CN103810729B - A kind of based on isocontour raster image vector quantized method - Google Patents

Abstract

The present invention is open a kind of based on isocontour raster image vector quantized method.First generated corresponding gray-scale map by raster image, then set up picture altitude field with the gray-scale map after smoothing；Extract the contour point in height field, and determine its color；Set up isocontour parameter curve mathematical notation by contour point, and determine the color of any point on equal pitch contour.The vector quantization being raster image with the parameter curve set of colouring information represents.When being represented reconstruction raster image by vector quantization, first according to the size of raster image yet to be built, the parameter curve of vector quantization is implemented scaling and discretization operations, determine position and the color of its each pixel occupied in image yet to be built；Using colored pixels as primary data, color method of diffusion is used to rebuild the raster image of vector representation.The present invention can carry out multiple dimensioned vectorized process to various raster images, and relevant parameter can be utilized to control the data volume of vectogram, vector representation can reconstruct the raster image of multiresolution.

Description

A kind of based on isocontour raster image vector quantized method

Technical field

The invention belongs to digital image processing field, relate to the vectorized process technology of a kind of raster image, particularly relate to A kind of raster image vector quantized method based on contour lines extraction.

Background technology

In digital image processing techniques field, two ways is had to describe piece image: grating representation and vector table Show mode.Iamge description is the rectangular lattice being made up of the discrete pixels of rule by grating representation, and the most each pixel is deposited Store up different shading values (brightness or color).Represent that the raster image that a width is bigger typically requires more data volume, take Bigger memory space；When raster image is zoomed in and out, at the boundary profile of color block areas, often produce zigzag Lose shape.The image of vector representation then represents image with geometric graphic elements such as point, straight line or polygons.Relative to raster image, vow Spirogram picture typically requires less data amount, is also easier to editor and amendment, and does not haves saw during image scaling Tooth loses shape and obscures the phenomenons such as distortion.Raster image and vector image have obtained extensively due to respective feature in different fields General application.Along with network and the development of communication technology and the increasingly extensive application of various high performance of mobile equipments, people's logarithm Amount of storage and the editability of word image are had higher requirement.In order to adapt to the current demand in multimedia application, in recent years The scholars carrying out image processing field have started to carry out coloured image the research work of vectorized process.The most existing multiple base Raster image vector quantized method in different technologies thought.

A kind of raster image vector quantized technology based on Octree Color Quantization Algorithm (see: Geng Guohua etc. based on eight forks The color quantization algorithm of tree construction. small-sized microcomputer system, 1997,18 (1): 24-29).The method first uses Octree face Color quantization algorithm reduces the number of colours of image, then goes out the region of each color composition with curve tracing.Such method is not Foot is, image volume is only melted into more color section, just can obtain reasonable vector quantization effect, therefore vector quantization literary composition The data volume of part is bigger.

Raster image vector quantized technology that one class is split based on image (see: Lecot G, Levy B.ARDECO: Automatic region detection and conversion.In:17^th Eurographics Symposium on Rendering,2006,1604-1616).This technology is by segmenting the image into some region units, then goes out often with curve tracing The border of individual zonule, determines the gradual change type Fill Color of each zonule tracked out simultaneously.The deficiency of such method is, no Can image that preferably apparent color details is complicated.

A kind of raster image vector quantized technology based on gradient grid (sees: Sun J, Liang L.Image vectorization using optimized gradient meshes.ACM Transactions on Graphics, 2007,26(3):1-7).Such technology as element figure with gradient grid, is divided into some gradient grids figure, passes through Interpolation calculation goes out the color between grid.This technology can the image of Precise Representation gradation of hue, but due to quadrilateral mesh itself Limitation, be relatively difficult to the image that vector quantization represents that some topological structure are complicated.

