Ancient painting color virtual restoration visual system based on artificial intelligence

Abstract

Compared with the prior art, the artificial intelligence-based ancient painting color virtual restoration system provided by the invention has the advantages that the to-be-restored ancient painting is taken as a target, the to-be-restored ancient painting is segmented in combination with visual analysis operation, and the texture of the ancient painting is extracted as a clue for distinguishing different images; tracking and extracting a texture result and spreading the texture result to other reference images to help an ancient painting restorer to quickly position the reference image; the color of the reference image is acquired, modeling is performed on the pigment mixing process, a color reproduction recommendation algorithm based on the human color mixing behavior is constructed, an ancient painting restorer is helped to understand the pigment mixing process, the accuracy and authenticity of color restoration of the ancient painting are improved, and restoration work of the faded ancient painting is promoted.

Description

Technical Field

[0001] The present invention relates to the field of ancient painting color restoration, and in particular to an ancient painting color virtual restoration visual system based on artificial intelligence. Background Art

[0002] As an important heritage of human civilization, traditional Chinese paintings (hereinafter referred to as ancient paintings) carry rich historical and artistic value. However, as time goes by, many ancient paintings face problems such as peeling and oxidation of pigments, causing their colors to gradually fade. This fading not only affects the visual beauty of ancient paintings, but also damages the historical information they convey. In order to restore the colors of faded ancient paintings, professional cultural relics restorers need to first examine the background of the ancient paintings to collect valuable color reference information, and then use relevant pigments that match their era background to restore the colors.

[0003] Taking flower and bird paintings as an example, ancient painting restorers need to first determine the type of object in the painting. Different types of objects have different texture and color characteristics. Then, they need to collect photographs related to the object to obtain accurate color insights. Although there are a large number of accessible photographs on the Internet, it is still very difficult for ancient painting restorers to quickly obtain pictures of objects of a specific type. This is because pictures on the Internet usually do not have precise species type labels, making it impossible for ancient painting restorers to search for pictures through label matching. Although tools such as Baidu Image Recognition can support retrieval based on image content, these tools usually lose a certain degree of accuracy in order to ensure a high recall rate, making the quality of the retrieval results unable to meet the needs of ancient painting restorers.

[0004] Later, many new visual analysis systems were developed to analyze images in a semantically aware way. For example, Reference 1 (A semantic-based method for visualizing large image collections [J], 2018, IEEE Transactions on Visualization and Computer Graphics) provides a semantic-based method for visualizing large image collections. It generates descriptive captions for images through image captioning technology using convolutional neural networks (CNNs). These captions can be converted into semantic keywords, and then combined with a novel co-embedding model to project images and related semantic keywords into the same 2D space, helping ancient painting restorers to view the semantic overview of image collections. However, the method of visualizing image collections based on semantics ignores other visual features of the image, and there are large differences between ancient paintings and natural images. As a kind of cultural and artistic work, ancient paintings have obvious styles, and ancient Chinese paintings have the characteristics of emphasizing lines, colors, and artistic conception. However, the restoration method for natural images does not take the style characteristics of ancient paintings into account during restoration, resulting in inconsistency between the style and artistic conception of the restored area and the entire image, which destroys the integrity and coherence of the restoration results of ancient paintings.

[0005] In addition, in the process of ancient painting restoration, after obtaining the correct color insights from the related pictures of the ancient paintings, the ancient painting restorer needs to judge whether these colors can be reproduced by ancient pigments. Specifically, the ancient painting restorer will manually select several basic pigments based on his work experience, and gradually approach the target color by constantly adjusting the mixing ratio between the pigments. However, for some junior ancient painting restorers, it is difficult to fully master all the color reproduction knowledge. They often need more trial and error of pigment mixing to complete the color reproduction work, which will cause unnecessary waste of some precious pigments.

