is calculated may be obtained, and the area between the two graphs becomes a similarity value.

The uniformity value included in the energy function of Equation 1 can be calculated by appropriately adjusting the weights given to the uniformity value of the tile size of Equation 4 and the uniformity value of the tile shape of Equation 5.

Finally, the degree of alignment value E _d is for each tile for which the mosaic image is obtained, whether or not tiles adjacent to the tile are well aligned along the flow line passing through the center of the tile for which the alignment value is to be obtained. 7 shows tiles arranged along a flow line. A process of calculating the alignment degree value will be described with reference to FIG. 7.

In FIG. 7, a tile for which an alignment value is to be obtained is t _i , and a flow line passing through the center of t _i is selected from a plurality of flow lines constituting a flow field extracted from an original image. Alignment of the next two tiles t _i while crossing the selected flow line to a position side by side on each side of the t _i and t _i ^l _i t ^r yi also is used for the calculation of the value. The degree of alignment value is calculated by measuring the distance from t _i ^l and t _i ^r to the flow line, which is given by Equation 6 below.

Here, E _a is arranged Figure, N is the number of tiles constituting the mosaic image T, dist (t _i, t _i ^r) is the distance between the flow line passing through the center of the t _i and t _i ^r, dist (t _i , ^l t _i) is the distance between the passing through the center of the flow line and the t _i t ^l _i, and h is used to normalize the alignment Fig value as the average height of all of the tiles that make up the mosaic image.

The values of the accuracy, uniformity, and degree of alignment in Equations 2, 3, and 6 have values between 0 and 1, and smaller values mean higher accuracy, uniformity, and degree of alignment. In addition, when the value of the energy function of Equation 1 is minimum, it means that the mosaic image is generated to well represent the characteristics of the andamento. Therefore, if the weight is positive, the values of accuracy, uniformity and alignment should be small to minimize the energy function. If the weight is negative, the values of accuracy, uniformity and alignment should be large.

The first vector determiner 430, the second vector determiner 440, and the third vector determiner 450, which will be described below, minimize the energy function value of Equation 1 to have an Andamento intended for the mosaic image. A first vector, a second vector, and a third vector are calculated in a direction to make reference, and the reference points on the original image are rearranged by the calculated first to third vectors.

The first vector determiner 430 determines, for each reference point, a first vector toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum.

At the reference point disposed on the original image, tiles having a preset shape and size are placed. At this time, each tile may have only a single color due to the nature of the mosaic. Therefore, to accurately represent the color of the original image, the tile placed at the reference point should not be located at the boundary between different colors in the original image. The first vector is calculated to move the position of the reference point so that one tile may be located in the same color region. In addition, since the first vector is related to the color of the image, the accuracy value of Equation 2 also represents the similarity of the color between the original image and the mosaic image, and thus the first vector is determined to reduce the accuracy value.

In order to calculate a first vector calculated for each reference point and moving the reference point away from the region of different colors, the density of the color in the region where the reference point is located in the original image is required. The first vector determiner 430 uses a method of determining the first vector by calculating the color density in the kernel by applying each kernel. The first vector determines a mean-shift vector directed to a dense portion having the same color as the color of the portion where the reference point is located in the kernel.

The density of colors in the kernel is calculated by Equation 1 below. At this time, the size of the kernel applied to each reference point is set equal to the area of the tile to be placed at each reference point. Therefore, dividing the area of the original image by the number of reference points gives the area of the kernel applied to each reference point.

Where n is the number of pixels in the kernel, h is the radius of the kernel, K () is the radially symmetric kernel, x is the position of the reference point to which the kernel is applied, and x _i is the position of the i-th pixel among the pixels included in the kernel. to be.

The first vector determiner 430 selects pixels having the same color as the color of the pixel in which the reference point is located on the original image among the pixels included in the kernel, calculates a sum of vectors directed to each pixel selected from the reference point, and Determined as the first vector. As a result, the first vector has a direction in which many pixels of the same color as the color of the pixel where the reference point is located, that is, a direction in which the density of the same color as the color of the part corresponding to the reference point is maximum.

