Research on Multi-scale Geometric Analysis and Compositional Optimization Methods in the Creation of Haikai Ink Figure Painting

The presentation of Chinese ink painting focuses on expressing the inner thoughts, emotions, and human attitudes of contemporary characters, conveying the spiritual connotations of traditional culture while showing the art creators’ humanistic concern and sense of social responsibility through the free expression of contemporary real life [1-4]. Nowadays, the creation of Chinese ink painting presents a prosperous situation, and the forms of creation are becoming more and more diversified. Flat painting enhances the artistic tension and expressive ability of the works with an easy-to-understand visual language [5-6]. In the process of collision and fusion of Chinese and Western art, Chinese ink painting has further explored and transformed, forming a unique artistic style of geometrical compositional layout, concise and generalized modeling, and flat and simple colors [7]. Chinese ink painting has always emphasized the linear characteristics, which is also the inheritance and development of the traditional Chinese concept of imagery modeling, and the line composition of its ink figure painting presents a strong individuality of style and aesthetic interest, and its basic composition has a vertical, horizontal, diagonal, central and other forms of expression [8-10].

Line compositions are expressed according to the different brush and ink styles of artists, and therefore Chinese ink painting is divided into several schools [11-12]. Among them, the Hai School inherited the tradition of its predecessors and integrated calligraphy, seal carving and other forms of artistic expression into painting, creating a grand and unrestrained artistic image of painting with strong and vigorous brushwork, rich ink, vivid and strong colors, and the layout of calligraphy and goldsmith’s stone, as well as the organic combination of poetry, calligraphy, and painting, which opened up new horizons for literati painting. Therefore, to interpret the painting language of Chinese ink painting, it is necessary to analyze the artistic language from multiple angles and compositional thinking.

Ink painting with white and color space to form a strong contrast, so that people appreciate the work focus on the color part, and literature [13] research shows that color space composition and brush strokes increase the complexity of ink painting. However, this often varies from person to person, with different perspectives on color perception and compositional appreciation. For this reason, literature [14] constructed a computational model for quantitative evaluation of Chinese ink painting aesthetics using deep learning, which can predict human aesthetic evaluation. Chinese ink painting has a long and colorful history, and there are several genres classified, but there is a cross-presentation of painting styles, which is difficult to identify. Literature [15] designed a multi-residual network under the condition of deeply correlated features to classify the artists and genres of Chinese ink paintings, which not only realized the digital management of the art library of Chinese ink paintings, but also improved the accuracy of the classification under the nuanced styles in the works. Differently, literature [16] constructed a model in the context of multi-level attention and multi-scale feature fusion for ink painting classification, which extracted and refined the linguistic features of ink paintings from three levels and three scales to ensure the accuracy of classification. In addition, literature [17] combines multilevel features and generative adversarial networks to achieve automatic coloring of Chinese ink paintings, which broadens the diversity of ink painting styles. Literature [18] directly utilized Python language, deep learning, convolutional neural network, and Node.js to design a Chinese ink painting creation program with image rendering as the main theme, and experiments verified the effectiveness of the program. Literature [19] conceived the idea of combining face images with Chinese ink paintings to generate ink paintings of portraits, for which a portrait drawing system was developed, which automatically recognizes and analyzes the features of the face by mixing the portrait image into the rendering system and then selects the appropriate recipe for configuration to generate the ink painting of the portrait.

With the above research, it can be seen that the current research direction of ink painting includes genre classification, visual appreciation, aesthetic evaluation, automatic coloring and automatic generation, etc., which lacks the analysis of ink painting itself. As for the creation of ink painting, understanding the composition and multi-scale understanding is the foundation of painting in order to avoid sky-high abstract paintings and losing the spirit of ink painting. As one of the representative schools of Chinese ink painting, the Hai School has an important influence on modern ink painting and other paintings.

This paper analyzes the background and artistic evolution of the Hai School of ink painting (changes in the use of color), and points out the characteristics of the formal language of painting that are common to ink figure painting. Multi-scale geometric analysis (Contourlet transform) is applied to the image processing of ink painting. The Contourlet transform is used to extract the features of ink figure paintings, normalize the ink images, reconstruct the gestures of the paintings in the ink paintings, and unify them into a standard image with the top of the target body of the paintings (figures, flowers, plants, etc.) facing upwards. The selection of LP filters in Contourlet transform is analyzed, and the performance of Contourlet transform is evaluated for image fusion and image reconstruction. Combine the image aesthetic evaluation indexes to evaluate the aesthetic quality of the reconstructed ink figure painting.

