CN103745444B - Based on the non-photorealistic image rendering intent of topological tree - Google Patents

Abstract

The invention discloses a kind of non-photorealistic image rendering intent based on topological tree, comprise step: step 1, the shape topological tree of setting up original image is expressed; Step 2, according to the shape attribute of shape each in shape topological tree, keeps shape topological tree Structure, deletes the shape that shape attribute does not meet threshold requirement; Step 3, by modifying to realize image rendering and reconstruct to shape in shape topological tree.The shape topological tree that the present invention is based on image is expressed, and modifies, to reach the object that non-photorealistic image is played up, and under the prerequisite of not losing image information, greatly can improve rendering efficiency to image basic comprising unit.

Description

Non-photorealistic image rendering method based on topology tree

Technical Field

The invention belongs to the field of image processing, and particularly relates to a non-photorealistic image rendering method based on a topological tree.

Background

Image Non-photorealistic rendering (NPR), in turn, is translated into Non-photorealistic rendering or stylistic rendering (stylistic rendering), which refers to the generation of Non-photorealistic, but hand-drawn, image technologies using computers. It originated from an interactive painting and mapping system that created digitized images by gradually adding artistic brush effects to the images. It is not aimed at the realism of the figures, but mainly at representing the artistic quality of the figures, simulating the works of art (even including defects in the works) or as an effective complement to the realistic figures. Non-photorealistic rendering does not pursue complete photorealism, the main objective being to represent an object in a concise, inclusive, aesthetically pleasing manner.

Research on non-photorealistic rendering of images has been a hot topic, and many researchers are working on automatic rendering and modification based on strokes^[1]～[6]. Most of these efforts rely on basic image analysis, i.e. full or partial structural representation of the image, such as edge detection^[1]Linear scale space^[6]Region extraction^[2]Table of significance^[4]Laplacian pyramid^[3]And the like.

Most of the existing image non-photorealistic rendering needs to process images through a specific painting model, and is inconvenient. If a model can be used to obtain different non-photorealistic rendering effects by only modifying a small number of parameters or processes, the image processing efficiency can be greatly improved

The relevant references are:

[1]ThomasStrothotteandStefanSchlechtweg,Non-PhotorealisticComputerGraphics:Modeling,Rendering,andAnimation.MorganKaufmannPublishersInc.,SanFrancisco,CA,USA,2002.

[2]P.Litinowicz,Processingimagesandvideoforanimpressionisteffect.InProc.ofSIGGRAPH’97,pp.407-414,1997.

[3]G.C.P.S.B.Gooch,Artisticvision:painterlyrenderingusingcomputervisiontechniques.InProc.ofNPAR,pp.83-90,2002.

[4]S.Brooks,Mixedmediapaintingandportraiture.IEEETrans.VisualizationandComputerGraphics,Vol.12,No.5,pp.1041-1054,2007.

[5]J.P.C.a.P.M.Hall,Painterlyrenderingusingimagesalience.InProc.ofEurographicsUKConference,p.122–128,2002.

[6]A.Hertzmann,PaintByRelaxation.InProc.ofInternationalConferenceonComputerGraphics,2001.

[7]A.Hertzmann,Painterlyrenderingwithcurvedbushstrokesofmultiplesizes.InProc.ofSIGGRAPH'98,pp.453-460,1988.

disclosure of Invention

Aiming at the defects in the prior art, the invention provides a topological tree-based non-photorealistic image rendering method which can greatly improve rendering efficiency.

In order to solve the technical problems, the invention adopts the following technical scheme:

a topological tree based non-photorealistic image rendering method comprises the following steps:

step 1, establishing a shape topological tree expression of an original image;

step 2, according to the shape attribute of each shape in the shape topological tree, maintaining the shape topological tree structure, and deleting the shape of which the shape attribute does not meet the requirement of a threshold value;

and 3, modifying the shape in the shape topology tree to realize image rendering and reconstruction.

Step 1 further comprises the sub-steps of:

1.1, converting an original color image into an HSV image, and taking an illumination intensity channel of the HSV image;

1.2 according to the illumination intensity level of the HSV image, acquiring a basic constitutional unit, namely a shape, of the image by adopting a level set algorithm;

1.3, representing each shape by adopting a cascade structure, establishing a shape topological tree expression, wherein the nodes of the shape topological tree represent the shapes, the shape represented by a father node comprises the shape represented by a child node in an image space, and a root node represents the whole image.