A kind of raster image vector quantized technology based on diffusion profile (sees: Orzan A.Diffusion curves:a vector representation for smooth-shaded images.ACM Transactions on Graphics, 2008,27(3):1-8).This technology is using diffusion profile as the geometric primitive of vector image, by using Bézier curve fitted figure The marginal information of picture, and determine that the color value information at control point, given curve both sides and fuzzy value information generate vector image, Rear employing Poisson diffusion couple vector image carries out rasterisation and rebuilds.The main uses of the method is used to set up cartoon image, energy Enough represent the image that color detail is complex, but amount of calculation is bigger.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, open a kind of based on isocontour raster image vector quantized method, pass through Extract the equal pitch contour in the gray-scale map height field of raster image, and use color diffusion technique etc. to realize the vector of raster image Changing, it is possible to make up problem computationally intensive in existing vector technology, the image that its rasterisation is rebuild can more approach original graph Picture；Meanwhile, the inventive method also supports the multi-resolution hierarchy in vector quantization process.

The present invention is by the following technical solutions:

A kind of based on isocontour raster image vector quantized method, the steps include:

(1) raster image is carried out gray processing pretreatment: order will the raster image of vector quantization be source images I₁, by source figure As I₁Transform into gray-scale map I₂If, it may be assumed that source images I₁Itself is gray level image, then make I₂=I₁；If source images I₁For cromogram Picture, then by coloured image is carried out gray processing process, obtain gray-scale map I₂；

(2) gray-scale map is filtered pretreatment: use the digital picture smothing filtering operator gray-scale map to raster image I₂It is smoothed, filters gray-scale map I₂In noise signal, the color change in softening image, obtain the gray scale after denoising Figure I₃；

(3) vector quantization sampled point is extracted: by gray-scale map I₃The gray value of middle pixel, as height value, sets up the height of image ?；The contour value parameter of series utilizing input extracts the contour point in gray-scale map height field, referred to as sampled point, and is determined by The color value that each contour point is corresponding, obtains the sampled point with colouring information；

(4) parameter curve of sampled point: use parameter curve method to be set up each bar by sampled point isocontour Parameter curve C₁；And determined parameter curve C by the colouring information of each sampled point₁The functional relation of upper difference color, thus To the parameter curve C that addition of colouring information₂；By each bar curve C₂The curve set constituted, is the vector quantization table of former raster image Show；

(5) rasterisation that vector quantization represents: according to the resolution set, each bar parameter curve C during vector quantization is represented₂ Carry out proportional scaling, obtain the parameter curve C that the vector quantization consistent with set resolution represents₃, and synchronously bent to parameter Line C₃On color corresponding relation be adjusted；By parameter curve C₃The enterprising line rasterization of image in new settings resolution is discrete Process, determine its each location of pixels occupied in image yet to be built；Then according to parameter curve C₃Upper additional color letter Breath, calculates the color value of above-mentioned pixel, above-mentioned pixel is included into image original pixels point set S yet to be built；

(6) color diffusion: using original pixels point set S as the raw information of image yet to be built, pixel therein is made Source is spread for color；By processes such as simulation conduction of heat, color diffusion source calculate undefined pixel in raster image yet to be built Color value, the rasterisation reconstructing vector image represents.

The present invention, on the basis of contour lines creation technology, proposes a kind of raster image vector quantized method.The method is borrowed Help the preprocessing means such as image gray processing, digital picture filtering, according to distinctive regular grid contour lines creation algorithm, more essence Really it is extracted the equal pitch contour of image as contour line, it is achieved that the vector quantization of raster image；Simultaneously also by equal pitch contour Carry out rasterization process, use color to spread the reconstruction of raster image.The principle of the invention is simple, easily controllable, calculate speed Degree is quick, can be used for carrying out various raster images multiple dimensioned vectorized process, and contour lines extraction parameter can be utilized Control the data volume of vector image, vector image can reconstruct the raster image of different resolution.

Accompanying drawing explanation

The flow chart of Fig. 1: the inventive method.

Fig. 2: gray-scale map example.

Fig. 3: the height field situation generated by image.

Fig. 4: the digital terrain elevation model represented by regular rectangular lattice.

Fig. 5: (a) (b) (c) (d) is that equal pitch contour is by four kinds of trends during adjacent grid limit.