2

Characteristics of ink figure painting

2.1

Shanghai Ink Painting

At the end of the Qing Dynasty and the beginning of the Republic of China, the Haikai School of Ink Painting, which originated in Shanghai, quickly rose to prominence with the momentum of “the gathering of the young and the wise”, forming an important landmark of the emerging cultural and artistic circle.

Born out of Chinese culture, Hai ink painting naturally inherits the philosophy of Confucianism and Taoism, and the cosmic concept of “God transcends reason” can be found in the art creations of Hai painters.

Under the aesthetic trend of seeking for newness and change, the Haikai ink painting does not just deny the tradition, but on the basis of integrating the traditional elements, it skillfully borrows the light and darkness, color, and perspective from the Western painting method, and achieves the appropriate innovation on the relationship between the master and the pupil. The aesthetics of Haikai Ink Painting is precisely a breakthrough in seeking a new painting method based on the node of black and white ink painting, which is a blend of the cultural characteristics of the East and the West. Although the watercolor painting style influences the aesthetics of painting creation, but it is in the bright seams and dark lines of the Haikai Ink Painting, which reflects the eclectic relationship of the Haikai Ink Painting in the development of art.

2.2

Evolution of the Sea School Painting Art

Haikai painting is a concentrated manifestation of the spirit of conscious reform in Chinese painting to adapt to the development of history. It inherits the remnants of the painting styles of the Ming and Qing dynasties, and initiates the new style of Chinese painting in the new century, which has become a turning point in the history of modern Chinese painting. Leading Chinese painting from the elegant culture of self-appreciation to secularization is the main manifestation of its reform results, making Chinese painting with the characteristics of art marketization and popularization in the modern sense.

The Haikai School of Painting combines traditional literati ink painting, which mainly expresses personal feelings, with the bright colors needed by the public, and changes the personal writing interest into the heavy-color writing required by the market. For example, Zhao Zhiqian combined traditional literati flowers with folk colors to create a new style of painting that was fresh, bright, and appreciated by both the elegant and the common people. Wu Changshuo, who introduced heavy-handed capitalism into the homes of the common people.

For the practicality and realism of the works of the Haikai School of Painting, flower and bird paintings with rich colors became the first choice of the Haikai School painters. This style catered to the needs of commercial activities and was popular with the general public. With the increase in foreign exchange rates, this style was inevitably influenced by Western art expression techniques. The traditional color “enhancement” and “abandonment” have had the right to shape and speak for themselves, integrating the realistic ink and strong colors since the Ming and Qing Dynasties, and adding the commercial public interest of the emerging era to form a new style of painting that is appreciated by both the elegant and the common people.

2.3

Characteristics of Ink Figure Painting Form Language

2.3.1

Formal Characteristics of Ink Figure Painting

The “form” is reflected in the painting, is in the expression of objective objects. The “form” will be changed due to the subjective treatment of the painter, and the painting will be deformed in some parts of the painting. The purpose of the treatment is to make the “form” itself more meaningful. Therefore, the “meaning of form” is no longer a mere visual depiction of nature. For example, if you draw a worker in a completely realistic way, it is a kind of feeling, which seems to lack some meaning. But if from the point of view of imagery, to make his feet bigger, neck thicker, bone joints bigger and so on to do some modeling treatment, so as to strengthen the image of the character, so that it highlights the character of the worker, the meaning of the shape will also be revealed.

2.3.2

Compositional styles

The development of traditional Chinese painting has been largely influenced by the cultural traditions of its own people. Under the influence of traditional Chinese culture, which is dominated by the philosophies of Confucianism, Taoism, and Buddhism, since the Wei and Jin dynasties, literati painters have mostly left a large number of blank spaces in their paintings, which are called “cloth white”. In order to pursue the artistic concept of high, elegant, quiet, and far-reaching, this approach is very popular.