8 is a diagram illustrating a first vector determined for one of reference points on an original image. Referring to FIG. 8, a kernel applied to a reference point disposed adjacent to a boundary line of different colors includes an area composed of two colors. Therefore, the reference point should be moved in a direction away from an area composed of colors different from the color of the portion where the reference point is located. In FIG. 8, the arrow indicated by the thick line indicates the first vector. When the reference point is moved in the direction of the first vector, the areas inside the kernel moved together with the reference point have the same color. Branches are more accurate when the tiles are placed. As a result, the effect of reducing the accuracy value can be obtained.

The second vector determiner 440 is based on the sum of a plurality of vectors generated such that the direction of the vector toward the other reference point adjacent to the reference point is opposite to the reference point and the magnitude is inversely proportional to the distance to the other reference point adjacent to the reference point. Determine the second vector.

The second vector is related to the uniformity value of Equation 3, and in order to improve the uniformity of the tiles in the mosaic image, the reference points which are the centers of the tiles must be evenly arranged to improve the uniformity, that is, in Equation 3 The second vector is calculated to reduce the uniformity value. In this case, a kernel having a preset size is applied to a reference point for calculating the second vector to select adjacent reference points considered for calculating the second vector, and the reference points included in the kernel are used for calculating the second vector.

9 is a diagram for describing a process of calculating a second vector. In FIG. 9, an elliptical kernel having a center reference point 910 as an origin with respect to the center reference point 910 for which the second vector is to be calculated is applied. The ratio between the major and minor axis of the kernel is determined by the shape of the tile, and the shape of the tile depends on the andamento of the mosaic image. In this case, it is preferable to arrange the kernel such that the long axis of the kernel contacts the flow line passing through the center reference point 910. In addition, the area of the kernel is set to be an integer multiple of the area of the tile to be disposed at the center reference point 910, it is preferable to be twice the area of the tile so that the kernel includes an appropriate number of reference points. Meanwhile, the area of the tile is a value obtained by dividing the area of the original image by the number of reference points as described above. Referring to FIG. 9, it can be seen that five reference points adjacent to the inside of the kernel applied to the central reference point 910 are included. The second vector is calculated from the sum of the generated vectors for these adjacent reference points.

The vector 930 generated between the center reference point 910 and one of the adjacent reference points, from which the second vector is to be calculated, is opposite in direction to the vector toward the adjacent reference point 920 from the center reference point 910. It has a size inversely proportional to the distance between the reference point 910 and the adjacent reference point 920. That is, as the distance between the center reference point 910 and the adjacent reference point 920 increases, the size of the vector 930 facing in the opposite direction becomes smaller, and the distance between the center reference point 910 and the adjacent reference point 920 becomes closer. As the size increases, the size of the vector 930 facing in the opposite direction increases. Five vectors have been generated for all five reference points adjacent to the center reference point 910 from FIG. 9, and these vectors represent the direction of the vector from the center reference point 910 to the adjacent reference point and between the center reference point 910 and the adjacent reference point. You can see that it was created according to the distance.

The second vector is calculated as the sum of the generated vectors equal to the number of reference points adjacent to the center reference point 910 for which the second vector is to be calculated. This can be expressed as Equation 8 below.

Here, v _r is the second vector, n is the number of adjacent reference points included in the kernel applied to the center reference point 910, v _i is a vector from the center reference point 910 to the i th reference point of the adjacent reference point, and kr _θ is The radius of the kernel applied to the central reference point 910. K also means that the kernel area is k times the tile area.

Referring to FIG. 9, it can be seen that a second vector, which is an arrow indicated by a thick line, is calculated by the sum of five vectors generated for reference points adjacent to the central reference point 910. By moving the center reference point 910 along the second vector, the distance between adjacent reference points is evened, thereby increasing the uniformity of the shape and size of the tile. That is, the uniformity value of Equation 3 can be reduced.

The third vector determiner 450 determines a reference flow line that crosses the reference point among the plurality of flow lines constituting the tangent flow field extracted from the original image for each reference point, and the reference point along the reference flow line from the reference flow line. A third vector is determined based on a component perpendicular to the reference flow line in the sum of the plurality of vectors directed to the auxiliary reference point positioned adjacent to. Here, the tangent flow field is generated from an edge tangent flow of the original image and used to determine a direction of arranging tiles constituting the mosaic image.

