Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation

After a lot of research and analysis, we found that most art historians distinguish the creators of ancient paintings mainly based on some typical strokes and ink technique characteristics reflected in the paintings when evaluating, analyzing, comparing and identifying the true and fake paintings. Artists often use a magnifying glass to see the details and local characteristics of a painting in order to identify the authenticity. And the overall characteristics of a painting can not accurately and completely interpret the artist's artistic style. Therefore, based on the description of the overall style of ink painting, this section studies the local area and stroke of ink painting in order to highlight the artist's grasp of the key local style.

Chinese painting is based on lines, which draw the outline, texture and volume. Therefore, the pen used in traditional Chinese painting mainly refers to the line, which is mainly represented by the slender pen path. The pen path is not only the basic element of ink painting, but also an important modeling means of ink painting. The brush track can reflect the skills of different painters, such as the direction, strength and speed of pen movement. Brushwork plays a decisive role in describing the artist's artistic style. Therefore, the primary task of extracting local features is to extract all brushwork in the whole painting, so as to locate the local area in the whole painting that can best reflect the artist's detailed brushwork information and brushwork features[9].

Edge detection technology can effectively capture the location of sharp changes in pixel gray value, so as to find line features, including image “edge” and “line”. “Edge” refers to the boundary between those regions with different local characteristics of the image, which is expressed as the discontinuity of the local image, such as the mutation of gray level, the mutation of texture structure and so on. The “line” can be considered as a pair of edges with small width and the same image characteristics in the middle area, that is, a pair of edges with small distance form a line. The edge detection of traditional Chinese painting can help to find the local feature areas with significant changes in the image attributes, so as to reflect the important events and changes of the attributes and the important structural attributes of the image. In this target local area, the gray histogram is taken to describe the detailed style information of the pen track: the following pen strength, the shape of the pen track, the distribution of the pen track and the hierarchical information between the pen tracks. In addition, two factors should be considered in local feature extraction: (1) detect the typical stroke information that can best reflect the painter's style; (2) locate the representative area that can best represent the painter's style on the whole image. Considering factor 1, this paper uses edge detection technology to extract all strokes in ink painting. For factor two, a window function is used to scan all areas of the whole image step by step to process all trace information. The proposed local feature extraction algorithm is as follows:

Let G(x, y) be a gray image, and extract all trace information as follows: (1) E(x, y)=B{∇s (G(x, y))} E\left({x,\,y} \right) = B\left\{{{\nabla _s}\,\left({G\left({x,\,y} \right)} \right)} \right\}

Where ∇_s represents Sobel operator and B(·) is a binarization equation, which binarizes the edge image of G(x, y) after edge detection by Sobel operator by using the sensitive threshold τ to obtain the binary image E(x, y). The pixels in E(x, y) are defined as follows: (2) e(x, y)={1if|∇s (G(x, y))|>τ0else} e\left({x,\,y} \right) = \left\{{\matrix{1 & {if\left| {{\nabla _s}\,\left({G\left({x,\,y} \right)} \right)} \right| > \tau} \cr 0 & {else} \cr}} \right\}

The next step is to segment the local region. There are many ways of region segmentation, such as quadtree method, ROI region of interest method, fixed size segmentation, etc. However, the fixed module segmentation method is adopted in this paper, which is simple and intuitive, and the experiment shows that the classification performance is very good. Inspired by image and video compression coding, the size of local area can generally be defined as 128×128, 64×64 or 32×32. In order to obtain enough detailed features without too much computation, this section defines a 64×64 pixel image block through experiments to locate the local area in an image that best reflects the characteristics of pen style: (3) Blockk(i, j)=ω(i, j)G(x−kΔ,y−kΔ) {Block}_k\left({i,\,j} \right) = \omega \left({i,\,j} \right)G\left({x - k\Delta,y - k\Delta} \right)

Where 0 < k < N, N represents the total number of image blocks, Δ represents the moving step of window function on the whole image, and Δ ∈ [1, 64]. For example, Δ = 1 means that the next window is the image block after the current window moves 1 pixel; If Δ = 64, it means that there will be no overlap between image blocks divided by window function. In order to weigh the operation speed and block as many blocks as possible to include all details, this paper selects 1 / 4 of the image block width and height as the value of Δ, that is, Δ = 16. In formula (3), ω (j, i) is a window function, which is defined as follows: (4) w(i, j)={1∀i, j∈[0, 64)0else} w\left({i,\,j} \right) = \left\{{\matrix{1 & {\forall i,\,j \in \left[{0,\,64} \right)} \cr 0 & {else} \cr}} \right\}

The most representative image block block_L (x, y) is extracted as follows: (5) BlockL(i, j)=arg max{η{blockk{E(x,y)}}} {Block}_L\left({i,\,j} \right) = \arg \,\max \left\{{\eta \left\{{{block}_k\left\{{E\left({x,y} \right)} \right\}} \right\}} \right\}

Where η is a counting function, which is defined as follows: (6) η=∑i=063∑j=063e(i,j) \eta = \sum\limits_{i = 0}^{63} {\sum\limits_{j = 0}^{63} {e\left({i,j} \right)}}

Therefore, block_L contains the most stroke detail features and is the most representative local area extracted. Therefore, extracting the detailed features of a painting from the local area block block_L (x, y) with the most strokes can best describe the local painting style of an artist[10].

