A method for converting three-dimensional patterns of traditional handicrafts into two-dimensional patterns

Abstract

A method for converting three-dimensional patterns of traditional handicrafts into two-dimensional patterns; first, the model of the three-dimensional surface is rotated to obtain a number of orthogonal projection fragments, so that there are as many overlapping parts as possible between the fragments; then, the obtained orthogonal projection fragments are used as units to perform grid division and affine transformation, and the non-developable surface is approximately processed into a developable surface; after the developable surface is obtained, the surface fragments are expanded by a boundary processing algorithm to eliminate the concave and convex feeling of the surface fragments; finally, these expanded fragments are spliced ​​into a complete two-dimensional image by a multi-plane splicing and fusion algorithm, and the integrity and aesthetics of the image are maintained. The example of the present invention can retain the original shape and color of the pattern, and complete the two-dimensionalization of the three-dimensional pattern surface without distortion.

Description

Technical Field

[0001] The invention relates to the fields of image processing and computer vision, and is a method for converting a three-dimensional pattern of a traditional handicraft into two dimensions involving surface development and image splicing. Background Art

[0002] As a spiritual resource of culture, the three-dimensional patterned surface of traditional handicrafts belongs to culture and is an integral part of culture. The digital dissemination of cultural heritage is an indispensable part of cultural confidence and cultural power. With the continuous development of high-tech, the digital technology of handicrafts has gradually matured. In particular, the development of three-dimensional craft technology has also expanded its scope of application, including cultural relics restoration, craft display, etc.

[0003] However, the focus of 3D process technology is still more concentrated on the modeling of the process. In addition to modeling, there are also a large number of patterns in traditional 3D surfaces. These patterns have rich geometric and color characteristics. In two-dimensional space, these pattern materials play an important role and can provide data sources for segmentation, annotation, vectorization and other processes. There are many types of 3D crafts, many of which are cylindrical and have curvature changes on a busbar. The two-dimensionalization of 3D surfaces has always been an important topic and research direction in computer graphics, but most research results are concentrated in the fields of machinery and industrial production, focusing only on the deformation of the surface mesh but not on the changes in the surface patterns.

[0004] For the topic of converting traditional 3D surfaces into 2D, the core issues include meshing, approximate conversion of non-developable surfaces into developable surfaces, development of developable surfaces, feature point extraction and matching, and image fusion. Existing methods can be applied to different steps in image processing, but have not been applied to the process of converting traditional 3D pattern surfaces into 2D. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problems encountered in the process of converting three-dimensional pattern surfaces into two-dimensional ones. This article proposes a method for converting three-dimensional patterns of traditional handicrafts into two-dimensional ones.

[0006] The present invention provides a method for converting a three-dimensional pattern of a traditional handicraft into a two-dimensional pattern, characterized by comprising the following steps:

[0007] Step 1: Construct an approximate rotating body of a traditional craft:

[0008] The traditional handicraft is rotated around the central axis by 2π / N to obtain an orthogonal projection segment image in the ZY plane, and the outer contour curves of the handicraft in the N orthogonal projection segment images are averaged and rotated around the central axis to obtain a rotating body;

[0009] Step 2: Project the 3D pattern on the non-developable surface to the developable surface:

[0010] A reference cylinder is constructed with the maximum width of the rotating body as the radius, and the N orthogonal projection segment images are geometrically corrected respectively, and projected onto the surface of the reference cylinder to obtain N transformed images;

[0011] Step 3: Get the unfolded view of the developable surface:

[0012] For each transformed image, extract the area with smaller distortion in the image and perform vertical segmentation to obtain a number of vertical strip-shaped areas, and then perform perspective transformation on the vertical strip-shaped areas to obtain an unfolded image;

[0013] Step 4: stitching based on multi-view plane images:

[0014] The unfolded image of any transformed image is taken as the initial unfolded image, and the x-axis direction is taken as the reference. Image stitching is performed in sequence on both sides of the initial unfolded image. When stitching images, adjacent unfolded images are first aligned and then image fusion and stitching are performed, and finally the two-dimensional result of the three-dimensional pattern of traditional handicrafts is obtained.

