CN103700064A - Anisotropism wavelet image processing method based on thermonuclear pyramid - Google Patents

Abstract

The invention provides an anisotropism wavelet image processing method based on a thermonuclear pyramid. According to the method, at the theoretical part, wavelets are obtained through thermonuclear difference between adjacent layers of an image pyramid, and are equal to negative one order derivation of a thermal diffusion partial differential equation, relative to time; at an implementation part that: 1), mapping images to be a weight undirected graph, coding structural characteristics into a Laplacian matrix, and achieving anisotropism thermal diffusion; 2), dividing the images into image subblocks with overlaps, calculating wavelets of all image blocks in a parallel mode, reducing calculated amount by using a block overlapping method and effectively eliminating blocking effects after recombination; 3), adopting Krylov subspace technology to accelerate image block wavelet transform calculation, and avoiding time-consuming matrix spectral factorization. At the application part, the method is applied to image processing with structural protecting function. The data related anisotropism wavelet system provided by the invention achieves structure protection multiscale decomposition for the images, and shows excellent performance in various image processing applications.

Description

Based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route

Technical field

The present invention relates to a kind of based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route.

Background technology

At computer picture and computer vision field; limit protecting filter is by extensive concern and research; and be applied in multiple Computer Image Processing application, such as: limit protection is level and smooth, details strengthens, image is painted, high dynamic range images compression, image stylization etc.Between nearest decades, the various algorithms with structure consciousness are suggested, and have obtained remarkable effect, effectively protect the intrinsic structure of image when the goal in research of this direction is level and smooth inessential details.

Structure consciousness wave filter can be divided into two large classes: local filter and global filtering device.Local filter is conventionally centered by certain pixel, all pixels around calculating with certain rule in neighborhood and the similarity between this central pixel point, the filtered gray-scale value of this pixel be around in neighborhood the weight of pixel and, its Typical Representative is two-sided filter.The emphasis of this research mainly concentrates on the similarity calculation method between pixel, and current algorithm is mainly to utilize gray-scale value, volume coordinate, geodesic distance etc., but this wave filter exists the defect on blurred picture border.The core concept of global filtering device is global optimization, when utilizing optimized principle to keep one-piece construction consistent, realize the filtering of image and process, the Typical Representative of such wave filter has based on weight least-squares algorithm (WLS) HeL0 global optimization method etc.The advantage of such wave filter be for can well protect the structural information of high-contrast, but cannot effectively process local detail, and filtered effect presents too level and smooth simultaneously.

The problem that at present structure consciousness wave filter faces has: how effectively to extract the structural information in image, during multiple dimensioned decomposition, how effectively to process remarkable limit, and how negative margin around halation phenomenon generation and eliminate gradient flop phenomenon.

In order to address the above problem; the present invention is based on thermonucleonics and proposed to have the anisotropy Wavelet image disposal route of structure consciousness; the method is encoded to the structural information of image in the structure of figure Laplacian Matrix; during multiple dimensioned decomposition, can effectively extract and protect the inherent structure information of image; the local wavelet algorithm proposing can be applicable in multiple computer vision Processing tasks, and presents remarkable effect.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the data independence of existing wave filter and the deficiency of structure consciousness, provide a kind of based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route.And by using based on image divide-and-conquer strategy and Krylov subspace algorithm, improved the practical feasibility of the relevant wavelet algorithm of data of inventing.

The technical solution used in the present invention is: a kind of based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route, comprise following a few part:

The theory of step (1), anisotropy small echo is derived: the deriving analysis of leading by the negative second order that is Gaussian function to Mexico's hat wavelet, and Gaussian function is the characteristic of the analytical solution of thermal diffusion partial differential equation in Euler space, this invention has provided the representation of Mexico's hat wavelet about thermonuclear, it is led about the negative single order of time for thermonuclear, and the discrete representation form of this small echo and Anisotropic Wavelet Transform and inverse transformation thereof have been defined;

Step (2), the anisotropy thermal diffusion based on figure Laplce: this invention has proposed a kind of limit weight mapping method, by grey scale pixel value and gradient magnitude, calculate similarity degree, image pixel lattice is mapped as to weight non-directed graph, thereby build, there is the figure Laplacian Matrix that structure consciousness is relevant with data, the intrinsic structural information that has slipped into image of this figure Laplce matrix computations method, therefore thermal diffusion is anisotropy, and formed small echo is anisotropic;