[0006] Reference 2 (Pigmento: Pigment-based image analysis and editing, 2018, IEEE Transactions on Visualization and Computer Graphics) provides a pigment-based image analysis and editing method, which generates some reasonable combination pigments by modeling the color of the painting as a per-pixel mixture of a small amount of pigments with multi-spectral absorption and scattering coefficients, thereby reducing the error of pigment combination. However, this method is based on end-to-end color reproduction, and it is easy to ignore the diversity of pigment combinations and the influence of expert knowledge in pigment combination and pigment restoration in the process of color restoration of ancient paintings, and cannot guarantee the accuracy and authenticity of the reproduction method. Summary of the invention

[0007] The purpose of the present invention is to provide a visual system for virtual restoration of ancient painting colors based on artificial intelligence. By combining technologies such as image segmentation, texture tracking and automatic color adjustment with a visual analysis interface, the system explores color restoration solutions for faded ancient paintings based on interactive visual analysis operations, helps ancient painting restorers to quickly locate reference images, reduces the cognitive burden of ancient painting restorers in searching for information and the trial-and-error cost of determining pigment mixing methods, ensures the accuracy and authenticity of ancient painting color restoration, and promotes the restoration of faded ancient paintings.

[0008] To achieve the above-mentioned purpose of the invention, an embodiment provides an ancient painting color virtual restoration system based on artificial intelligence, comprising: a database module, a segmentation view module, a reference view module and an annotation view module;

[0009] The database module is used to store data related to color restoration of ancient paintings, including high-definition digital images of ancient paintings to be restored, reference images of various flowers and birds, and physical property data of traditional painting pigments.

[0010] The segmentation view module provides a drawing board, a foldable panel and a list for displaying the ancient painting information and the texture information extracted from the ancient painting, wherein the drawing board is used to visualize the ancient painting to be restored and perform texture segmentation and extraction on the ancient painting to be restored, the foldable panel provides the background and subject content related to the ancient painting to be restored, and the list includes a segmentation list and an annotation list for visualizing the extraction results and annotation results of the ancient painting texture;

[0011] The reference view module provides a toolbar and a grid-based image browsing component for collecting reference images corresponding to the texture of the ancient painting for texture tracking, wherein the toolbar integrates a variety of tools for collecting reference images for obtaining reference images corresponding to the extraction results of the ancient painting texture, and combines the grid-based image browsing component for texture tracking;

[0012] The annotation view module provides an image display window, a color annotation panel, a color palette and a color space visualization component for visualizing the details of texture tracking results and extracting colors, adjusting colors and displaying the mixing process of pigments, and obtaining a mixing solution of pigments.

[0013] In one embodiment, the texture segmentation and extraction includes: the ancient painting restorer manually selects the labeled positive prompt points with segmentation intentions and the labeled negative prompt points with exclusion intentions, and based on the labeled positive prompt points and the labeled negative prompt points, the texture segmentation results are automatically generated through the texture extraction model and texture extraction is performed to obtain the extraction results of the ancient painting texture.

[0014] In one embodiment, a color histogram is provided in the segmentation list of the segmentation view, which displays the color distribution of the extraction results of each ancient painting texture through color coding, wherein the height of the color histogram shows the frequency of occurrence of the color in the texture tracking result.

[0015] In one embodiment, the multiple tools for collecting reference images include: an image search box, a page navigation button, a texture tracking button, an image annotation button, and a reference confirmation button, which are used to retrieve reference images related to the extraction results or annotation results of ancient painting textures from reference images, extract additional textures in combination with texture tracking models and image annotations, and improve texture tracking results, wherein reference images related to the extraction results or annotation results of ancient painting textures retrieved from reference images are displayed in the form of a grid layout.

[0016] In one embodiment, the extraction of additional texture by combining a texture tracking model and image annotation includes: based on the texture tracking model, automatically identifying similar areas between the reference image and the extraction result or annotation result of the ancient painting texture, generating a texture map, and extracting additional texture with the help of an image annotation button.

[0017] In one embodiment, the grid-based image browsing component provides a texture color filter and an object posture filter for obtaining object reference images with different texture colors and postures;

[0018] The texture color filter includes color blocks, which correspond to color bars in the color histogram;

[0019] The object posture filter constructs a posture vector, projects the posture vector to a two-dimensional scatter plot using the t-SNE algorithm, and calculates the similarity of the object posture, wherein each scatter point in the two-dimensional scatter plot represents a reference image, and the distance between the scatter points represents the similarity of the object posture.

[0020] In one embodiment, the color annotation panel includes a texture display window, an annotation constructor and a pigment annotation list. Based on the texture image in the texture display window, the annotation constructor extracts the real color in the texture image and adjusts the basic pigment and quantity to minimize the color difference, and the color annotation result is displayed in the pigment annotation list.