The step 1.2 is specifically as follows:

defining a level set according to the illumination intensity level of the HSV image, wherein the level set is a level set binary image which comprises one or more independent holes, and filling the holes with pixels corresponding to the positions of the original color image to obtain independent shapes; and continuously increasing the illumination intensity value, and obtaining the corresponding independent shape by adopting a level set algorithm.

And step 1.3, combining the shapes corresponding to the illumination intensities into a cascade tree structure according to the illumination intensity sequence.

And step 1.3, establishing the shape topological tree expression by adopting a rapid level set transformation method.

The shape attribute described in step 2 includes a shape aspect ratioWherein λ is₁And λ₂Is the eigenvalue of the second order inertia matrix of shape, and₁＞λ₂deleting ∈ the aspect ratio in the shape topology tree is not less than the aspect ratio threshold₀The shape of (2).

The shape attribute in the step 2 comprises the shape area, namely the sum of pixels in the shape, and the area in the deleted shape topological tree is not more than an area threshold A₀The shape of (2).

The shape attribute described in step 2 includes the compactness of the shapeWherein, A (S)_i) Is the area of the shape, λ₁And λ₂Is the eigenvalue of the second order inertia matrix of shape, and₁＞λ₂deleting the shape topology tree with a compactness not greater than a compactness threshold k₀The shape of (2).

The shape attribute described in step 2 includes a shape-to-scale ratioWherein, A (S)_i) Is the area of the shape, S_i ^rIndicates the shape S_iThe r level ancestor shape in the shape topological tree, M is the self-defined series range, the scale ratio in the deleted shape topological tree is not more than the scale ratio threshold α₀The shape of (2).

The first specific scheme of the step 3 further comprises the following substeps:

3.1 maintaining the relative structure of the shape topology tree, adopting the main shaft deflection angle theta (S) of each shape_i) The shape of the rotation, wherein,(x, y) is the pixel coordinates in the shape;is the shape center position index;

3.2, giving a shape s, and respectively adjusting the shape attribute of the shape s aiming at each shape in the shape topological tree to ensure that the difference between the shape attribute of the shape s and the shape attribute of the shape in the shape topological tree is minimum;

3.3 for each shape in the shape topology tree, counting the average value of the colors of all pixels in the shape in the original color image, and filling the corresponding pixels in the shape by using the average value of the colors; replacing each shape in the shape topology tree by the new shape s to obtain an updated shape topology tree;

3.4 reconstructing the image based on the updated shape topology tree to obtain a shape rendered image.

The second embodiment of step 3 further comprises the substeps of:

3.1 for shape S in shape topology Tree_iRespectively calculating the principal axis deflection angle theta (S)_i)： $\mathrm{\θ}\left(S_i\right)={\tan }^{-1}\frac{{\∫}_{S_i}(y-\stackrel{\‾}{y})\mathrm{dx}}{{\∫}_{S_i}(x-\stackrel{\‾}{x})\mathrm{dy}},$ And produce a series of satisfaction ${\left(\frac{\mathrm{\Δx}}{{\mathrm{\λ}}_1}\right)}^2+{\left(\frac{\mathrm{\Δy}}{{\mathrm{\λ}}_2}\right)}^2\≤\mathrm{\ρ}$ Of (a) is given, wherein₁And λ₂Is the eigenvalue of the second order inertia matrix of shape, and₁＞λ₂(ii) a ρ is the custom oscillation amplitude;

3.2 generating the shape s from each set of variables (Δ x, Δ y)_i' { (x + Δ x, y + Δ y) }, and for shape s_iCarrying out random rotation and position processing to obtain a processed shape;

3.3 all processed shapes and shapes S in the shape topology Tree_iSuperposing to obtain the shape s_i″；

3.4, processing all shapes in the shape topology tree by steps 3.1-3.3 respectively to obtain a modified shape topology tree;

and 3.5, reconstructing the image based on the modified shape topology tree to obtain an oil painting rendering image.