10 is a diagram illustrating reference points disposed on an original image and a reference flow line intersecting with one reference point. Referring to FIG. 10, a third vector is calculated for the center reference point 1010 that intersects the reference flow line 1050, and the center reference point 1010 along the reference flow line 1050 is calculated to calculate the third vector. Auxiliary reference points 1020 and 1030 located on both sides are used. In this case, the reference flow line 1050 may not be located adjacent to a specific reference point among a plurality of reference points adjacent to the central reference point 1010, and may pass obscurely between the plurality of reference points. In this case, in order to clearly determine the auxiliary reference points 1020 and 1030 used for the calculation of the third vector, the third vector determiner 450 uses a Voronoi diagram.

That is, the third vector determiner 450 generates a temporary Voronoi diagram composed of a plurality of temporary Voronoi cells based on a plurality of reference points on the original image, and then includes one temporary Voronoi cell including the center reference point 1010. The reference points included in the temporary Voronoi cells that share the edge of the reference flow line 1050 and pass through the shared edges are determined as auxiliary reference points 1020 and 1030 for calculating the third vector. Referring to FIG. 10, in the temporary Voronoi diagram generated on the original image, one edge is shared with the Voronoi cell 1015 including the center reference point 1010, and the reference flow line 1050 is used as the shared edge. The reference points included in the two temporary vorono cells 1025 and 1035 passing through are used as auxiliary reference points 1020 and 1030.

The third vector is determined in such a form as to minimize the sum of the distances between the auxiliary reference points 1020 and 1030 and the reference flow line 1050. That is, when the auxiliary reference points 1020 and 1030 for calculating the third vector are determined, the third vector calculator 450 calculates a vector heading from the reference flow line 1050 to the respective auxiliary reference points 1020 and 1030. A third vector is determined based on the component perpendicular to the reference flow line in the sum. At this time, the direction of the third vector is the same as the direction of the component perpendicular to the reference flow line, and the size of the third vector is 1/2 of the size of the vertical component. The size of the third vector is 1/2 of the vertical component because the alignment of the tiles may be lowered if the central reference point 1010 is moved too much.

Finally, the final vector calculator 460 multiplies the first vector, the second vector, and the third vector by weights, and adds them to calculate the final vector for each reference point.

The first vector, the second vector, and the third vector described above are determined to increase the accuracy, uniformity, and degree of alignment of the tiles disposed at each reference point, thereby finally minimizing an energy function value of Equation 1. However, each reference point is not relocated every time the first vector to the third vector is determined, and when the first vector to the third vector are all determined, the reference point is rearranged by the final vector calculated therefrom.

In this case, the weights multiplied by the first to third vectors are the same as the weights w _d , w _r, and w _a included in Equation 1, respectively, and reflect values of the andamento of the mosaic image to be generated. For example, when the Andamento of the mosaic image is set to Opus Tesselatum, Opus Tesselatum has a high uniformity and a high degree of alignment as compared to the accuracy as shown in Table 1. That is, the energy function of Equation 1 reflects a high accuracy value and low uniformity and alignment values. Therefore, the weight multiplied by the first vector is set higher than the weight multiplied by the second vector and the third vector.

The tile placement unit 470 generates a Voronoi diagram for the repositioned reference points according to the final vector calculated for each reference point, and arranges a tile in each Voronoi cell constituting the Voronoi diagram to generate a mosaic image. Create

The mosaic image is generated by placing a tile, which is a unit component of the mosaic image, at each reference point repositioned on the original image or the canvas of the same size. In this case, the color of the tile becomes the same as the color of the point where the reference point at which the tile is disposed is located in the original image. In addition, the shape of the tile to be arranged may be the same as each of the Voronoi cells constituting the Voronoi diagram generated for the repositioned reference points, or may have a shape of a circle or polygon included in each Voronoi cell.

The shape of the Voronoi cell constituting the Voronoi diagram generated for the arrangement of the tiles is different from the shape of the Voronoi cell constituting the temporary Voronoi diagram generated by the third vector generator 450 to determine the auxiliary reference point. Do. The temporary Voronoi diagram generated by the third vector generator 450 is for reference points initially placed on the original image, and the Voronoi diagram generated by the tile placement unit 470 is rearranged by the final vector. For reference points. The relocated reference points also reflect the Andamento's characteristics of the mosaic image generated from the original image.

On the other hand, the mosaic image can be generated by generating a Voronoi diagram and arranging tiles as it is for the reference points rearranged by the final vector, but by adjusting each Voronoi cell constituting the Voronoi diagram, It is necessary to allow closer mosaic images to be generated. To this end, the tile placement unit 470 includes a first edge adjustment unit 472, a second edge adjustment unit 474, and a third edge adjustment unit 476.