[0015] The present invention is based on the two-dimensionalization of three-dimensional pattern surfaces of traditional crafts. Through the specific algorithm details described above, the entire process of two-dimensionalization of three-dimensional pattern surfaces of traditional crafts is completed to obtain a two-dimensional result. For the two-dimensionalization results of different three-dimensional pattern surfaces of traditional crafts, the shape and proportion of the three-dimensional surface pattern are basically retained, and it has good versatility. Therefore, for the three-dimensional pattern surfaces of crafts whose top-view cross-sections are concentric circles and the bottle body is covered with patterns, the present invention can realize the two-dimensionalization of three-dimensional surfaces through the algorithm of this article, regardless of the format, lighting, material, craft, specific shape of the three-dimensional surface, and the type, clarity and resolution of the bottle body pattern. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 This is a flow chart of a method for converting a three-dimensional pattern surface into two-dimensional surface based on traditional technology according to an embodiment of the invention.

[0018] Figure 2 This is a schematic diagram of a traditional handicraft - a vase.

[0019] Figure 3(a) is a randomly selected orthogonal projection segment image.

[0020] FIG3( b ) is another randomly selected orthogonal projection segment image.

[0021] FIG4( a ) is a schematic diagram of gridding (38×4) of an orthogonal projection segment image.

[0022] FIG4( b ) is a projection diagram of FIG4( a ) on a reference cylinder.

[0023] FIG5( a ) is a schematic diagram of gridding (12×4) of orthogonal projection segment images.

[0024] FIG5( b ) is a projection of FIG5( a ) onto a reference cylinder.

[0025] Figure 6 Schematic diagram of the segmentation of the 80% area in the center of the projection image.

[0026] Figure 7 For Figure 6 The image after the central 80% area is expanded.

[0027] Figure 8 This is the two-dimensional result of the three-dimensional pattern on the vase. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] like Figure 1 The figure shows a flow chart of a method for converting a three-dimensional pattern surface into two-dimensional form based on a traditional process according to an embodiment of the present invention. The principle of the method is as follows: first, a set of orthogonal projection surface images are obtained by rotating the model in situ for one circle; then, all images are meshed and affine transformed to approximate the non-developable surface into a developable surface; then, the developable surface is expanded by projection transformation to obtain a set of expanded planes; this set of multi-view planes is image stitched, and the images are spliced ​​from the center to both sides by extracting and matching feature points and fusion of images, so as to improve the splicing efficiency and avoid problems such as tilt when stitching one image at a time, so as to complete the two-dimensionalization of the three-dimensional pattern surface of the process.

[0030] like Figure 2 The figure shows a traditional handicraft - a vase, with a three-dimensional pattern painted on the surface. The method of this embodiment aims to unfold the three-dimensional pattern into a flat image.

[0031] The method for converting a three-dimensional pattern of a traditional handicraft into a two-dimensional pattern in this embodiment includes the following steps:

[0032] S110, the surface of the three-dimensional pattern surface of the craft is approximately regarded as an easily calculated geometric solid of rotation, and the projection of the three-dimensional craft perpendicular to the Z axis is used as the axial section by orthogonal projection. The solid of rotation formed by rotating the axial section is used as the reference solid of rotation of the three-dimensional pattern surface of the craft. Since the solid of rotation has relatively obvious geometric features, it can be used as a reference for calculation in subsequent steps.

[0033] In the process of obtaining the orthogonal projection of the three-dimensional pattern surface of the process, considering that the axial cross-section shapes of the three-dimensional pattern surface of the process in each direction may be different, it is necessary to obtain an orthogonal projection segment image in the ZY plane every time the traditional craft rotates 2π / N around the central axis, and obtain a total of N orthogonal projection segment images. In this embodiment, N is 18, that is, the orthogonal projection segment image is obtained every time the traditional craft rotates 20°. As shown in Figure 3(a) and Figure 3(b), two randomly selected orthogonal projection segment images.

[0034] These orthogonal projection segment images pass through the coordinate origin and are parallel to the Z axis, that is, these orthogonal projection segment images are in the ZY plane. The outer contour curves of the craftwork in these 18 orthogonal projection segment images are averaged and rotated around the central axis to obtain a rotating body.