Nowadays, with the rapid development of information technology, contemporary expressive ink figure painters have made valuable explorations on the compositional form of the picture based on the basis of real life. They have always grasped the characteristics of the times and boldly pioneered to create new styles of composition with great aesthetic concepts of the time [20-21]. 1)

Full composition is in reference to the white space composition in traditional paintings, especially in literati paintings. Traditional paintings are deeply influenced by the idea of “the unity of heaven and man”, and the position of the painting is usually presented in the way of “leaving heaven and earth”, leaving a lot of blank space at the top and bottom of the picture. In the middle, the main objects are placed, forming a harmonious unity of heaven, earth, and human beings, which together form a complete world of life.

2)

However, it is worth noting that ‘full’ does not mean blindly pile up all the objects. Rather, it means selectively highlighting the parts that best embody the spirit of nature and the essence of art, thus guiding the viewer’s gaze to focus on the core of the picture.

3)

In the composition of ink figure painting, in addition to the above-mentioned compositional form of pursuing “extreme fullness”, there is another form that deliberately seeks “simplicity”. “Simplified”, as a form of composition as opposed to “complex”, is in an extremely concise and generalized way. The picture is refined and condensed, simple but not simple. The composition is presented in a “simple” way, but it reflects a more profound and quiet meaning.

4)

Arranged compositions are made in a scattered perspective. Repeatedly, the figures are arranged in a certain pattern, and sometimes the picture is characterized by symmetry. It is usually used to express the relationship between group and individual.

5)

Split composition is a commonly used compositional method in painting creation, emphasizing the decomposition and reorganization of the picture. Generally, a specific space is divided and disassembled through different forms of lines, and reorganized in different forms to form a picture with a sense of form that is in line with the creator’s aesthetic interests and artistic propositions. The divided picture is not limited by the size, space and shape of things, and the divided shape can be figurative. It can also be an abstract shape, mainly for the purpose of creating a new spatial form for the picture. The divided parts of the image exist both in the overall connection and independently of each other, and the displacement and deformation between the localized parts are present in the whole. This kind of deformation and dislocation between the local and the whole enriches the relationship of the picture, making the original real-life space present a new spatial form, and creating visual opposites and formal aesthetics.

3

Application of Contourlet Transform in Image Processing of Ink Painting

3.1

Multiscale Geometric Analysis-Contourlet Transformation

The Contourlet transform is an extension of the wavelet transform and is characterized by localization, multidirectionality, multiscale, critical sampling, and anisotropy. Its basis functions are distributed over multiple scales and directions and have flexible aspect ratios. Thus, Contourlet can approximate the optimal efficient representation to describe any one-dimensional smooth edge. It can describe smooth curves with fewer coefficients than the wavelet transform and can accurately simulate the geometric structure of an image [22-23].

The Contourlet transform was originally proposed in the discrete domain as a computational framework for multi-scale, multi-directional discrete images. It has only since been generalized to the continuous domain and its properties analyzed. In its transformation process, multiscale analysis and multidirectional analysis are performed separately. The basic idea is to first “capture” singularities (or isolated breakpoints at edges) by multiscale decomposition of the image using the Laplace Pyramid (LP) transform. The high-frequency components from each level of pyramid decomposition are then directionally filtered using a two-dimensional directional filter bank (DFB). The directional filter bank connects the singularities distributed in the same direction into lines and combines them into a single coefficient, thus forming the basic contour segment.

3.1.1

Pyramid Decomposition

The Laplacian pyramid will produce a low-pass sampled image and a high-frequency component contour after each level of decomposition. And this decomposition iterates on the low-frequency component image. The reverse direction is the decoding process of the image, a process that completely reconstructs the original image.

3.1.2

Directional Filter/Directional Filter Banks

Directional filtering captures the directional information of an image efficiently. The directional component of an image corresponds to a wedge-shaped region in a two-dimensional spectrum. A small angle (i.e., the angle enclosed by a sector) sector digital filter with an arbitrary direction (the direction of the sector), whose bandpass region is a wedge, is also known as a directional digital filter.