The third embodiment of step 3 further comprises the substeps of:

3.1 for shape S in shape topology Tree_iRespectively counting the shape S_iThe number of pixels in a rectangular window with the scale of (2t +1) and each pixel as the center;

3.2 judging the number of pixels in the rectangular window and the area of the rectangular window, and if the number of pixels in the rectangular window is smaller than the area of the rectangular window, giving up the central pixel of the rectangular window;

3.3 pairs of shapes S_iAll the pixels in the image are processed in steps 3.1-3.2, and the shape S_iTransformation to new shape s_i′；

3.4, respectively completing the steps 3.1-3.3 for each shape in the shape topology tree to obtain a modified shape topology tree, and reconstructing an image based on the modified shape topology tree to obtain a fuzzy rendering image.

Compared with the prior art, the invention has the following characteristics:

1. and constructing an image geometric structure based on the shape topological tree expression, namely expressing an image through the cascade connection or the inclusion relation of the shapes, and recovering the original image based on the shape topological tree.

2. And directly modifying, resetting, replacing and the like the shape in the shape topology tree to obtain the modified shape topology tree, and restoring the modified shape topology tree to realize image rendering.

3. And replacing the shape in the shape topology tree by using the new shape to obtain a modified shape topology tree, and restoring the modified shape topology tree to realize image rendering.

4. The topological tree expression is a complete expression, so that any information of the image is not lost, and the topological tree expression can adapt to any subtle operation of the image; in addition, the topology tree expression is a multi-scale expression and can provide multi-scale analysis of the image, the topology tree is a simple cascading relation tree of shapes, so that the image rendering operation can be converted into a simple modification operation of the shapes, and fig. 1 is a result of performing shape replacement on an original image.

Drawings

FIG. 1 is an example of image rendering, where graph (a) is an original color image, graph (b) is a circle rendered image, graph (c) is a line rendered image, and graph (d) is a dictionary-shaped rendered image;

FIG. 2 is an example of geometric rendering of an image, where graph (a) is an original color image, graph (b) is a circle rendered image, graph (c) is a line rendered image, and graph (d) is a dictionary-shaped rendered image;

FIG. 3 is an example of ink rendering of an image, where (a) and (c) are original color images and (b) and (d) are rendered images of a canvas;

fig. 4 is an example of watercolor rendering of an image, where fig. (a) and (c) are original color images, and fig. (b) and (d) are watercolor rendered images.

Detailed Description

The technical solution of the present invention will be further explained with reference to the accompanying drawings and the detailed description.

Step 1, establishing a shape topological tree expression of an image.

This step is well known in the art. The specific implementation method comprises the following steps:

for a given color image I, convert it into HSV image I₁And taking an HSV image illumination intensity channel, calculating a topological tree structure based on a level set algorithm, and establishing a shape topological tree expression of the image.

The level set is defined as:

χ_l(I_l)＝{p∈Ω;I_l(p)≥l}

（1）

χ^l(I_l)＝{p∈Ω;I_l(p)≤l}

wherein, χ_l(I_l) Representing an image I₁The upper level set of (a); chi shape^l(I_l) Representing an image I₁Omega is the image space, p is the image pixel point index, L ∈ [ 1., L]Representing increasing image illumination intensity levels.

The level set may be considered as a binary image, i.e. comprising parts belonging to the level or parts not belonging to the level. The level set binary image contains one or more individual holes that represent pixels outside the level set. The holes are filled with pixels corresponding to the positions of the holes in the original image I, so that independent shapes can be obtained, and the shapes are basic constitutional units of the image. By increasing the value of the illumination intensity l, a corresponding level set, i.e. a corresponding shape, can be obtained. Combining the shapes into a tree structure according to the sequence of the corresponding illumination intensity, and obtaining the shape topology tree T ═ S (S) of the image_i)_i＝1,...,NWherein S is_iIs an independent shape, i is the shape index and N is the total number of shapes.

The obtained shape topology tree includes all information of the image in the independent shape S_iAnd will be independent of shape S_iRepresented by a cascade structure. Specifically, all shapes obtained from all level sets form a cascaded shape topology tree according to the size and the inclusion relationship, wherein each node represents a shape, the shape represented by a parent node spatially contains the shape represented by a child node, and the root node represents the whole image. In addition, the shape topology tree can be obtained by directly using Fast Level Set Transformation (FLST) algorithm, which is not described herein.

For HSV image I₁Topology tree structure of (S) ═ S_i)_i＝1,...,NTo shape S_iRespectively averaging RGB three-channel colors of all the contained pixels to obtain the shape S_iColor index c of_i∈R³Shape S_iAdding color information of (to) the topology tree structure T ═ S_i)_i＝1,...,NObtaining a final shape topology tree T ═ (S)_i,c_i)_i＝1,...,N。

And 2, selecting the shape.