The first edge adjusting unit 472 to the third edge adjusting unit 476 move the edge forming the Voronoi cell to minimize the energy function of Equation 1. Therefore, the first edge adjuster 472 to the third edge adjuster 476 move the edge only when the value of the energy function decreases due to the movement of the edge. This edge movement process is performed for all edges of the Voronoi diagram and is repeated until the value of the energy function no longer decreases or as an auxiliary criterion until the value of the energy function is below a preset threshold. Hereinafter, operations of the first edge adjusting unit 472 to the third edge adjusting unit 476 will be described in detail.

The first edge adjuster 472 moves a reference edge that is sequentially selected among the plurality of edges forming each Voronoi cell so that a ratio of pixels having the same color among the pixels included in the Voronoi cell including the reference edge is increased. To increase.

The function of the first edge adjuster 472 is similar to that of the first vector determiner 430, and moves the edges so that all pixels included in the Voronoi cell have the same color. However, even when the edges are moved, all pixels may not have the same color. Therefore, a method similar to the first vector may be determined to thereby move each edge.

Just as the first vector determiner 430 calculates the density of the color using the kernel to determine the first vector, the first edge adjuster 472 also applies a kernel to the reference edge to obtain a vector for moving the reference edge. Decide The radius of the kernel is set to 1/2 of the reference edge length so that the reference edge is the diameter of the kernel.

The density of colors in the kernel is calculated by the following equation (9). This applies when the kernel is split into two partial kernels by the reference edge.

Where n is the number of pixels in one partial kernel, m is the number of pixels in the other partial kernel, h is the radius of the kernel, K () is the radially symmetric kernel, and y ₁ and y2 are the reference edges. Where x _i is the position of the i th pixel among the pixels included in each partial kernel.

The first edge adjuster 472 moves the reference edge by the min shift vector calculated from Equation 9 above, and if necessary, rotates the reference edge so as to be perpendicular to the direction indicated by the min shift vector, thereby providing the same color to the Voronoi cell. Branches can be made to include more pixels. By moving the reference edge as described above, the ratio of pixels having the same color may be increased as compared to the Voronoi cell initially generated by the tile placement unit 470.

The second edge adjusting unit 474 is directed toward the center of the Voronoi cell having a large difference from the average value of the areas of the plurality of Voronoi cells among the two adjacent Voronoi cells sharing the reference edge, and the two adjacent Voronoi sharing the reference edge. The reference edge is moved by a vector having a size determined based on the difference in the area of the cell.

The second edge adjuster 474 performs a function similar to the second vector determiner 440 and moves the reference edges sequentially selected from the plurality of edges so that the size of each Voronoi cell is uniform. At this time, the direction of the vector for moving the reference edge is toward the center of the Voronoi cell having a larger difference from the average value of the area of the relatively larger Voronoi cell, that is, all the Moronoi cells, among the adjacent Voronoi cells sharing the reference edge. In addition, the magnitude of the vector is calculated by the following equation (10).

Where mag is the magnitude of the vector moving the reference edge, s ₁ and s ₂ are the area of two adjacent Voronoi cells sharing the reference edge, and l is the length of the reference edge.

Finally, the third edge adjuster 476 moves the reference edge by the third vector determined with respect to the center of the Voronoi cell including the reference edge.

The third vector determiner 450 determines the third vector with respect to each reference point and moves the reference point according to the determined third vector, but the third edge adjuster 476 is positioned at the center of the Voronoi cell including the reference edge. The third vector is determined and the reference edge is moved according to the determined third vector to increase the alignment between the Voronoi cells. Determination of the third vector with respect to the center of the Voronoi cell including the reference edge is the same as described above, and thus a detailed description thereof will be omitted. As the edge of the Voronoi cell is moved, the center of the Voronoi cell is also moved, resulting in the same effect as moving the reference point.

11 is a flowchart illustrating a process of performing a preferred embodiment of the Andamento based mosaic image generating method according to the present invention.

Referring to FIG. 11, the image input unit 410 receives an original image for generating a mosaic image (S1110). Next, the reference point arranging unit 420 randomly arranges a predetermined number of reference points on the original image (S1120). The number of reference points is equal to the number of tiles constituting the mosaic image.