[0021] In one embodiment, the annotation constructor uses a semi-automatic recommendation algorithm based on a greedy strategy to optimize the pigment mixing solution through the pigment quantity and the mixing result of the basic pigment;

[0022] The color palette described provides an optimized pigment mixing scheme based on the chain matrix color palette, and visualizes the mixing relationship and the mixing process of the pigments.

[0023] In one embodiment, the pigment mixing process uses a pigment mixing model to predict the mixing result of any two pigments, by receiving two pigments to be mixed {p 1 , p 2 The reflectance spectrum of 1 (q=q 1 ), {r 2 (q=q 2 )} and the number multiple {m 1 , m 2}, output the mixed pigment p mixed The reflectance spectrum {r mixed (q=q 1 *m 1 +q 2 *m 2 )}, where the reflectance spectrum r is a one-dimensional vector representing the spectral measurement value at different wavelengths after the pigment p is applied to a unit area of ​​the substrate with a pigment mass q, and the quantity multiple m represents the multiple of the total amount of pigment p used in the mixing process relative to the pigment mass q.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] Compared with the prior art, the artificial intelligence-based ancient painting color virtual restoration system provided by the present invention takes the ancient paintings to be restored as the target, combines visual analysis operations to segment the ancient paintings to be restored, extracts the texture of the ancient paintings as clues to distinguish different images, tracks the extracted texture results and propagates them to other reference images, and helps ancient painting restorers to quickly locate the reference image; obtains the color of the reference image, models the mixing process of the pigments, and constructs a color reproduction recommendation algorithm based on human color mixing behavior, which helps ancient painting restorers understand the pigment mixing process, improves the accuracy and authenticity of the color restoration of ancient paintings, and promotes the restoration of faded ancient paintings. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] 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 are briefly introduced below.

[0027] Figure 1 This is a schematic diagram of the structure of the ancient painting color virtual restoration system based on artificial intelligence;

[0028] Figure 2 This is a schematic diagram of the visualization interface for virtual restoration of ancient painting colors based on artificial intelligence;

[0029] Figure 3 Schematic diagram of the interactive results of virtual restoration of ancient painting colors based on artificial intelligence. DETAILED DESCRIPTION

[0030] To make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation methods described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0031] In order to help ancient painting restorers quickly locate reference images related to faded objects, reduce the cognitive burden of ancient painting restorers in searching for information and the trial-and-error cost of determining pigment mixing methods, the embodiment provides an ancient painting color virtual restoration system based on artificial intelligence, which combines target segmentation, texture tracking, and automatic color adjustment technologies with a visual analysis interface to explore faded ancient painting color restoration solutions based on interactive visual analysis operations. Figure 1 As shown, the artificial intelligence-based ancient painting color virtual restoration system provided in the embodiment includes: a database module, a segmentation view module, a reference view module and a labeling view module.

[0032] In the embodiment, the database module stores core data related to the task of color restoration of ancient paintings, including high-definition digital images of faded ancient paintings, photographic images of various flowers and birds, and physical property data of traditional painting pigments, and reduces unnecessary bandwidth consumption by providing index addresses of relevant data in the database.

[0033] In an embodiment, the segmentation view module includes a drawing board, a foldable panel, and two lists for displaying the segmentation and annotation information of the extracted texture. The drawing board is used to display ancient paintings containing faded objects, and the foldable panel integrates the background and subject content related to the paintings. In order to facilitate the ancient painting restorer to efficiently extract the object texture, the view is equipped with a floating toolbar, providing a variety of interactive segmentation tools, including: marking positive prompt points, marking negative prompt points, undo, redo, delete all marked points, and crop the current segmentation area.

[0034] With these tools, ancient painting restorers can quickly perform texture segmentation and extraction on faded objects in ancient paintings to be restored. Specifically, the restorer clicks on the target area to be segmented to generate annotated positive prompt points indicating the segmentation intention, or clicks on the area not to be segmented to generate annotated negative prompt points indicating the exclusion intention; the model uses these prompt points to automatically generate high-quality segmentation results.