The central problem of a directional filter bank is how to divide the directional frequency to the desired accuracy and be able to keep the number of samples constant. Among other things, the problem of keeping the number of samples constant can be solved using subsampling. In a sampling system with a multidimensional multisampling rate, the samples are often defined on a grid, where a d × d matrix of non-singular integers represents a d-dimensional grid. And for a defined sampling grid, its representation is often not unique. M extraction of x(n) can be expressed in equation (1): (1) $x d [n] = x [M n]$

The number of samples after sampling is 1/|M| of the number before sampling. Therefore, after extending the sampling rate from one to two dimensions, the sampling factor will also change from the original integer to a non-singular sampling matrix of 2 × 2. Equations (2) and (3) are a few commonly used sampling matrices. If four two-dimensional matrices R0, R1, R2, and R3, all modulo 1, are used for sampling, the number of samples can be kept constant. However, the sample positions will change, which is called resampling. And Q₀ and Q₁ are called Quincunx sampling matrices. Namely: (2) $R_{0} = (\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}) R_{1} = (\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}) R_{2} = (\begin{matrix} 1 & 0 \\ - 1 & 1 \end{matrix}) R_{3} = (\begin{matrix} 1 & 0 \\ - 1 & 1 \end{matrix})$ (3) $Q_{0} = (\begin{matrix} 1 & - 1 \\ 1 & 1 \end{matrix}) Q_{1} = (\begin{matrix} 1 & 1 \\ - 1 & 1 \end{matrix}) D_{0} = (\begin{matrix} 2 & 0 \\ 0 & 1 \end{matrix}) D_{1} = (\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix})$

A two-dimensional two-channel filter bank can be constructed using the Quincunx sampling matrix.

Its conclusion is very similar to the one-dimensional two-channel filter bank using two-extraction and two-interpolation, as shown in Equation (4): (4) $\begin{array}{l} X (ω) = \frac{1}{2} [H_{0} (ω) G_{0} (ω) + H_{1} (ω) G_{1} (ω)] X_{0} (ω) \\ + \frac{1}{2} [H_{0} (ω + π) G_{0} (ω) + H_{1} (ω + π) G_{1} (ω)] X_{0} (ω + π) \end{array}$

where π = (π, π)^T.

The complete reconstruction condition is shown in the following equation: (5) $H_{0} (ω) G_{0} (ω) + H_{1} (ω) G_{1} (ω) = 2$ (6) $H_{0} (ω + π) G_{0} (ω) + H_{1} (ω + π) G_{1} (ω) = 0$

If, H₀, H₁, G₀ and G₁ represent directional filters, then the input signal can be decomposed into different directions while ensuring that it can be completely reconstructed. At the same time the number of samples can be kept constant. For the output of the two-dimensional two-channel Quincunx sampling filter bank, then the filtering continues with the two-dimensional two-channel Quincunx sampling filter bank, which can form a binary tree.

3.1.3

Analysis of Contourlet transformations

The Contourlet transform has the following main properties: 1)

If both LP and DFB are fully reconstructive filters, then the Contourlet transform can also be fully reconstructive, so the Contourlet transform provides a frame operator.

2)

If both LP and DFB use orthogonal filters, then the Contourlet transform provides a tight frame with frame bound of 1.

3)

The Contourlet transform is a redundant transform with a redundancy rate of less than 4/3.

4)

Assuming that a l_j-level DFB is used at level J of the LP, then the support interval of the base image of the Contourlet transform is: (7) $w i d t h \approx 2^{j}, l e n g t h \approx 2^{j + 1, - 2}$

5)

The Contourlet transform provides a flexible multi-resolution multi-direction decomposition of the image Since it allows a different number of direction decompositions at each scale, the Contourlet transform satisfies the law of anisotropy of scales.

Since the multiscale multidirectional decomposition in the Contourlet transform has been decoupled, it is possible to obtain different numbers of directional decompositions at different scales. In this way, a flexible multiscale as well as multidirectional expansion can be obtained. In addition, the complete binary tree structure used in the DFB in the Contourlet transform can be generalized to an arbitrary tree structure.

3.2

Contourlet transform based image feature extraction

The contour features of the target image are characterized by extracting the feature volume to provide input parameters for model training. The Contourlet transform is used to extract the low-frequency features and high-frequency energy features respectively.

The low-frequency feature vector contains most of the energy information and can smoothly approximate the contour information of the image. This part of the component can be used as the base feature vector. However, target images taken under different lights in the actual collected images contain high-frequency noise, and the low-frequency component of the Contourlet transform is not sensitive to light transformations.