The first vector determiner 430 determines, for each reference point, a first vector toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum (S1130). In addition, the second vector determiner 440 is based on the sum of a plurality of vectors generated such that the direction is opposite to a vector toward another reference point adjacent to the reference point and inversely proportional to the distance to another reference point adjacent to the reference point with respect to each reference point. In operation S1140, a second vector is determined. The third vector determiner 450 determines a reference flow line that crosses the reference point among the plurality of flow lines constituting the tangent flow field extracted from the original image for each reference point, and the reference point along the reference flow line from the reference flow line. A third vector is determined based on a component perpendicular to the reference flow line from the sum of the plurality of vectors heading to the auxiliary reference point positioned adjacent to (S1150). Since the process of determining the first vector, the second vector, and the third vector has been described above, a detailed description thereof will be omitted.

When the first to third vectors are determined, the final vector determiner 460 multiplies the first vector, the second vector, and the third vector by weight, and adds them to calculate the final vector for each reference point (S1160). . Finally, the tile placement unit 470 generates a Voronoi diagram based on the repositioned reference points according to the final vector calculated for each reference point, and a plurality of the same shape as each of the Voronoi cells constituting the Voronoi diagram. The tile is arranged to generate a mosaic image (S1170). In this case, the first edge adjuster 472, the second edge adjuster 474, and the third edge adjuster 476 repeatedly move the edges between the Voronoi cells in order to minimize the value of the energy function of Equation 1. Can be done.

12A to 12G illustrate an original image, a tangent flow field extracted from an original image, a layout of a reference point when only a second vector is applied to the reference point, a mosaic image generated when only the second vector is applied to the reference point, and a third on the reference point. FIG. 11 illustrates a layout of a reference point when only a vector is applied, an arrangement of a reference point when all of the first vectors to a third vector are applied, and a mosaic image generated when all of the first to third vectors are applied. 12A to 12G, since the first to third vectors all represent the characteristics of andamento, it can be seen that when all three vectors are applied, a mosaic image showing the characteristics of the andamento can be generated. have.

13 is a view showing a first embodiment of a mosaic image generated by the present invention. The weights multiplied by the first to third vectors to generate the mosaic image of FIG. 13 are w _d = 0.2, w _r = 0.3 (w _shape = 0.55, w _size = 0.45), and w _a = 0.5, respectively. Was set.

14 is a view showing a second embodiment of the mosaic image generated by the present invention. For the mosaic image of FIG. 14, the weight values multiplied by the first to third vectors are w _d = 0.25, w _r = 0.35 (w _shape = 0.5, w _size = 0.5), and w _a = 0.4, respectively. Was set. When compared with the mosaic image of FIG. 13, it can be seen that the flow of tile arrangement appears differently due to the change in the weight value.

15 is a view showing a third embodiment of a mosaic image generated by the present invention. The mosaic image of FIG. 15 was generated by weights set as w _d = 0.25, w _r = 0.3 (w _shape = 0.4, w _size = 0.6), and w _a = 0.45. The flow of tile arrangement shown in the mosaic image of FIG. 15 is also different from that of the mosaic images of FIGS. 13 and 14. It is confirmed from the embodiments of FIGS. 13 to 15 that a mosaic image expressing well-designed andamento can be generated by adjusting a weight value multiplied by the first to third vectors.

16A to 16C are diagrams illustrating mosaic images generated by different weights multiplied by first to third vectors from the same original image.

In the mosaic image of FIG. 16A, the weights multiplied by the first to third vectors are set to w _d = 0.2, w _r = 0.3 (w _shape = 0.5, w _size = 0.5), and w _a = 0.5, respectively. Opus Musivum represents Andamento. In addition, the mosaic image of FIG. 16B was generated by a weight value set to w _d = 0.25, w _r = 0.5 (w _shape = 0.5, w _size = 0.5), and w _a = 0.25, and represents Andamento of Opus Classicum. . Finally, for the mosaic image of FIG. 16C, the weight values are set to w _d = 0.5, w _r = -1.5 (w _shape = 0.65, w _size = 0.35), and w _a = 0 to represent Andamento of Opus Palladianum. . It can be seen from FIG. 16A to FIG. 16C that even when the same original image is set differently, the mosaic image having a completely different andamento can be generated.

The invention can also be embodied as computer readable code on a computer readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored. Examples of the computer-readable recording medium include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like, and may be implemented in the form of a carrier wave (for example, transmission via the Internet) . The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.