[0035] The extracted textures will be automatically stored in the segmentation list of the segmentation view, and the successfully annotated textures will be transferred to the annotation list. The segmentation list is equipped with a color histogram, which displays the color distribution of the extraction results of each ancient painting texture through color coding. The height of the color histogram shows the frequency of occurrence of the color in the texture tracking results, helping ancient painting restorers to identify color differences and thus improve the distinction between different object variants.

[0036] In an embodiment, the reference view includes a top toolbar and a grid-based image browsing component. The top toolbar integrates a variety of tools for collecting reference images, including an image search box, a page navigation button, a texture tracking button, an image annotation button, and a reference confirmation button.

[0037] The ancient painting restorer enters the name of the object in the image search box and retrieves related images from the photographic image database. The search results are displayed in a grid layout by default, and the layout can be switched through the page navigation button. By clicking the texture tracking button, the ancient painting restorer starts the texture tracking model. The texture tracking model automatically identifies similar areas between the reference image and the annotated results of the ancient painting texture based on the manually extracted texture features, and generates corresponding texture maps that are propagated to other reference images.

[0038] The restorer can further fine-tune the texture tracking results to ensure that the texture mapping effect in different images is consistent with the original image, and extract additional textures with the help of the image annotation button to improve the texture tracking results. The improved texture tracking results will serve as additional clues for distinguishing different object images. When the restorer determines the reference object, the new reference image is imported into the annotation view module through the reference confirmation button.

[0039] In addition, texture color filters and object posture filters are also provided in the grid-based image browsing component, so that ancient painting restorers can easily access object reference images with different texture colors and texture postures. The texture color filter is composed of color blocks, each of which corresponds to a color bar in the color histogram. Based on the tracked texture results, the object posture vector is constructed and projected into a two-dimensional scatter plot using the t-SNE algorithm to calculate the similarity of the object posture. The two-dimensional scatter plot is used as a posture filter, where each scatter point represents an image and the distance between the scatter points indicates the similarity of the object posture.

[0040] In an embodiment, the annotation view module includes an image display window, a color annotation panel, a chain matrix-based palette, and a color space visualization component. The image display window is used to display the details of the reference image obtained from the reference view module, supports zooming and dragging interactions, and helps the ancient painting restorer adjust the image to a suitable observation scale. The color annotation panel includes a texture display window, an annotation constructor, and an annotation list. The ancient painting restorer can extract the true color in the image through the annotation constructor, select the basic pigment and its quantity, and use the slider tool for precise adjustment. In addition, the color annotation panel also sets a pigment color preview function to display the color changes of the basic pigment and the mixed pigment in real time, helping the ancient painting restorer to compare the difference between the mixed pigment and the true color. When the color difference is less than the preset threshold, the ancient painting restorer can add the successfully restored mixing scheme to the annotation list to adjust the pigment mixing scheme.

[0041] In addition, the annotation view module integrates a semi-automatic recommendation algorithm based on a greedy strategy. The ancient painting restorer can trigger the pigment mixing suggestion through the recommendation button. The algorithm provides an optimized pigment mixing path based on the pigment quantity and mixing exploration results, and intuitively displays the mixing relationship of the pigments through a palette based on a chain matrix. The ancient painting restorer selects a pigment mixing method in the palette matrix, and the system will dynamically expand the exploration path to clearly display the pigment mixing process.

[0042] The pigment mixing process uses a pigment mixing model to predict the mixing result of any two pigments. The pigment mixing model consists of a five-layer fully connected neural network and is trained on a public pigment mixing dataset. 1 , p 2 The reflectance spectrum of 1 (q=q 1 ), {r 2 (q=q 2 )} and the number multiple {m 1 , m 2}, output the mixed pigment p mixed The reflectance spectrum {r mixed (q=q 1 *m 1 +q 2 *m 2 )}, where the reflection spectrum r is a one-dimensional vector of length 41, which represents the spectral measurement values ​​of pigment p at 41 different wavelengths after the pigment mass q is applied to the unit area of ​​the substrate, and the quantity multiple m represents the multiple of the total amount of pigment p used in the mixing process relative to the pigment mass q.

[0043] To improve the visualization effect, when the mixed pigments are similar in color, the color space visualization component uses spatial relationships to display the differences between pigments, making it easier for ancient painting restorers to identify and manipulate the pigment mixing process in the palette.