Step (3), thermal image are assessed the divide-and-conquer strategy of calculation: by the Laplacian Matrix calculating in step (2), because image dimension is when larger, the dimension of corresponding Laplacian Matrix will increase fast, thereby caused the storage of large-scale matrix and feature decomposition extremely difficult, therefore this invents the Gauss's decay characteristics based on thermonuclear, use image block calculative strategy has been proposed, and each interblock exists overlapping, realize the parallel computation of each image subblock thermonuclear, improved the practical feasibility of the wavelet algorithm proposing; For further accelerating algorithm, this invention proposes to realize with Krylov sub-space technique the quick calculating of wavelet transformation;

Step (4), anisotropy Wavelet image are processed: Fast implementation in the theory derivation based on step (1) and step (2), step (3); the anisotropy small echo proposing can be applied to multiplely having during image that structural defence requires processes, such as image smoothing, figure image intensifying, the operation of high-definition image tone, image stylization etc.

Further, the wavelet method described in step (1) is anisotropic, not only has the various characteristics of Mexico's hat wavelet, but also built-in data are relevant and the characteristic of structure consciousness.

Further, the computing method of the figure Laplacian Matrix described in step (2), are mapped as limit weight by pixel gray-scale value and gradient magnitude, have good limit and stop and structural defence characteristic.

Further, the use of passing through image to be divided into image block and the Krylov subspace method with lap described in step (3), while having avoided high, the global characteristics of consumption decomposes, and has strengthened the practical feasibility of the local wavelet algorithm proposing.

Principle of the present invention is:

(1) by tight mathematical derivation, in Euler space, Ke Jiang Mexico hat wavelet is expressed as thermonuclear and leads about the negative single order of time, and the thermonuclear that its discrete representation form is adjacent yardstick is poor, and this invention has provided the representation of Mexico's hat wavelet about matrix spectra.The small echo that the method proposes is except having the characteristic of Mexico's hat wavelet, also built-in data dependence.This invention, by building multiscale space with thermonuclear pyramid and time, makes formed small echo have the multiple dimensioned concept on room and time.

(2) small echo proposed by the invention mainly lays particular emphasis on structure consciousness and anisotropy, make formed small echo there is good limit and stop characteristic, this invention is weighed the similarity between pixel based on grey scale pixel value and gradient magnitude, and be mapped as heat conducting limit weight, by the method, the structural information efficient coding of image has been arrived in small echo, made formed small echo there is anisotropy.

(3) the spectral factorization time complexity of large-scale matrix is O(n ³), therefore conventionally cannot carry out direct spectral factorization operation to the Laplacian Matrix by after the mapping of image lattice, also limited greatly the practical feasibility of the method, the present invention proposes image to carry out the divide-and-conquer strategy that piecemeal builds small echo for this reason, and interblock exists overlapping, the blocking effect while having eliminated image reorganization in the time of overlap partition strategy accelerating algorithm.This invention has simultaneously utilized Krylov sub-space technique, further improves the speed of Anisotropic Wavelet Transform.

The present invention's advantage is compared with prior art:

1, the small echo based on thermonuclear gold tower that the present invention proposes, the structure that makes on the one hand small echo is that data are relevant, has improved the structure consciousness ability of small echo, makes on the other hand proposed small echo have the multiple dimensioned characteristic on time and space.

2, contrast existing limit protection filtering method, the wavelet method based on physical thermal diffusion that the present invention proposes, has better structured coding and limit protective value.

3, the image divide-and-conquer strategy that the present invention proposes, has avoided the spectral factorization of higher dimensional matrix, has effectively accelerated wavelet transformation, has improved the feasibility of algorithm.