The high-frequency coefficients are able to reflect information about the target’s edges and details in all directions, which is a feature that is highly recognized. Therefore, this method selects the high-frequency feature vector as the correction vector for network training, and the low-frequency feature training can be corrected using the correction idea of a neural network.

3.3

New Compositional Approach of Sea School Ink Figure Painting

Composition is the general structure of a picture. Expanded, it means the interconnectedness of the images on the screen and the overall structure of the form, is the way to reveal the typical characteristics of the image, is the means to express the ideas and mood, is the centralized embodiment of the beauty of the form. In ink painting, it is the “layout” or “chapter”.

The most distinctive feature of traditional figure painting composition is scattered perspective. Scattered perspective is the Chinese painter’s perspective on the object to take a flat position, the near scene and distant scene on the same plane overlap. The painter takes a view of the natural world from a personal perspective, and it is not a passive record of vision, but rather a selection made by the painter. Painting psychologically expected figures or scenes to construct content that is not limited by time and space. By recombining figures and objects from different time and space, creating a visual dynamic.

Unlike previous ink figure paintings, contemporary ink figure painters constantly try to borrow Western elements to construct new forms of composition and make the composition more diversified. Modern means are used to express the general environment of life in contemporary society, close to the reality of the eyes. Painters use their own feelings as the main subjective motif, which can be found to be more expressed in the subjective treatment of space. While conventional painting builds space through conventional composition, what distinguishes contemporary ink figure painting is the disorder of space, which can also be called non-logical space.

3.3.1

Basic Painting Processes

To map a visible image into HIS space, the commonly used color spaces are RGB color space and HIS color space.RGB color space is commonly used in computer color monitor display systems.In RGB, R stands for red, G stands for green, and B stands for blue. The three colors are superimposed to form other colors [24].

Individual R, G, B channel are 0-255 grayscale map, when the three colors are superimposed by the ratio can form a color image, the three channels of the image correlation is large, respectively, to deal with the image of a single channel will seriously affect the color distribution of the original data. HIS color space contains brightness I (intensity), chromaticity H (hue) and saturation S (saturation) three elements. These three elements are very low correlation, which makes it possible to process the three components of the HIS space individually.

The HIS positive transformation formula: (8) $(\begin{matrix} I \\ v_{1} \\ v_{2} \end{matrix}) = (\begin{matrix} 1 / 3 & 1 / 3 & 1 / 3 \\ - \sqrt{2} / 6 & - \sqrt{2} / 6 & 2 \sqrt{2} / 6 \\ 1 / \sqrt{2} & - 1 / \sqrt{2} & 0 \end{matrix}) (\begin{matrix} R \\ G \\ B \end{matrix})$ (9) $H = \arctan \frac{v_{2}}{v_{1}}, S = \sqrt{v_{1}^{2} + v_{2}^{2}}$

In image fusion, the luminance component I is extracted using Eq. (8).This component contains rich detailed texture information of the visible light image. The component I is used as the raw data for the visible light image to participate in fusion with the corresponding infrared image. The fused image is I_new which contains the detailed texture information in the visible image and the luminance information in the infrared image, and after obtaining I_new, the color fusion image is obtained by adding the hue and saturation information using Equation (9).

The HIS inverse transformation Eq: (10) $(\begin{matrix} R_{n e w} \\ G_{n e w} \\ B_{n e w} \end{matrix}) = (\begin{matrix} 1 & - 1 / \sqrt{2} & 1 / \sqrt{2} \\ 1 & - 1 / \sqrt{2} & - 1 / \sqrt{2} \\ 1 & \sqrt{2} & 0 \end{matrix}) (\begin{matrix} I_{n e w} \\ v_{1} \\ v_{2} \end{matrix})$

3.3.2

Image Geometry Reconstruction

The geometric reconstruction of the image mainly includes image preprocessing and reconstruction of the target pose of the ink figure. Image preprocessing is an important step to improve the recognition accuracy, the purpose of which is to normalize the image. And remove the influence of irrelevant background environment in the image to highlight the target region to be recognized.

Divided into two steps, step 1 performs image geometric normalization. Since the position and size of the target in the sea school ink figure paintings are different, it will affect the recognition effect, and the target image needs to be corrected by calibration and positioning. In this paper, the region of the target to be recognized is enlarged and the image is calibrated to pixels of 64×64, which makes the target features more obvious.