Fig. 6: by the equal pitch contour bunch example of two kinds of different resolutions of image zooming-out in accompanying drawing 2, (a) is that low resolution is contour Line bunch, (b) is high-resolution equal pitch contour bunch.

Fig. 7: the actual example of raster image contour lines extraction；Wherein (a) is original image, and (b) (c) (d) is equal pitch contour Number is respectively n=3, the equal pitch contour of the different scale extracted when n=5, n=10.

Fig. 8: the data change over condition during raster image vector quantized；Wherein (a) is original image, and (b) is equal pitch contour Geometric representation, (c) is the vector representation of image colorant (gray scale).

Fig. 9: represented the raster image of the different scale reconstructed by vector quantization；Wherein (a) (b) (c) is equal pitch contour respectively Number is n=3, when n=5, n=10, the raster image of the different scale reconstructed.

Detailed description of the invention

With embodiment, the present invention is elaborated below in conjunction with the accompanying drawings.

As it is shown in figure 1, the raster image vector quantized method of the present invention is made up of vector quantization stage and reconstruction stage two parts altogether, Being correlated with, it is as follows to be embodied as step:

Raster image I according to user's input₁And vector quantization controls parameter (Gaussian Blur coefficient δ, equal pitch contour number n Deng), the vector image of structure raster image.

1. pair raster image carries out gray processing pretreatment: in the present embodiment, if I₁For gray level image, then gray-scale map I₂=I₁, Gray processing has worked；If I₁For coloured image, then weighted mean method is used the RGB information of colored raster images pixel to be turned Change half-tone information into, obtain corresponding gray-scale map I₂, specific practice is: set colored raster images I₁In any one pixel p (x, y) RBG color component be respectively r, g, b, be weighted averagely obtaining its gray value being gray=α r+ β g+ γ b to them, wherein Parameter alpha, β, γ (alpha+beta+γ=1) carry out value according to the importance etc. of corresponding color component.Owing to human eye is to green sensitivity Spending the highest, redness is taken second place, blue minimum, and the weighted average formula that the present embodiment uses is: gray=0.30r+0.59g+0.11b. Obviously, gradation of image value in interval [0,1].Fig. 2 is the example of a gray-scale map.

2. pair gray-scale map carries out smothing filtering pretreatment: the present embodiment uses Gaussian filter to gray-scale map I₂Smooth Process, and regulate the wave filter degree to image smoothing by support width parameter δ of Gaussian function.In the process realized In, first by one-dimensional Gaussian function:

$K=\frac{1}{\sqrt{2\mathrm{\π\δ}}}{e}^{-\frac{i*i}{2\mathrm{\δ}*\mathrm{\δ}}}---\left(1\right)$

Wherein i is blur radius, and template and width parameter δ by setting are calculated one-dimensional gaussian filtering core, and It is normalized the coefficient T obtaining one-dimensional gaussian filtering；Then by first for coefficient T and gray-scale map I₂In in the x-direction as The gray value of vegetarian refreshments is weighted averagely, obtains " temporarily " gray-scale map, transposition " temporarily " gray-scale map, obtains gray-scale map I'₂.Profit again With coefficient T and gray-scale map I'₂In the gray value of pixel in the y-direction be weighted averagely；Image transposition is gone back to original position, Obtain the gray-scale map I filtered₃。

3. extract vector quantization sampled point: the present embodiment is by extracting the contour point in gray-scale map height field as raster image Vector quantization sampled point.First by the preprocessed gray-scale map I obtained₃Gray value as height value, generate the height of image Field (seeing accompanying drawing 3)；Then by gray-scale map I₃In pixel p (x, y) as regular grid node, constructs by regular rectangular shape Digital terrain elevation model (seeing accompanying drawing 4) represented by grid.If minima and the maximum of elevation divide in picture altitude field Wei h_minAnd h_max, then according to the equal pitch contour number n, the vertical separation value Δ h that can obtain between adjacent contour set it is:

$\mathrm{\Δh}=\frac{h_{\max }-h_{\min }}{n-1}---\left(2\right)$

At this moment, height value h is taken_i:

h_i=h_min+ i × Δ h, (i=0,1,2 ..., n) (3) are as each bar equal pitch contour C that will extract_iHeight value. In extracting gray-scale map, height value is h_iContour point during, first all Grid Edges in regular grid are all labeled as " untreated "；Finding height value again is h_iEqual pitch contour C_iOn seed points v_k, method particularly includes: successively in scanning rule grid It is labeled as the Grid Edge e of " untreated ", and the limit e of mark scan is " processed ".Relatively equal pitch contour C_iHeight value h_iWith limit Two summits of eWith) height valueWithRelation, it is judged that equal pitch contour C_iWith limit e whether phase Hand over:

If $\left(h_k^1\text{-}{h}_i\right)(h_k^2-h_i)>0,$ Then C_iDo not intersect with limit e；

If (Then C_iIntersect with limit e, relevant intersection v (x, y) can be calculated by following formula:

$\left\{\begin{array}{c}x=x_k^1+\frac{h_i-h_k^i}{h_1^2-h_k^1}(x_k^2-x_k^1)\\ y=y_k^1+\frac{h_i-h_k^1}{h_k^2-h_k^1}(y_k^2-y_k^1)\end{array}\right.---\left(4\right)$

And (x y) is stored in dique L by v.

Then with v, (x, y) is seed points, is followed the trail of by limit e and finds current equal pitch contour C_iUpper v (follow the trail of by x, follow-up some y) Direction is as shown in Figure 5: for rectangle rule grid, all pick up from Grid Edge due to sampled point, equal pitch contour C_iBy adjacent The trend of grid cell have four kinds may: from top to bottom, from left and right, from bottom to top, from right and left.According to equal pitch contour C_iWalk To, it is judged which bar and equal pitch contour C in other three Grid Edges in the grid at e place, limit_iIntersect, calculate corresponding intersection point, And be deposited in queue L, the Grid Edge that mark access is crossed simultaneously is " processed ".Using above-mentioned intersection point as new seed Point, recurrence finds C_iOn follow-up point, until C_iUpper all of contour point has been searched for.It is labeled as " processed " if searched Grid Edge, or search follow-up point and be positioned on the border of regular grid, then terminate recursive search process.If searching labelling For the Grid Edge of " processed ", then current equal pitch contour C_iFor closed curve, C_iOn all contour points searched for；If searching Follow-up point is positioned on regular grid border, then regard current equal pitch contour C_iFor open curve, the most again from initial seed points v (x, y) Rise, continue search for contour point along current isocontour opposite direction, and the contour point searched is inserted into another of queue L End.Recursive search repeatedly, until searching till follow-up point is positioned on regular grid border.At this moment, C_iUpper all of contour point Search completes.

It follows that continue to scan in regular grid the Grid Edge being labeled as " untreated ", searching height value is h_iContour Point, until having searched for all of Grid Edge.If there being new contour point found, illustrate that there is more than one height value is h_iEtc. High line, uses process similar to above to determine its contour point；Repeatedly such, until height value is h_iEqual pitch contour be search Out.Each queue L only stores the contour point on an equal pitch contour, if having the high level such as a plurality of is h_iEqual pitch contour, respectively by it Be stored in different queue L.Accompanying drawing 6 is the equal pitch contour bunch of the two kinds of different resolutions extracted by accompanying drawing 4.

By initial raster image I₁In pixel and regular grid node one_to_one corresponding, and take the face of regular grid node Colour is source images I₁The color value of middle respective pixel point.Making height value is h_iArbitrary contour point v_kCorresponding color value is v_k(r_k,g_k,b_k), its value can be by the color value on two summits on the Grid Edge at vk placeWith And height valueWithInterpolation obtains, and computational methods are:

$s_k=s_k^1+\frac{h_i-h_k^1}{h_k^2-h_k^1}(s_k^2-s_k^1),s=r,g,b---\left(5\right)$

The contour point that addition of colouring information is raster image I₁Vector quantization sampled point.