Accompanying drawing explanation

Fig. 1 is based on the pyramidal anisotropy Wavelet image of thermonuclear processing flow chart;

Fig. 2 is the discrete construction schematic diagram based on thermonuclear pyramid small echo;

Fig. 3 is the structure consciousness scatter diagram of small echo;

Fig. 4 is limit weight mapping schematic diagram; Wherein, (a): former figure; (b): gradient magnitude; (c): spatial similarity; (d): similarity of the present invention;

Fig. 5 is image divide-and-conquer strategy schematic diagram;

Fig. 6 is the level and smooth schematic diagram of one-dimensional signal; Wherein, (a): WLS algorithm (2008); (b): Subr et al.(2009); (c): DT algorithm (2011); (d): algorithm of the present invention;

Fig. 7 is image smoothing contrast schematic diagram; Wherein, (a): input picture; (b): WLS algorithm (2008); (c): DT algorithm (2011); (d): L0 algorithm (2011); (e): algorithm of the present invention;

Fig. 8 is that image detail strengthens Contrast on effect schematic diagram; Wherein, (a): WLS algorithm (2008); (b): EAW algorithm (2009); (c): DT algorithm (2011); (d): algorithm of the present invention;

Fig. 9 is high-definition image tone operation contrast schematic diagram; Wherein, (a): WLS algorithm (2008); (b): EAW algorithm (2009); (c): DT algorithm (2011); (d): L0 algorithm (2011); (e): algorithm of the present invention.

Embodiment

Below in conjunction with the drawings and the specific embodiments, further illustrate the present invention.

Fig. 1 has provided the overall process flow based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route.

The invention provides a kind ofly based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route, it is theoretical derives and key step is described below:

1. the theory based on the pyramidal anisotropy small echo of thermonuclear is derived

The method, by analyzing the potential mathematical relation of thermonuclear and Mexico's hat wavelet, has provided the representation of the local small echo of anisotropy proposed by the invention.First, the negative second order that Mexico's hat wavelet is Gaussian function is led, and its expression formula may be defined as

this expression formula and thermal diffusion partial differential equation

have close contact, wherein Δ is Laplace operator.In Euler space, Gaussian function G (x, t) is the analytical solution of thermal diffusion equation, and definable Mexico hat wavelet is that Gaussian function is led about the negative single order of time t thus,

on popular, the solution of thermal diffusion partial differential equation is referred to as thermonuclear, therefore in Euler space, can substitute Gaussian function with thermonuclear, the thermonuclear representation of Mexico's hat wavelet is defined as thermonuclear and leads about the negative single order of time t,

by means of the spectral factorization of Laplacian Matrix, the Mexico's hat wavelet based on thermonuclear representation is defined as

λ wherein _iand φ _ibe respectively resulting i the eigenwert of Laplacian Matrix spectral factorization and corresponding proper vector thereof, and all eigenwerts are non-negative, and meet ascending order and arrange (0=λ ₀< λ ₁≤ λ ₂≤ ...), proper vector forms one group of orthogonal basis.

Mexico's hat wavelet based on above is about the derivation of thermonuclear representation, and the present invention has further defined the discrete representation form of this small echo, and it is poor that the small echo invented may be defined as the thermonuclear of adjacent time t: Ψ (x, y, t _i)=h (x, y, t _i)-h (x, y, t _i+1), wherein t represents yardstick the time, and little t has represented HFS, and large t is relevant to low frequency, therefore can construct by different time t a metric space.

The present invention has simultaneously applied proposed small echo in thermonuclear pyramid structure, makes this small echo possess multilayer metric space, and in like manner small echo defined above, may be defined as Ψ (x, y, t based on the pyramidal small echo of thermonuclear _i, k)=h (x, y, t _i, k)-↑ h (x, y, t _i, k+1), h (x, y, t wherein _i, k) be expressed as k layer t _ithermonuclear value constantly, the operation of symbol " ↑ " presentation video up-sampling.Fig. 2 has provided the discrete construction schematic diagram based on thermonuclear pyramid small echo.