Although the preferred embodiments of the present invention have been shown and described above, the present invention is not limited to the specific preferred embodiments described above, and the present invention belongs to the present invention without departing from the gist of the present invention as claimed in the claims. Various modifications can be made by those skilled in the art, and such changes are within the scope of the claims.

1 is a view for explaining a variety of Andamento,

2A to 2E are diagrams showing examples of mosaics with andamentos of Opus Tesselatum, Opus Classicum, Opus Musivum, Opus Palladianum, and Opus Sectile, respectively;

3A-3E show examples of mosaics implemented in computer graphics by conventional methods,

4 is a block diagram showing the configuration of a preferred embodiment of the mosaic image generating apparatus according to the present invention;

5 is a view showing a color difference between an original image and a mosaic image;

6 is a view for explaining a process of obtaining the uniformity of the tile shape;

7 shows tiles arranged along a flow line;

8 shows a first vector determined for one of the reference points on the original image;

9 is a view for explaining a process of calculating a second vector;

10 is a diagram illustrating reference flow lines intersecting one reference point and reference points disposed on the original image;

11 is a flowchart illustrating a process of performing a preferred embodiment of the Andamento based mosaic image generating method according to the present invention;

12A to 12G illustrate an original image, a tangent flow field extracted from an original image, a layout of a reference point when only a second vector is applied to the reference point, a mosaic image generated when only the second vector is applied to the reference point, and a third on the reference point. A diagram showing a layout of a reference point when only a vector is applied, a layout of a reference point when all of the first to third vectors are applied, and a mosaic image generated when all of the first to third vectors are applied;

13 is a view showing a first embodiment of a mosaic image generated by the present invention;

14 shows a second embodiment of a mosaic image produced by the present invention;

15 is a view showing a third embodiment of a mosaic image generated by the present invention, and

16A to 16C are diagrams illustrating mosaic images generated by different weights multiplied by first to third vectors from the same original image.

Claims (15)

An image input unit configured to receive an original image for generating a mosaic image; A reference point arranging unit which randomly arranges a predetermined number of reference points with respect to the original image; A first vector determiner configured to determine a first vector toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum with respect to each reference point; A second vector is determined for each reference point based on the sum of a plurality of vectors generated in a direction opposite to a vector toward another reference point adjacent to the reference point and whose magnitude is inversely proportional to the distance to another reference point adjacent to the reference point. A second vector determiner; For each reference point, a reference flow line intersecting the reference point is determined among a plurality of flow lines constituting a tangent flow field extracted from the original image, and adjacent to the reference point along the reference flow line from the reference flow line. A third vector determiner configured to determine a third vector based on a component perpendicular to the reference flow line from a sum of a plurality of vectors directed to an auxiliary reference point located; A final vector determiner configured to multiply the first vector, the second vector, and the third vector by a predetermined weight, and add the multiplied weights to calculate a final vector for each reference point; And Tiles for generating a mosaic image by generating a Voronoi diagram for the reference points rearranged according to the final vector calculated for each reference point, and placing a tile in each Voronoi cell constituting the Voronoi diagram. Arrangement unit; Mosaic image generating apparatus comprising a. The method of claim 1, The tile arrangement unit, A first edge configured to increase a ratio of pixels having the same color among pixels included in the Voronoi cell including the reference edge by moving a reference edge selected sequentially among the plurality of edges forming each Voronoi cell; Adjusting unit; A vector having a size determined based on a difference in the area of two adjacent Voronoi cells sharing the reference edge toward the center of the Voronoi cell having the larger area and sharing the reference edge; A second edge adjusting unit moving the reference edge by the second edge adjusting unit; And And a third edge adjuster configured to move the reference edge by the third vector determined with respect to the center of the Voronoi cell including the reference edge. 3. The method of claim 2, Wherein the second edge adjuster moves the reference edge by a vector having a size calculated by Equation A below: Equation A

Where mag is the magnitude of the vector moving the reference edge, s ₁ and s ₂ are the area of two adjacent Voronoi cells sharing the reference edge, and l is the length of the reference edge. The method according to claim 1 or 2, The first vector determiner applies a kernel having a predetermined size with respect to the reference point, and selects pixels that are the same as the color of the pixel corresponding to the reference point among pixels included in the kernel on the original image, and select the pixel selected from the reference point. And the first vector is determined by the sum of the vectors directed to each. The method according to claim 1 or 2, Wherein the second vector determiner applies a kernel having a predetermined size to a center reference point sequentially selected from among the reference points, and determines the second vector by Equation B below: Equation B