[0035] S120, using the idea of ​​equiangular cylindrical projection to transform the non-developable rotation body, and obtain the orthogonal projection fragment of the developable surface. In order to fit the characteristics of the traditional three-dimensional pattern surface itself, it is necessary to improve this projection transformation to obtain the orthogonal projection of the developable cylinder. The details are as follows:

[0036] First, a reference cylinder surrounding the axial section is constructed through the axial section of the rotating body. The radius of the cylinder is the longest width of the axial section of the rotating body. In order to avoid the interference of the shape of the three-dimensional pattern surface itself and to restore the texture of the three-dimensional pattern surface itself to the maximum extent, it is necessary to perform an affine transformation on the orthogonal projection of the three-dimensional pattern surface to simulate the orthogonal projection of the reference cylinder. The affine transformation formula from the original image point p0 to the transformed point p1 is as follows, where T is the affine transformation matrix.

[0037]

[0038] When three pairs of corresponding points before and after the transformation are known, the affine transformation matrix T can be calculated. The calculation formula is as follows:

[0039]

[0040] Among them, a, b, c, d, e, and f are parameters of the affine transformation matrix T.

[0041] It is necessary to keep the y-axis coordinate of the orthogonal projection image of the three-dimensional pattern surface unchanged and map the x-axis coordinate to the x-axis coordinate of the reference cylinder. In order to reduce the amount of calculation, the orthogonal projection fragment image is processed by M*L gridding, and the image in each grid is transformed into the projection image of the cylinder to realize the projection of the orthogonal projection fragment image on the reference cylinder. As shown in Figure 4(a) and Figure 4(b), they are respectively the 28×4 gridding schematic diagrams of the orthogonal projection fragment image and its projection on the reference cylinder. As shown in Figure 5(a) and Figure 5(b), they are respectively the 12×4 gridding schematic diagrams of the orthogonal projection fragment image and its projection on the reference cylinder. The affine transformation matrix used for the projection is solved using the correspondence between the grid points:

[0042] Solve the corresponding affine transformation matrix T m·l , m is the row number of the grid, l is the column number of the grid, m=1,2,3…,M, l=1,2,3…,L, and the formula for solving the position of all transformed pixels is as follows:

[0043]

[0044] In the formula, the symbols mean: width t represents the horizontal distance of pixel point t relative to the grid coordinate origin p0, width represents the width of the orthogonal projection fragment image, height t It represents the vertical distance of pixel point t relative to the coordinate origin p0 of the grid, and height represents the height of the orthogonal projection fragment image.

[0045] S130, for each transformed image, extracting a region with smaller distortion in the image and performing vertical segmentation to obtain a plurality of vertical strip-shaped regions, and then performing perspective transformation on the vertical strip-shaped regions to obtain an unfolded image.

[0046] In this step, the characteristics of the projection image are used to reversely calculate its actual position on the surface of the cylinder using the boundary processing algorithm. The flattening method is as follows:

[0047] For each orthogonal projection segment, due to the large deformation around the image, in order to reduce the deformation and completely retain the process surface pattern, only 80% of the area in the middle of the image is taken for calculation. This part of the image is equivalent to the projection of a fan-shaped arc surface. In order to reduce the amount of calculation, these areas are divided into multiple areas with different slopes. The image is approximated as a polyhedral cylinder, and then expanded using perspective transformation. Since the projection range of an orthogonal projection is 180 degrees, and the projection image only takes 80% of the range, the expanded image area is only asin(0.8) / 90=29.52%. When performing regional segmentation, the cutting range of the middle part is large, and the cutting range of the two sides is small. The specific width formula is as follows:

[0048]

[0049] Wherein, A=180°*0.8 / k, k is the number of cuts of the cut area, index is the serial number of the cut area, index increases from the middle to both sides, the middle is 0, and the two sides are the largest, w0=0.8*W, W is the width of the reference cylinder. In this embodiment, k is 9, and the 80% area in the middle of each projection is divided into 9 parts. Figure 6 Shown is a schematic diagram of the segmentation of the central 80% area of ​​the projection image in Figure 5. Figure 7 For Figure 6 The image after the central 80% area is expanded.

[0050] S140, using an image stitching algorithm based on multi-view stitching, based on a single-view stitching algorithm, taking the x-axis direction of the initial unfolded image as a reference, to ensure that the stitched two-dimensional result is still a rectangle. At the same time, taking advantage of the end-to-end connection of the process three-dimensional pattern surface rotating body, stitching is continuously performed on both sides of the initial unfolded image to reduce the deformation error of the stitched image, thereby obtaining a two-dimensional result. Figure 8 This is the two-dimensional result of the three-dimensional pattern on the vase.