For shape S_iThe shape S is defined by { (x, y); (x, y ∈ Ω) }_iOrder of (p + q) of (u)_pq(S_i)：

${\mathrm{\μ}}_{\mathrm{pq}}\left(S_i\right)=\∫\underset{S_i}{\∫}{(x-\stackrel{\‾}{x})}^p{(y-\stackrel{\‾}{y})}^q\mathrm{dxdy}---\left(2\right)$

Wherein (x, y) is the shape S_iA middle pixel coordinate; Ω is the image space; p and q are the norm of x and y, respectively;indicates the shape S_iThe position index of the center, i.e., the center of gravity.

$\stackrel{\‾}{x}=\frac{1}{{\mathrm{\μ}}_{00}\left(S_i\right)}\underset{S_i}{\∫\∫}\mathrm{xdxdy}---\left(3\right)$

$\stackrel{\‾}{y}=\frac{1}{{\mathrm{\μ}}_{00}\left(S_i\right)}\underset{S_i}{\∫\∫}\mathrm{ydxdy}---\left(4\right)$

In formulae (3) to (4), μ₀₀(S_i) Is in the shape S_i0 order of moment, i.e. shape S_iIs defined as the shape S_iTotal number of middle pixels.

Considering the stability and invariance of the shape, the second moment of the shape has the strongest representation meaning and is the most stable, so the invention utilizes the characteristic value lambda of the second-order inertia matrix C(s) of the shape₁And λ₂Shape selection is made, and₁＞λ₂。

$C\left(s\right)=\left(\begin{array}{cc}{\mathrm{\μ}}_{20}\left(s\right)& {\mathrm{\μ}}_{11}\left(s\right)\\ {\mathrm{\μ}}_{11}\left(s\right)& {\mathrm{\μ}}_{02}\left(s\right)\end{array}\right)---\left(5\right)$

shape selection is to select important and representative shapes in the shape topology tree and remove the miscellaneous points in the image. Shape attributes are defined by classifying shapes as meaningful and meaningless according to their attributes:

aspect ratioArea A (S)_i)＝μ₀₀(S_i) Compactness degreeRatio of sum to sizeWherein S is_i ^rIndicates the shape S_iAnd (4) in the topology tree, the shape of the ancestors at the r-th layer, and M is a self-defined series range.

Among the above shape attributes, aspect ratio ∈ (S)_i) Define the shape S_iA larger aspect ratio indicates a flatter shape, and a smaller aspect ratio indicates a rounder shape; area A (S)_i) Define the shape S_iSize; compactness kappa (S)_i) Define the shape S_iConcentration of medium pixels, larger compactness indicates more irregular shape, smaller compactness indicates more round shape, and scale ratio α (S)_i) Define the shape S_iIn relation to the shape of its parent node, a larger scale ratio indicates the shape S_iThe larger the difference from the upper shape, the smaller the scale ratio indicates the shape S_iThe smaller the difference in shape from the upper layer.

For all shapes in the shape topology tree, respectively judging whether each shape should be reserved based on the shape attribute:

(1) if shape S_iAspect ratio ∈ (S)_i)＜∈₀Then the shape S is retained_iI.e. keeping the aspect ratio less than the aspect ratio threshold ∈₀The shape of (a);

(2) if shape S_iArea A (S) of_i)＞A₀Then the shape S is retained_iI.e. the remaining area is greater than the area threshold A₀The shape of (a);

(3) if shape S_iIs of (a) is of_i)＞κ₀Then the shape S is retained_iI.e. keeping the compactness larger than the compactness threshold k₀The shape of (a);

(4) if shape S_iScale ratio of α (S)_i)＞α₀Then the shape S is retained_iI.e. keeping the scaling ratio greater than the scaling ratio threshold α₀The shape of (2).

And (4) judging whether each shape in the shape topology tree is reserved or not by adopting one or more judgment modes in the (1) to (4). The shape attribute threshold values such as the aspect ratio threshold value, the area threshold value, the compactness threshold value, and the scale ratio threshold value are set empirically and manually.

And 3, rendering and reconstructing the image.