Gray scale normalization is performed in step 2. As different images are greatly affected by the environment, it is necessary to compensate for the images obtained under different lighting conditions and light directions, in order to attenuate the changes in the image signals captured under different environmental conditions, and to facilitate the extraction of the subsequent feature vectors.

The color relationship and brushstroke diversity unique to ink and wash figure paintings cause some interference in feature recognition. It is necessary to reconstruct the ink figures, flowers and plants and other target bodies in the paintings with gestures, extract the center point of the target of the paintings, and perform equal-scale translation and rotation along its axis, which can normalize the ink figure target to an upward image. First extract the center origin of the ink figure target body: (11) ${\bar{x}}^{'} = \frac{\sum_{x = a}^{b} \sum_{y = c}^{d} x^{'} \cdot f (x^{'}, y^{'})}{\sum_{x = a}^{b} \sum_{y = c}^{d} f (x^{'}, y^{'})}$ (12) ${\bar{y}}^{'} = \frac{\sum_{x = a}^{b} \sum_{y = c}^{d} y^{'} \cdot f (x^{'}, y^{'})}{\sum_{x = a}^{b} \sum_{y = c}^{d} f (x^{'}, y^{'})}$

Where $f (x^{'}, y^{'})$ is the image function. When $(x^{'}, y^{'})$ belongs to the target area, $f (x^{'}, y^{'}) = 1$ . When $(x^{'}, y^{'})$ does not belong to the target area, $f (x^{'}, y^{'}) = 0$ . a, b, c, d is the tracking window boundary coordinates.

After obtaining the round point, make a straight line around it with 0° to 360°. Find the edge point of the ink figure image on that straight line. The angle corr.esponding to the longest line segment from the edge point to the center α is the direction of the image axis. The position of the edge point is the position of the image. Similarly, the coordinates of the target body of the ink figure can be found by searching for the target edge point from the head of the painting through the center to the bottom of the painting. Rotating the axis direction along angle α converts the inked figure target image into a standard image of the painting upwards.

4

Image processing of sea school ink figures

4.1

Filter Selection

In Contourlet transform, the selection of LP filter also affects the processing results to some extent. Through experiments, the results are compared and appropriate filters are selected. Using the method of improved image feature extraction algorithm based on Contourlet transform, five classical images are selected and just the type of LP filter in Contourlet transform is changed and all the results are compared.

The experimental results of LP filter selection are shown in Table 1. In the table, “9-7” is the double quadrature filter improved by Do and Vetterli. “pkva” is the pyramid filter.

Table 1.

The LP filter selects the experimental results

Image	9-7		Pkva		5-3		Burt
Image	SNR/dB	PSNR/dB	SNR/dB	PSNR/dB	SNR/dB	PSNR/dB	SNR/dB	PSNR/dB
Barbara	14.2	75.4	13.1	74.5	13.5	75.2	13.2	74.2
Peppers	18.3	79.1	15.4	77.3	18.1	78.4	17.4	78.5
Zoneplate	4.1	61.2	2.3	59.1	3.6	60.5	3.5	60.1
Mandril_gray	9.0	73.7	7.2	71.3	8.4	73.2	8.1	73.1
Lena	17.4	80.5	17.3	77.3	15.4	80.1	16.1	78.6

Among these four types of LP filters, it can be seen from the comparison of the results that both SNR and PSNR, the results of the “9-7” treatment compare favorably with the other types of pyramid filters. The “9-7” biorthogonal filter optimizes the SNR and PSNR values for the five sample images. Taking image Lena as an example, the PSNR value is 80.5 dB after processing by “9-7” dual orthogonal filter; therefore, “9-7” is used as the LP filter in the Contourlet correlation processing in this paper.

4.2

Image fusion based on Contourlet coefficient correlation

In order to verify the feasibility of the proposed method in this paper, a set of images that have been aligned are selected for fusion experiments, including left-focused and right-focused images, clear reference images. The image sizes are all 256*256.

The proposed algorithm is compared with the wavelet-based pixel-point method, wavelet-based window algorithm, Contourlet-based pixel-point method and Contourlet-based window algorithm. Five objective metrics are selected for quantitative analysis, they are information entropy, joint entropy, mutual information (MI), edge strength, and average gradient (AG).