Accompanying drawing 7 is the actual example of raster image contour lines extraction.Wherein Fig. 7 (a) is original grating image, Fig. 7 (b) C () (d) is equal pitch contour number n=3 respectively, the equal pitch contour of the different scale extracted when n=5, n=10.

4. the parameter curve of sampled point: set a wherein isocontour sampled point and be classified as l_i(i=1,2 ..., m), first First according to sampling point range l_iThe control vertex p of reverse B-spline Curve_i(i=0,1,…,m,m+1).By B-spline Curve Character, have p_i-1+4p_i+p_i+1=6l_i(i=1,2 ..., m), wherein have m equation, m+2 unknown number, supplement suitable border Condition, i.e. increases by two equations, makes above-mentioned equation group to solve.

In the present embodiment, for open curve, that given is first control point p on the border of free end points, i.e. curve₀With Second control point p₁Overlap, the m+1 control point p_m+1With m-th control point p_mOverlap, even p₀=p₁, p_m+1=p_m, square can be obtained The equation group of formation formula

$\left[\begin{array}{ccccccc}5& 1& 0& ...& 0& 0& 0\\ 1& 4& 1& ...& 0& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& ...& 1& 4& 1\\ 0& 0& 0& ...& 0& 1& 5\end{array}\right]\left[\begin{array}{c}{p}_1\\ p_2\\ \·\\ \·\\ \·\\ p_{m-1}\\ p_m\end{array}\right]=6\left[\begin{array}{c}{l}_1\\ l_2\\ \·\\ \·\\ \·\\ l_{m-1}\\ l_m\end{array}\right]---\left(6\right)$

Chasing method is used to solve the control vertex p obtaining cubic B-spline_i；

For closed curve, its boundary condition is p₀=p_m, p_m+1=p₁, then the equation group that matrix form represents can be obtained

$\left[\begin{array}{ccccccc}4& 1& 0& ...& 0& 0& 1\\ 1& 4& 1& ...& 0& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& ...& 1& 4& 1\\ 1& 0& 0& ...& 0& 1& 4\end{array}\right]\left[\begin{array}{c}{p}_1\\ p_2\\ \·\\ \·\\ \·\\ p_{m-1}\\ p_m\end{array}\right]=6\left[\begin{array}{c}{l}_1\\ l_2\\ \·\\ \·\\ \·\\ l_{m-1}\\ l_m\end{array}\right]---\left(7\right)$

Square-root method is used to solve the control vertex p obtaining cubic B-spline_i。

According to control vertex p_i, can obtain B-spline curve curve:

$L_i\left(t\right)=\frac{1}{6}\left[\begin{array}{cccc}1& t& t^2& t^3\end{array}\right]\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{p}_{i-3}\\ p_{i-2}\\ p_{i-1}\\ p_i\end{array}\right]t\∈\begin{array}{c}\left[\begin{array}{c}\mathrm{0,1}\end{array}\right]\end{array};i=\mathrm{3,4},......,m+1---\left(8\right)$

By control point p_iIt is end to end and through oversampled points row l that interpolation goes out m bar_iB-spline curves section, the parameter of the highest line Represent C₁。

According to the colouring information of each sampled point, interpolation goes out equal pitch contour C₁The color value of upper difference, obtains addition of color The parameter curve C of information₂.Each bar C₂Set, the vector quantization being former raster image represents.

Accompanying drawing 8 is the example of raster image vector quantized process.Wherein Fig. 8 (a) is original grating image；Fig. 8 (b) is image Vector quantization represent, in figure, curve is represented by parameter curve；Fig. 8 (c) is the vector representation of coloring (gray scale).