And after the shape selection step is completed on the shape topology tree, obtaining a shape topology tree T ', and the step achieves the aim of image rendering by modifying the shape topology tree T'. The invention provides three image rendering schemes, including geometric redrawing of images, oil redrawing of images and fuzzy redrawing of images. The three image rendering schemes are explained below.

(1) Geometric redrawing of images

The geometric redrawing of the image is to replace the shape in the shape topology tree T' with a shape with a similar structure, which is realized by giving a shape s (such as an ellipse, a line or a dictionary shape) and performing the following operations:

(a) the shape is biased.

Keeping the cascade relation among all shapes in the shape topological tree unchanged, and keeping the shape S in the shape topological tree_iCalculating the principal axis deflection angle theta (S) by using the following formula_i)：

$\mathrm{\θ}\left(S_i\right)={\tan }^{-1}\frac{{\∫}_{S_i}(y-\stackrel{\‾}{y})\mathrm{dx}}{{\∫}_{S_i}(x-\stackrel{\‾}{x})\mathrm{dy}}---\left(6\right)$

In the formula (6), (x, y) is the shape S_iA middle pixel coordinate;indicates the shape S_iThe position index of the center can be obtained by calculation using equations (3) and (4).

Using the main shaft deflection angle theta (S)_i) Rotation shape S_iThe method specifically comprises the following steps: shape S_iEach pixel in (1) is multiplied by a rotation variation matrix, in this embodiment $M\left(\mathrm{\θ}\right)=\left[\begin{array}{cc}\cos \mathrm{\θ}\left(S_I\right)& -\sin \mathrm{\θ}\left(S_I\right)\\ \sin \mathrm{\θ}\left(S_I\right)& \cos \mathrm{\θ}\left(S_I\right)\end{array}\right].$

(b) And (4) geometric transformation.

Keeping the relative structure of the shape topology tree unchanged, for each shape S in the shape topology tree_iRespectively calculating the areas A (S)_i) Aspect ratio ∈ (S)_i) And compactness kappa (S)_i). Adjusting the area, aspect ratio and compactness of the shape S to match the shape S with the shape S_iMost similar, namely D (S, S) in the formula_i) Minimum:

D(s，S_i)＝|∈(S_i)-∈(s)|+|κ(S_ii)-κ(s)|+|A(S_i)-A(S)|(7)

the shape S and the shape S are defined in the formula (7)_iSimilarity D (S, S)_i)。

(c) And (6) color correction.

Keeping the relative structure of the shape topology tree unchanged, for each shape S in the shape topology tree_iRespectively calculate the colors (S) thereof_i,c_i). The specific method comprises the following steps: for shape S_iRespectively counting the average value of RGB three-channel colors in the original image I, and utilizing the color average value of each pixel to calculate the shape S_iFilling corresponding pixels in the pixel array; obtaining the shape S by the method in step (b)_iThe most similar shape S, each shape S in the shape topology tree T_iThe replacement with the shape s results in an updated shape topology tree T ".

(d) And (5) image reconstruction.

And reconstructing the rendered image based on the shape topology tree T', and realizing image reconstruction by directly using a recovery algorithm provided by the MegaWave library, which is not described herein any more. The final experimental effect is shown in fig. 2.

(2) Redrawing of oil painting

The oil painting redrawing of the image is to render the digital image into an image with oil painting style. The invention provides a shape dithering method, which generates a large amount of redundant information through shape dithering and generates an oscillation boundary to obtain a fuzzy oil painting effect, and comprises the following specific steps:

(a) for each shape S in the shape topology tree_iCalculating the principal axis deflection angle theta (S) by respectively adopting the formula (6)_i) And produce a series of satisfactionOf (a) is given, wherein₁And λ₂Respectively, the characteristic values of the shape second-order inertia matrix, wherein rho is self-defined oscillation amplitude, and the bigger rho is, the stronger the oscillation effect is, and the more fuzzy the generated image is.

Using the main shaft deflection angle theta (S)_i) Rotational variables (Δ x, Δ y), such that (Δ x, Δ y)^T＝M(θ(S_i))(Δx,Δy)^TWherein $M\left(\mathrm{\θ}\left(S_i\right)\right)=\left[\begin{array}{cc}\cos \mathrm{\θ}\left(S_i\right)& -\sin \mathrm{\θ}\left(S_i\right)\\ \sin \mathrm{\θ}\left(S_i\right)& \cos \mathrm{\θ}\left(S_i\right)\end{array}\right].$

(b) generating a new shape s for each set of variables (Δ x, Δ y)_i' { (x + Δ x, y + Δ y) }, (x, y) is the shape S on the shape topology tree_iA middle pixel; shape s_i' random rotation and location processing, i.e. shape s_i' randomly deflect an angle and randomly shift a position.