In essence, the design idea of local representative region location algorithm based on Sobel edge detection algorithm follows the following principles: (1)

The result of edge detection contains the position information of all strokes;

The implementation of this design has many advantages, which are listed as follows:

(1) The influence of the choice of threshold value on stroke extraction. Once we have calculated the derivative, the next step is to give a threshold to determine where the edge is.

The lower the threshold, the more edges can be detected, the more vulnerable the result is to the influence of image noise, and the easier it is to pick out irrelevant features from the image. In contrast, a high threshold will lose thin or short segments. A common method is threshold selection with hysteresis. This method uses different thresholds to find edges. The first is to use a threshold upper limit to find the starting point of the edge line. Once a starting point is found, we track the edge path point by point on the image. When it is greater than the lower limit of the threshold, we keep recording the edge position until the value is less than the lower limit. However, this method needs to find the appropriate threshold for each image of each artist, and requires human participation, which violates the principle of automatic classification and takes too much time[11].

(2) After region localization, the local features extract the histogram from the gray image, instead of simply considering the shape, color and other information of the edge after edge detection, so as to make the local features more comprehensive and effective.

The overall characteristics of the image can well describe the layout, pen and ink force distribution and other characteristics of the whole image from a macro perspective. On the other hand, the local characteristics of the image describe the detailed information of the pen track concentrated in a small neighborhood, and show the local characteristics of the image, such as the intensity, distribution, shape and contour of the pen track, which can reflect the detailed pen operation information and characteristics of the painter.

Moreover, according to the observation, when Chinese art historians identify whether art works are fakes or appreciate paintings, they often hang the paintings in the distance and observe the whole painting from the macro perspectives of overall momentum, white space layout, object and image distribution in the paintings. Then, put the painting in front of you and use a magnifying glass to carefully observe a certain stroke feature, or carefully experience the painter's treatment method and stroke characteristics in a local area of a certain detail. Finally, the comprehensive evaluation and appreciation results are given based on the two factors.

Information is a description of the uncertainty of the motion state or existence mode of things. Information entropy is a concept used to measure the amount of information in information theory. It describes the uncertainty of the source and the average amount of information of all targets in the source. Information quantity is the central concept of information theory. Taking entropy as the uncertainty of a random event or the measure of information quantity, it lays the scientific theoretical foundation of modern information theory and greatly promotes the development of information theory. Suppose X is the set of random variables x, p(x) represents its probability density, and the information entropy of random variable X is defined as: (7) H(X)=−∑xp(x)log p(x) H\left(X \right) = - \sum\limits_x {p\left(x \right)\log \,p\left(x \right)}

The direct value H of a random variable with X value range {x₁,…, x_n} is defined as: (8) H(x)=E(I(x)) H\left(x \right) = E\left({I\left(x \right)} \right)

Information entropy reflects the degree of uncertainty of information. In classical probability theory, it is expressed as the degree of uncertainty of random variables; In the theory of fuzzy mathematics, information entropy reflects the degree of fuzziness of things. The size of information line reflects our mastery of information. The more information we master, the smaller the information line. Therefore, it is very important to evaluate the information expected value of paintings.

The diffusion equation is a nonlinear partial differential equation, and the diffusion tensor needs to be updated in each iterative evolution. However, due to the existence of Gaussian convolution, the amount of calculation is very large. In order to reduce the amount of calculation, the pseudo linear directional diffusion equation is adopted in this paper. The main idea is that the diffusion tensor is updated only after a finite number of iterations, rather than every iteration. It is expressed as follows: (9) ∂u∂t=trace(DH) {{\partial u} \over {\partial t}} = trace\left({DH} \right)

According to the above analysis, this paper proposes to use the following directional diffusion equation for image enhancement: (10) ∂u∂t=λ1uθ1θ2+λ2uθ1θ2 {{\partial u} \over {\partial t}} = {\lambda _1}{u_{\theta 1\theta 2}} + {\lambda _2}{u_{\theta 1\theta 2}}

From the perspective of diffusion, the formula is actually a nonlinear diffusion along directions θ₁ and θ₂. in this paper, it is called directional diffusion equation, because the value of λ is generally very small. Therefore, the diffusion equation mainly diffuses along the direction, that is, the diffusion along the grain direction. Such diffusion is not easy to be disturbed by the complex situation of local diffusion direction, and can always follow the grain diffusion diagram. The results show that this method can also enhance the image along the original beard pattern in the beard area with complex local direction information, and its performance is better than the correlation diffusion equation. This characteristic determines that this method is more suitable for fingerprint image enhancement[12].

In this paper, the pseudo linear strategy is based on the diffusion equation, which mainly evolves along the grain direction, and this diffusion method will not cause the sharp change of the grain on the fingerprint image, so the diffusion tensor dependent on the grain direction will not mutate in a finite evolution. Therefore, the pseudo linear method can be adopted in the finite iterative evolution. It can basically keep the enhancement result consistent with the nonlinear diffusion result while improving the operation efficiency. The specific implementation of the formula is basically consistent with the formula, as long as the diffusion tensor is updated periodically. The selection of update cycle and the space-time step adopted are larger than the relevant space-time step ratio, so a shorter update cycle should be selected; on the contrary, a longer update cycle should be selected.