Here, v _r is the second vector, n is the number of reference points included in the kernel and adjacent to the center reference point, v _i is a vector from the center reference point to the i th reference point of n adjacent reference points, and kr _θ is Radius of the kernel. The method according to claim 1 or 2, The third vector determiner generates a temporary Voronoi diagram composed of a plurality of temporary Voronoi cells based on the plurality of reference points, and shares one edge with the temporary Voronoi cell including a center reference point sequentially selected from the reference points. And determining a reference point included in the temporary Voronoi cell through which the reference flow line passes through the shared edge as the auxiliary reference point. The method according to claim 1 or 2, And the weight has a value between -1 and 1, and the sum of three weight values multiplied by the first to third vectors is 1. An image input step of receiving an original image for generating a mosaic image; A reference point arranging step of randomly arranging a predetermined number of reference points with respect to the original image; A first vector determining step of determining a first vector for each reference point toward a point where the density of the same color as the color of the portion corresponding to the reference point in the original image is maximum; A second vector is determined for each reference point based on the sum of a plurality of vectors generated in a direction opposite to a vector toward another reference point adjacent to the reference point and whose magnitude is inversely proportional to the distance to another reference point adjacent to the reference point. Determining a second vector; For each reference point, a reference flow line intersecting the reference point is determined among a plurality of flow lines constituting a tangent flow field extracted from the original image, and adjacent to the reference point along the reference flow line from the reference flow line. A third vector determining step of determining a third vector based on a component perpendicular to the reference flow line in the sum of the plurality of vectors directed to the located auxiliary reference point; A final vector determination step of multiplying the first vector, the second vector, and the third vector by a predetermined weight, and then adding them to calculate a final vector for each reference point; And Tiles for generating a mosaic image by generating a Voronoi diagram for the reference points rearranged according to the final vector calculated for each reference point, and placing a tile in each Voronoi cell constituting the Voronoi diagram. Arranging step; Mosaic image generation method comprising the. The method of claim 8, The tile arrangement step, A reference edge that is sequentially selected from among a plurality of edges forming each of the Voronoi cells so that at least a predetermined number of pixels among the pixels included in the Voronoi cell including the reference edge have the same color; 1 edge adjustment step; A vector having a size determined based on a difference in the area of two adjacent Voronoi cells sharing the reference edge toward the center of the Voronoi cell having the larger area and sharing the reference edge; A second edge adjusting step of moving the reference edge; And And a third edge adjusting step of moving the reference edge by the third vector determined with respect to the center of the Voronoi cell including the reference edge. The method of claim 9, And in the second edge adjustment step, move the reference edge by a vector having a size calculated by Equation A below. Equation A

Where mag is the magnitude of the vector moving the reference edge, s ₁ and s ₂ are the area of two adjacent Voronoi cells sharing the reference edge, and l is the length of the reference edge. The method according to claim 8 or 9, In the first vector determining step, a kernel having a predetermined size is applied to the reference point, and pixels of the pixel corresponding to the reference point are selected from the pixels included in the kernel on the original image to select from the reference point. And determining the first vector by the sum of vectors directed to each of the selected pixels. The method according to claim 8 or 9, In the second vector determination step, applying a kernel of a predetermined size to the central reference point sequentially selected from the reference points, and determines the second vector according to the following equation B : Equation B

Here, v _r is the second vector, n is the number of reference points included in the kernel and adjacent to the center reference point, v _i is a vector from the center reference point to the i th reference point of n adjacent reference points, and kr _θ is Radius of the kernel. The method according to claim 8 or 9, In the third vector determining step, a temporary Voronoi diagram composed of a plurality of temporary Voronoi cells is generated based on the plurality of reference points, and the temporary Voronoi cell and one edge including a center reference point sequentially selected from the reference points are generated. And determining a reference point included in the temporary Voronoi cell through which the reference flow line passes through the shared edge as the auxiliary reference point. The method according to claim 8 or 9, And the weight has a value between -1 and 1, and the sum of three weight values multiplied by the first to third vectors is 1. A computer-readable recording medium having recorded thereon a program for executing the mosaic image generating method according to claim 8 or 9.

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