5. the rasterisation of parameter curve: according to the resolution set, by the control point of proportional scaling B-spline curves p_i, to parameter curve bunch C₂Zoom in and out process, be allowed to adapt with the size of image yet to be built, the C after scaling₂For image yet to be built Vector quantization represent, note for C₃.The present embodiment uses the rasterization algorithm of algebraically B-spline curves based on regularity conditions, right Parameter curve C₃In the image yet to be built enterprising line raster discrete processes of new settings resolution, determine that it is shared in image yet to be built According to each location of pixels (specific practice sees: Huang Jinji. algebraic curve real-time Rasterization. Zhejiang: Zhejiang University, 2012: 40-51)；Then according to the colouring information that parameter curve is additional, (x, y), by above-mentioned pixel to calculate color value c of above-mentioned pixel It is included into image original pixels point set S yet to be built.

6. color diffusion: the present embodiment is first according to image original pixels point set S yet to be built, by raster image I yet to be built Pixel be respectively labeled as " colored spots " and " non-staining point ", be wherein included into set S pixel be labeled as " colored spots ", remaining Pixel is classified as " non-staining point ".

Scanning the pixel in raster image I yet to be built successively, if " colored spots ", (x, y) in the process of iteration for its color value i Middle holding initial value is constant, i.e. and i (x, y)=c (x, y)；" if non-staining point ", its color value i (x, y) during iteration, By constantly solve Laplace equation carry out color diffusion obtain.The color diffusion of the present embodiment uses 5 differences of Laplace Cellular represents:

Δ i (x, y)=4i (x, y)-(i (x-1), y)+i (x+1, y)+i (x, y+1)+i (x, y-1))=0 (9)

Iterative process is by Artificial Control, and when the color value of image tends towards stability, iteration terminates, and the reconstruction of raster image is complete Become.

Accompanying drawing 9 is the example of the raster image reconstruction of different scale.Wherein Fig. 9 (a) (b) (c) is equal pitch contour number n=respectively The raster image of the different scale rebuild when 3, n=5, n=10.

Claims (1)

1., based on an isocontour raster image vector quantized method, the steps include:

(1) raster image is carried out gray processing pretreatment: order will the raster image of vector quantization be source images I₁, by source images I₁ Transform into gray-scale map I₂If, it may be assumed that source images I₁Itself is gray level image, then make I₂=I₁；If source images I₁For coloured image, Then by coloured image is carried out gray processing process, obtain gray-scale map I₂；

(2) gray-scale map is filtered pretreatment: use the digital picture smothing filtering operator gray-scale map I to raster image₂Carry out Smoothing processing, filters gray-scale map I₂In noise signal, the color change in softening image, obtain the gray-scale map I after denoising₃；

(3) vector quantization sampled point is extracted: by gray-scale map I₃The gray value of middle pixel, as height value, sets up the height field of image；Profit Extract the contour point in gray-scale map height field, referred to as sampled point by the contour value parameter of series of input, and be determined by each etc. The color value that high point is corresponding, obtains the sampled point with colouring information；

(4) parameter curve of sampled point: use parameter curve method to be set up the isocontour parameter of each bar by sampled point Curve C₁；And determined parameter curve C by the colouring information of each sampled point₁The functional relation of upper difference color, thus obtain attached Add the parameter curve C of colouring information₂；By each bar curve C₂The curve set constituted, the vector quantization being former raster image represents；

(5) rasterisation that vector quantization represents: according to the resolution set, each bar parameter curve C during vector quantization is represented₂Carry out Proportional scaling, obtains the parameter curve C that the vector quantization consistent with set resolution represents₃, and synchronously to parameter curve C₃On Color corresponding relation be adjusted；By parameter curve C₃Image enterprising line raster discrete processes in new settings resolution, Determine its each location of pixels occupied in image yet to be built；Then according to parameter curve C₃Upper additional colouring information, meter Calculate parameter curve C₃The color value of each occupied pixel, and each pixel calculating color value is included into image yet to be built Original pixels point set S；

(6) color diffusion: using original pixels point set S as the raw information of image yet to be built, using pixel therein as face Color diffusion source；By processes such as simulation conduction of heat, color diffusion source calculate the color of undefined pixel in raster image yet to be built Value, the rasterisation reconstructing vector image represents.