(c) The average of all new shapes is compared to the original shape S_iOverlapping to obtain final shape s_i″。

(d) And (c) respectively processing all shapes in the shape topology tree in the steps (a) to (c), obtaining the modified shape topology tree, and recovering the rendered image from the modified shape topology tree by directly using a recovery algorithm provided by a MegaWave library. The effect of the best test is shown in FIG. 3.

(3) Blurred redrawing of images

The image fuzzy redrawing is to carry out fuzzy processing on the digital image to generate an image with a watercolor effect. The invention provides an image fuzzy redrawing method based on shape median filtering, which comprises the following steps:

(a) given a median filtering scale (2t +1), S is applied to each shape in the shape topology tree_iFor shape S { (x, y) }_iAll the contained pixel points (x)_k,y_k) And respectively counting the number of pixels in a rectangular window with the scale of (2t +1) and each pixel point as the center.

(b) And if the number of pixels in the rectangular window is less than half of the area of the rectangular window, discarding the central pixel of the rectangular window.

(c) For shape S_iAfter all the pixels in the shape S have completed steps (a) - (b)_iTransformation to new shape s_i′。

(d) And (4) respectively completing the steps (a) to (c) for each shape in the shape topology tree to obtain a modified shape topology tree, and directly recovering the rendered image from the modified shape topology tree by using a recovery algorithm provided by a MegaWave library. The effect of the best test is shown in FIG. 4.

Claims (9)

1. The non-photorealistic image rendering method based on the topology tree is characterized by comprising the following steps of:

step 1, establishing a shape topological tree expression of an original image;

step 2, according to the shape attribute of each shape in the shape topological tree, maintaining the shape topological tree structure, and deleting the shape of which the shape attribute does not meet the requirement of a threshold value;

step 3, modifying the shape in the shape topology tree to realize image rendering and reconstruction;

step 3 further comprises the sub-steps of:

3.1 maintaining the relative structure of the shape topology tree, adopting the main shaft deflection angle theta (S) of each shape_i) The shape of the rotation, wherein,(x, y) is the pixel coordinates in the shape;is the shape center position index;

3.2, giving a shape s, and respectively adjusting the shape attribute of the shape s aiming at each shape in the shape topological tree to ensure that the difference between the shape attribute of the shape s and the shape attribute of the shape in the shape topological tree is minimum;

3.3 for each shape in the shape topology tree, counting the average value of the colors of all pixels in the shape in the original color image, and filling the corresponding pixels in the shape by using the average value of the colors; replacing each shape in the shape topology tree by the new shape s to obtain an updated shape topology tree;

3.4 reconstructing the image based on the updated shape topology tree to obtain a shape rendered image.

2. The non-photorealistic image rendering method based on the topology tree is characterized by comprising the following steps of:

step 1, establishing a shape topological tree expression of an original image;

step 2, according to the shape attribute of each shape in the shape topological tree, maintaining the shape topological tree structure, and deleting the shape of which the shape attribute does not meet the requirement of a threshold value;

step 3, modifying the shape in the shape topology tree to realize image rendering and reconstruction;

step 3 further comprises the sub-steps of:

3.1 for shape S in shape topology Tree_iRespectively calculating the principal axis deflection angle theta (S)_i)： $\mathrm{\θ}\left(S_i\right)={\tan }^{-1}\frac{{\∫}_{S_i}(y-\stackrel{\‾}{y})dx}{{\∫}_{S_i}(x-\stackrel{\‾}{x})dy},$ And produce a series of satisfaction ${\left(\frac{\mathrm{\Δ}x}{{\mathrm{\λ}}_1}\right)}^2+{\left(\frac{\mathrm{\Δ}y}{{\mathrm{\λ}}_2}\right)}^2\≤\mathrm{\ρ}$ Of (a) is given, wherein₁And λ₂Is the eigenvalue of the second order inertia matrix of shape, and₁＞λ₂(ii) a ρ is the custom oscillation amplitude;

3.2 root of Chinese AraliaGenerating the shape s from each set of variables (Δ x, Δ y)_i' { (x + Δ x, y + Δ y) }, and for shape s_iCarrying out random rotation and position processing to obtain a processed shape;

3.3 all processed shapes and shapes S in the shape topology Tree_iSuperposing to obtain the shape s_i”；

3.4, processing all shapes in the shape topology tree by steps 3.1-3.3 respectively to obtain a modified shape topology tree;

and 3.5, reconstructing the image based on the modified shape topology tree to obtain an oil painting rendering image.