[0044] In order to better illustrate the technical effect of the present invention, a virtual restoration is performed by taking an ancient painting to be restored as an example, and the specific implementation steps are as follows:

[0045] (1) View the content of ancient paintings. Ancient painting restorers can interactively check the degree of fading of objects in the ancient paintings to be restored by dragging and zooming the drawing board.

[0046] (2) Learn the names of faded objects. Ancient painting restorers click the folding panel on the left ( Figure 2 a1) in the figure to understand the basic information of the ancient painting. In most cases, the names of related objects can be found from it.

[0047] (3) Search for relevant reference images. Ancient painting restorers can enter the name of an object in the search box and search the database to find reference images related to the object.

[0048] (4) Extracting the texture of faded objects. To determine the identity of faded objects, ancient painting restorers can use segmentation tools ( Figure 2 a4) in extracting the textures of objects in ancient paintings, which are regarded as key clues to determine the identity of objects.

[0049] (5) Extract additional tracking references. Due to the fading problem, textures extracted directly from ancient paintings cannot produce good tracking results. Ancient painting restorers can click the image annotation button ( Figure 2 b1 in the figure), switch a reference image to the drawing board, and then use the segmentation tool again to extract the corresponding object texture ( Figure 2 Then, the restorer can click the Texture Tracking button ( Figure 2 b1) in to perform texture tracking function.

[0050] (6) View the potential color distribution of the texture. After the tracking function is completed, the ancient painting restorer can view the potential color distribution of different textures in the texture list ( Figure 2 and click on these textures to view the corresponding tracking results in the Reference view.

[0051] (7) Analyze posture features. Ancient painting restorers use object posture filters ( Figure 2 b3) Understand the similarity of different objects in posture features, and use lasso interaction to quickly locate the photographic image containing a specific object posture. The positioning result is as follows Figure 3 As shown in a in .

[0052] (8) Filter texture color. Ancient painting restorers can filter texture color by Figure 2 b2) View photographic images of different object variants ( Figure 3 b) and select images that meet specific color constraints as reference images for annotation ( Figure 2 c1 in ).

[0053] (9) Mark the original color. For each texture in the object texture list, the ancient painting restorer needs to mark its original color and the corresponding pigment mixing method one by one. Figure 2 c2 in the above example.

[0054] (10) Seek pigment mixing methods. When an ancient painting restorer encounters an unfamiliar color, he can click the recommendation button ( Figure 2 c2) in , seeking help from automatic recommendation algorithms. List of hybrid methods ( Figure 2c4) will update the recommended blending method in a timely manner, and the palette based on the chain matrix ( Figure 2 c4) will also show the detailed steps of its pigment mixing ( Figure 3 c1 in ).

[0055] (11) Explore pigment mixing methods. The recommended mixing method may result in color mutation ( Figure 3 In this case, the restorer can rediscover a more reliable method of mixing pigments through the palette.

[0056] (12) Complete the annotation task. After completing the annotation of all textures and colors, the ancient painting restorer can click the confirmation button ( Figure 2 c3) in the figure to complete the color restoration of faded ancient paintings.

[0057] The artificial intelligence-based ancient painting color virtual restoration system of this embodiment can help ancient painting restorers quickly locate reference images related to faded objects, and can also automatically recommend pigment mixing methods for a certain color, thereby reducing the cognitive burden of ancient painting restorers in searching for information and the trial-and-error cost of determining pigment mixing methods, thereby promoting the restoration of faded ancient paintings.

[0058] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An artificial intelligence-based virtual restoration visual system for ancient painting colors, characterized in that: The ancient painting color virtual restoration system includes: a database module, a segmentation view module, a reference view module and a marking view module; The database module is used to store data related to color restoration of ancient paintings, including high-definition digital images of ancient paintings to be restored, reference images of various flowers and birds, and physical property data of traditional painting pigments. The segmentation view module provides a drawing board, a foldable panel and a list for displaying the ancient painting information and the texture information extracted from the ancient painting, wherein the drawing board is used to visualize the ancient painting to be restored and perform texture segmentation and extraction on the ancient painting to be restored, the foldable panel provides the background and subject content related to the ancient painting to be restored, and the list includes a segmentation list and an annotation list for visualizing the extraction results and annotation results of the ancient painting texture; The reference view module provides a toolbar and a grid-based image browsing component for collecting reference images corresponding to the texture of the ancient painting for texture tracking, wherein the toolbar integrates a variety of tools for collecting reference images for obtaining reference images corresponding to the extraction results of the ancient painting texture, and combines the grid-based image browsing component for texture tracking; The annotation view module provides an image display window, a color annotation panel, a color palette and a color space visualization component for visualizing the details of texture tracking results and extracting colors, adjusting colors and displaying the mixing process of pigments, and obtaining a mixing solution of pigments.