The objective evaluation of multifocus fusion image performance is shown in Table 2. The larger value of both information entropy and joint entropy indicates that the average information of the image is more and the quality of fusion is better. The larger the value of mutual information in the case where the image has been aligned, the more information the fused image acquires from the source image, and the better the fusion effect. The larger the value of edge intensity, the more obvious the contour information of the image and the more prominent the edges. The larger the value of the average gradient, the higher the image clarity.

Table 2.

Multi-focus fusion image performance objective evaluation

Method	Entropy	joint-entropy	MI	edge-intensity	AG
Wavelet pixel-based	8.965	11.213	5.231	55.124	5.321
Wavelet window-based	9.123	12.005	6.554	71.019	6.659
Contourlet pixel-based	9.047	12.396	5.703	66.278	7.113
Contourlet window-based	9.258	12.347	6.445	70.124	7.536
Algorithm of this article	9.461	12.565	6.857	75.313	7.789

This algorithm’s fused image is optimal in terms of information entropy, joint entropy, mutual information, edge strength, and average gradient, which is in accordance with subjective evaluation results. This indicates that the fused image obtained by this algorithm is more capable of extracting the information from the original image and highlighting the edge information features.

In order to further illustrate the effectiveness and extensiveness of the algorithms in this paper, the ink representative images of a group of painters (Li Xiaoxuan, Fu Lei, Wang Qiao, Yue Xiaofei, etc.) are chosen for comparison experiments. The algorithms for comparison are still the same five algorithms used in the above experiments.

The Contourlet window algorithm has richer textures than the Contourlet pixel point algorithm. Overall, the three Contourlet-based algorithms are significantly better than the two wavelet algorithms. And the algorithm in this paper is the closest to the source image in terms of brightness, and the white area is brighter than the other algorithms with clearer details.

At the same time, objective evaluation of the fusion results is necessary. Information entropy, edge intensity, and average gradient are chosen to quantitatively analyze this experiment. The objective evaluation of the image fusion performance of ink figure paintings is shown in Figure 1. The specific values of the three evaluation indexes are given in the figure. The information entropy, edge strength, and average gradient of this paper’s algorithm in the processing of classical ink figure paintings are 7.956, 44.869, and 7.669, respectively.From the numerical values, it can be seen that this paper’s algorithm has an obvious advantage.

4.3

Contourlet transform based image reconstruction

In order to demonstrate the performance of the algorithm proposed in this paper, the Lena image, Barbara image of 512×512 pixels is used in this section for simulation experiments.

The tower structure in the Contourlet transform uses a 9-7 dual orthogonal filter bank and the DFB uses a pkva lattice filter bank. A 4-level decomposition is used and the number of directions at each level is 4. The chunk size B is taken to be 32. The parameter λ is taken to be 10. The image noise is an additive Gaussian white noise with a mean of 0.01 and a standard deviation of 3. The noise level is 0.1.

Comparison of Lena and Barbara’s performance in reconstructing images under three sparse bases is shown in Fig. 2. The PSNR values of the reconstructed images are given in Figs. (a) and (b) for the Lena image and the Barbara image with sampling rates of 0.1, 0.2, 0.3, 0.4, and 0.5 in the case of this paper’s method, the traditional Contourlet method, the DWT method, and the DCT method, respectively.

It can be seen that for these two classical images with different sparse transforms, the PSNR values of the reconstructed images using the improved reconstruction algorithm of Contourlet transform in this paper are higher than the other sparse transforms. This indicates that the algorithm in this paper is able to reconstruct the images better, both for the Lena map with less texture details and for the Barbara map with more texture details.

4.4

Aesthetic Evaluation of Ink Figure Painting

By constructing a dataset of Haikai ink figure paintings, the aesthetic evaluation of the ink figure images in the database is carried out to analyze the aesthetic design of ink figure paintings based on multi-scale geometric analysis and image geometric reconstruction. Since the aesthetic evaluation data of the pictures are greatly influenced by subjective factors, it is necessary to verify the consistency between the aesthetic evaluation of this paper and the user evaluation in the database, i.e., to verify the degree of consistency between high and low aesthetic division.