[0051] The specific method is to take the unfolded image of any transformed image as the initial unfolded image, take the x-axis direction as the reference, and perform image stitching in sequence on both sides of the initial unfolded image. When stitching images, first align the adjacent unfolded images and then perform image fusion and stitching, and finally obtain the two-dimensional result of the three-dimensional pattern of traditional handicrafts.

[0052] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solution formed by equivalent replacement or equivalent transformation falls within the protection scope required by the present invention.

Claims

1. A method for converting a three-dimensional pattern of a traditional handicraft into a two-dimensional pattern, comprising the following steps: Step 1: Construct an approximate rotating body of a traditional craft: The traditional handicraft is rotated around the central axis by 2π / N to obtain an orthogonal projection segment image in the ZY plane, and the outer contour curves of the handicraft in the N orthogonal projection segment images are averaged and rotated around the central axis to obtain a rotating body; Step 2: Project the 3D pattern on the non-developable surface to the developable surface: A reference cylinder is constructed with the maximum width of the rotating body as the radius, and the N orthogonal projection segment images are geometrically corrected respectively, and projected onto the surface of the reference cylinder to obtain N transformed images; Step 3: Get the unfolded view of the developable surface: For each transformed image, extract the area with smaller distortion in the image and perform vertical segmentation to obtain a number of vertical strip-shaped areas, and then perform perspective transformation on the vertical strip-shaped areas to obtain an unfolded image; Step 4: stitching based on multi-view plane images: The unfolded image of any transformed image is taken as the initial unfolded image, and the x-axis direction is taken as the reference. Image stitching is performed in sequence on both sides of the initial unfolded image. When stitching images, adjacent unfolded images are first aligned and then image fusion and stitching are performed, and finally the two-dimensional result of the three-dimensional pattern of traditional handicrafts is obtained.

2. The method for converting a three-dimensional surface into two-dimensional surface based on non-traditional technology according to claim 1, characterized in that: In step 1, the rotating body obtained based on the traditional handicraft is in the shape of a bottle, and its top-view cross-sections are all concentric circles.

3. The method for converting a three-dimensional surface into two-dimensional surface based on non-traditional technology according to claim 1, characterized in that: The traditional handicraft is a three-dimensional data model.

4. The method for converting a three-dimensional surface into two-dimensional surface based on non-traditional technology according to claim 1, characterized in that: In step 2, the orthogonal projection segment image is subjected to M*L gridding, and the image in each grid is transformed into a projection image of the reference cylinder. The affine transformation matrix used for the projection is solved using the correspondence relationship of the grid points: The affine transformation formula from the original image point p0 to the transformed point p1 is as follows, where T is the affine transformation matrix: When three pairs of corresponding points before and after the transformation are known, the affine transformation matrix T can be calculated: Among them, a, b, c, d, e, and f are parameters of the affine transformation matrix T.

5. The method for converting a three-dimensional surface into two-dimensional surface based on non-traditional technology according to claim 1, characterized in that: In step 2, for each grid, the corresponding relationship between grid points is used to solve the corresponding affine transformation matrix T m·l , m is the row number of the grid, l is the column number of the grid, m=1,2,3…,M, l=1,2,3…,L, and the formula for solving the position of all transformed pixels is as follows: In the formula, the symbols mean: width t represents the horizontal distance of pixel point t relative to the grid coordinate origin p0, width represents the width of the orthogonal projection fragment image, height t It represents the vertical distance of pixel point t relative to the coordinate origin p0 of the grid, and height represents the height of the orthogonal projection fragment image.

6. The method for converting a three-dimensional surface into two-dimensional surface based on non-traditional technology according to claim 1, characterized in that: In step 3, the area with smaller distortion in the orthogonal projection segment image is the area of ​​80% of the area in the center of the image.

7. The method for converting a three-dimensional surface into two-dimensional surface based on non-traditional technology according to claim 1, characterized in that: When performing region segmentation, the cutting range of the middle part is large, and the cutting range of the two sides is small. The specific calculation formula for the width is as follows: Wherein, A=180°*0.8 / k, k is the number of cuts in the cutting area, index is the serial number of the cutting area, index increases from the middle to both sides, the middle is 0, and the two sides are the largest, w0=0.8*W, W is the width of the reference cylinder.

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