2. The ancient painting color virtual restoration visual system according to claim 1 is characterized in that: The texture segmentation and extraction includes: the ancient painting restorer manually selects the annotated positive prompt points with segmentation intention and the annotated negative prompt points with exclusion intention, and based on the annotated positive prompt points and the annotated negative prompt points, the texture segmentation result is automatically generated through the texture extraction model and texture extraction is performed to obtain the extraction result of the ancient painting texture.

3. The ancient painting color virtual restoration visual system according to claim 1 is characterized in that: A color histogram is provided in the segmentation list of the segmentation view, which displays the color distribution of the extraction results of each ancient painting texture through color coding, wherein the height of the color histogram displays the frequency of occurrence of the color in the texture tracking result.

4. The ancient painting color virtual restoration visual system according to claim 1 is characterized in that: The various tools for collecting reference images include: an image search box, a page navigation button, a texture tracking button, an image annotation button and a reference confirmation button, which are used to retrieve reference images related to the extraction results or annotation results of ancient painting textures from reference images, extract additional textures in combination with texture tracking models and image annotations, and improve texture tracking results, wherein reference images related to the extraction results or annotation results of ancient painting textures retrieved from reference images are displayed in the form of a grid layout.

5. The ancient painting color virtual restoration visual system according to claim 4 is characterized in that: The method of extracting additional texture by combining the texture tracking model and the image annotation includes: automatically identifying similar areas between the reference image and the extraction result or annotation result of the ancient painting texture based on the texture tracking model, generating a texture map, and extracting additional texture with the help of an image annotation button.

6. The ancient painting color virtual restoration visual system according to claim 1 is characterized in that: The grid-based image browsing component provides a texture color filter and an object posture filter for obtaining object reference images with different texture colors and postures; The texture color filter includes color blocks, which correspond to color bars in the color histogram; The object posture filter constructs a posture vector, projects the posture vector to a two-dimensional scatter plot using the t-SNE algorithm, and calculates the similarity of the object posture, wherein each scatter point in the two-dimensional scatter plot represents a reference image, and the distance between the scatter points represents the similarity of the object posture.

7. The ancient painting color virtual restoration visual system according to claim 1 is characterized in that: The color annotation panel includes a texture display window, an annotation constructor and a pigment annotation list. Based on the texture image in the texture display window, the annotation constructor extracts the real color in the texture image and adjusts the basic pigment and quantity to minimize the color difference, and the color annotation result is displayed in the pigment annotation list.

8. The ancient painting color virtual restoration visual system according to claim 7 is characterized in that: The annotation constructor uses a semi-automatic recommendation algorithm based on a greedy strategy to optimize the pigment mixing scheme through the pigment quantity and the mixing result of the basic pigment; The color palette described provides an optimized pigment mixing scheme based on the chain matrix color palette, and visualizes the mixing relationship and the mixing process of the pigments.

9. The ancient painting color virtual restoration visual system according to claim 8 is characterized in that: The pigment mixing process uses a pigment mixing model to predict the mixing result of any two pigments, by receiving two pigments to be mixed {p1, p z } reflectance spectrum {r1(q=q1), {r2(q=q2)} and quantity multiple {m1, m2}, output the mixed pigment p mixed The reflectance spectrum {r mixed (q=q1*m1+q2*m2)}, where the reflection spectrum r is a one-dimensional vector, which represents the spectral measurement value at different wavelengths after the pigment p is applied on the unit area of ​​the substrate with the pigment mass q, and the quantity multiple m represents the multiple of the total amount of pigment p used in the mixing process relative to the pigment mass q.

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