In order to achieve the purpose of meticulously analyzing the aesthetics of the images of Haikai ink figures, this paper calculates the total aesthetic score of the images by weighting the evaluation results of the four attributes of the images, and selects the appropriate threshold to classify them as high or low aesthetic images. The total score is calculated as follows: (13) $E = w_{1} E_{S} + w_{2} E_{C} + w_{3} E_{R} + w_{4} E_{M}$

Where E_S is saturation, E_C is contrast. E_R is sharpness, and E_M is composition.

The image is judged using the following equation: (14) ${\begin{array}{l} I \in High aesthetic image E (I) \geq 0.65 \\ I \in Low aesthetic image E (I) < 0.65 \end{array}$ $$\{ \matrix{ {I \in {\rm{High}}\,{\rm{aesthetic}}\,{\rm{image}}\,E\left( I \right) \ge 0.65} \hfill \cr {I \in {\rm{Low}}\,{\rm{aesthetic}}\,{\rm{image}}\,E\left( I \right) \lt 0.65} \hfill \cr } $$

Up to this point, image aesthetic evaluation can be regarded as a classification problem to categorize images with high and low aesthetics.

The above image aesthetics evaluation method is applied to evaluate the Haikai ink figure paintings after Contourlet transformation and geometric reconstruction.

The scores of each evaluation attribute of the ink figure paintings after composition optimization are shown in Table 3, and the images were enhanced with sharpness, contrast and saturation correspondingly.

Table 3.

The evaluation properties of the optimized water and ink objects were scored

Painting label	Saturation degree E_S	Contrast ratio E_C	Clarity E_R	Composition E_M
Original painting 1	0.8563	0.2365	0.3659	0.7869
Optimized painting 1	0.9224	0.8024	0.7551	0.8334
Original painting 2	0.1635	0.7545	0.9582	0.6543
Optimized painting 2	0.8759	0.8213	0.9966	0.7169
Original painting 3	0.1025	0.6569	0.2874	0.7585
Optimized painting 3	0.5964	0.7254	0.8531	0.9367

From the experimental results, it can be seen that in visual observation, the enhanced image is richer in detail information, and the composition E_M dimensions are all acquired different levels of optimization, and the multifaceted visual effects are better than the original image. The total aesthetic evaluation score of the sea school ink figure painting after Contourlet transformation and geometric reconstruction is higher. In the quantitative evaluation results, all aspects of the evaluation results of the Contourlet transformed image are significantly improved compared to the original image.

5

Conclusion

This paper proposes a contourlet transform, which is used to extract the image features of Haikai ink figure paintings. The composition optimization of ink and wash figure paintings is achieved by transforming the basic color of the ink and wash figure paintings and seeking the axes of the paintings to reconstruct the image gesture. 1)

Comparing the effect of the combination of “9-7”, Pkva, 5-3 and Burt LP filters and Contourlet transform, it can be seen from the two indicators of SNR and PSNR that the “9-7” processing results are better. Thus, in this paper, the “9-7” LP filter and Contourlet transform are selected for image processing.

2)

In the image fusion and comparison processing, the algorithm proposed in this paper has a significant advantage over other algorithms, which can fit the original image more closely and highlight the edge information characteristics of the image.

3)

The Contourlet transform is used to process and geometrically reconstruct the ink and watercolor paintings, and the saturation E_S, contrast E_C, sharpness E_R, and composition E_M image aesthetic evaluation elements are used to evaluate the aesthetics of the ink and watercolor paintings optimized for composition. After the Contourlet transformation, the saturation, contrast, clarity, and composition of the ink figure paintings are improved to different degrees.

Lingua:: Inglese

Frequenza di pubblicazione:: 1 volte all'anno
Argomenti della rivista:: Scienze biologiche, Scienze della vita, altro, Matematica, Matematica applicata, Matematica generale, Fisica, Fisica, altro

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Research on Multi-scale Geometric Analysis and Compositional Optimization Methods in the Creation of Haikai Ink Figure Painting

Momo Feng

Ying Bai

Pubblicato online: 24 mar 2025

Ricevuto: 14 nov 2024

Accettato: 27 feb 2025

DOI: https://doi.org/10.2478/amns-2025-0787

Parole chiaveContourlet transform, LP filter, Image geometric reconstruction, Color space transformation, Ink figure painting

© 2025 Momo Feng et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Parole chiave
Contourlet transform, LP filter, Image geometric reconstruction, Color space transformation, Ink figure painting