3. The non-photorealistic image rendering method based on the topology tree is characterized by comprising the following steps of:

step 1, establishing a shape topological tree expression of an original image;

step 2, according to the shape attribute of each shape in the shape topological tree, maintaining the shape topological tree structure, and deleting the shape of which the shape attribute does not meet the requirement of a threshold value;

step 3, modifying the shape in the shape topology tree to realize image rendering and reconstruction;

step 3 further comprises the sub-steps of:

3.1 for shape S in shape topology Tree_iRespectively counting the shape S_iThe number of pixels in a rectangular window with the scale of (2t +1) and each pixel as the center;

3.2 judging the number of pixels in the rectangular window and the area of the rectangular window, and if the number of pixels in the rectangular window is smaller than the area of the rectangular window, giving up the central pixel of the rectangular window;

3.3 pairs of shapes S_iAll the pixels in the image are processed in steps 3.1-3.2, and the shape S_iTransformation to New shape s'_i；

3.4, respectively completing the steps 3.1-3.3 for each shape in the shape topology tree to obtain a modified shape topology tree, and reconstructing an image based on the modified shape topology tree to obtain a fuzzy rendering image.

4. The method for rendering the non-photorealistic image based on the topology tree according to any one of claims 1 to 3, wherein:

step 1 further comprises the sub-steps of:

1.1, converting an original color image into an HSV image, and taking an illumination intensity channel of the HSV image;

1.2 according to the illumination intensity level of the HSV image, acquiring a basic constitutional unit, namely a shape, of the image by adopting a level set algorithm;

1.3, representing each shape by adopting a cascade structure, establishing a shape topological tree expression, wherein the nodes of the shape topological tree represent the shapes, the shape represented by a father node comprises the shape represented by a child node in an image space, and a root node represents the whole image.

5. The method of claim 4 for non-photorealistic image rendering based on a topology tree, wherein:

the step 1.2 is specifically as follows:

defining a level set according to the illumination intensity level of the HSV image, wherein the level set is a level set binary image which comprises one or more independent holes, and filling the holes with pixels corresponding to the positions of the original color image to obtain independent shapes; and continuously increasing the illumination intensity value, and obtaining the corresponding independent shape by adopting a level set algorithm.

6. The method for rendering the non-photorealistic image based on the topology tree according to any one of claims 1 to 3, wherein:

the shape attribute described in step 2 includes a shape aspect ratioWherein λ is₁And λ₂Is the eigenvalue of the second order inertia matrix of shape, and₁＞λ₂deleting ∈ the aspect ratio in the shape topology tree is not less than the aspect ratio threshold₀The shape of (2).

7. The method for rendering the non-photorealistic image based on the topology tree according to any one of claims 1 to 3, wherein:

the shape attribute in the step 2 comprises the shape area, namely the sum of pixels in the shape, and the area in the deleted shape topological tree is not more than the area threshold valueThe shape of (2).

8. The method for rendering the non-photorealistic image based on the topology tree according to any one of claims 1 to 3, wherein:

the shape attribute described in step 2 includes the compactness of the shapeWherein,is the area of the shape, λ₁And λ₂Is the eigenvalue of the second order inertia matrix of shape, and₁＞λ₂deleting the shape topology tree with a compactness not greater than a compactness threshold k₀The shape of (2).

9. The method for rendering the non-photorealistic image based on the topology tree according to any one of claims 1 to 3, wherein:

the shape attribute described in step 2 includes a shape-to-scale ratioWherein,is the area of the shape, S_i ^rIndicates the shape S_iIn the shape topological tree, the shape of an ancestor at the r-th layer, M is a self-defined stage range; deleting the shape topology tree with the scale ratio not greater than the scale ratio thresholdα₀The shape of (2).