Small echo based on thermonuclear gold tower proposed by the invention not only has the Multi scale characteristic of pyramid structure, also has the multiple dimensioned characteristic in pyramidal layer simultaneously, and this small echo depends on the partial structurtes of image and good concussion Decay Rate.Because invented small echo is derived by thermonuclear, so this small echo inherited all multiattributes of thermonuclear, such as: symmetry, multiple dimensioned, stability, Gauss's decay, be rich in the characteristics such as information.In addition, this small echo also has other characteristics, such as zero-mean, convergence etc.Below provide the mathematical analysis of correlation properties:

Zero-mean: preset time t and pyramidal layer value k, for x, about the thermonuclear of any y, meet 0≤h (x, y, t _i, k)≤1 He

based on the discrete representation form of invention small echo be that adjacent layer thermonuclear is poor, so this small echo meets the characteristic of zero-mean, ${\mathrm{\&Sigma;}}_{y=1}^N\mathrm{\&psi;}(x,y,t,k)=0.$

Convergence: for given layer value k, during for t → ∞, thermonuclear

reach steady state (SS), while being therefore t → ∞, Ψ (x, y, t, k)=0 reaches convergence.

Fig. 3 provides small echo of the present invention at the dispersal waveform figure of different time t, and as seen from the figure, small echo of the present invention is that data are relevant, has good structure consciousness and concussion Decay Rate.

Wavelet transformation and inverse transformation: based on the pyramidal small echo of heat, can be applicable in the multiple dimensioned decomposition of image, the wavelet transformation of its image is defined as:

<> is inner product operation, and W (x, t, k) is referred to as wavelet coefficient, and for fixed bed value k, l multi-scale wavelet transformation of image can generate l levels of detail

he Yige basic unit

this has been deconstructed into a multiscale space of layer k for multiple dimensioned minute.Because the thermonuclear that the discrete form of invented small echo is adjacent yardstick is poor, so the inverse transformation of this small echo only needs simple add operation to realize the Image Reconstruction of pyramid k layer,

so the inverse transformation of this small echo is fastish.

2. anisotropy small echo is about the computing method of figure Laplacian Matrix

In order effectively to extract the structural information of image, and be encoded in invented small echo and go, the present invention proposes to utilize grey scale pixel value and gradient magnitude to assess similarity, builds a weight non-directed graph G=(V, E), thus map image is that a two dimension is popular.Wherein summit V is corresponding to the pixel lattice in image, and the limit E between summit is determined by the weighted value of non-directed graph.

For each summit, limit weight is being controlled heat conducting speed, has played vital effect in anisotropy small echo, and limit weight is larger, and similarity is stronger, and thermal diffusion is faster, otherwise slower, even hot cannot conduction (when limit weight is zero).Therefore partial structurtes are mapped as limit weight and aspect the structural defence of small echo, are playing conclusive effect, and this weight has determined which structure should be protected, and which unessential information should be weakened.Below provide the detailed description of limit weighing computation method:

(1), the limit weight calculation based on gray-scale value

Conventionally similar gray-scale value should have higher similarity, should give higher limit weight, consider the impact of noise simultaneously, the present invention utilizes the gray scale vector in pixel local window to substitute simply and calculates limit weight with single grey scale pixel value, thereby improve noise immunity and the robustness of limit Weight algorithm, therefore based on gray-scale value, obtain limit weighing computation method as follows:

$s_{\mathrm{int}}(i,j)=\left\{\begin{array}{ccc}\exp (-{\left(\frac{d(i,j)}{{\mathrm{\&sigma;}}_{\mathrm{int}}}\right)}^2)& \mathrm{if}& j\&Element;N\left(i\right)\\ 0& & \mathrm{otherwise}\end{array}\right.,d(i,j)=\left|\right|{\stackrel{\&RightArrow;}{I_i}-\stackrel{\&RightArrow;}{I_j}\left|\right|}_2.$

Wherein d (i, j) represents the distance between pixel i and pixel j, and N (i) represents that the N of pixel i encircles all pixels in neighborhood,

with

the vector representation form that has represented respectively all pixels in pixel i and pixel j local window, ‖ ‖ ₂represented L2 normal form, parameter σ _intrepresented standard deviation; this parameter is for the structural defence ability of control algolithm; in order to make this parameter can be applicable to the image of different contrast; we need to be by the distance d (i between pixel; j) normalize to [0; 1], in actual image processing application, the span of this parameter is [0.05,0.3].

(2), the limit weight calculation based on gradient magnitude

Limit weighing computation method based on gray-scale value only can be weighed the similarity of color space above, lacks the concept of spatial similarity sex determination, and the method that therefore need to introduce spatial character aids in the calculating of limit weight between pixel.The most also that the simplest method is by volume coordinate (i, j) introduce in this calculating, but the calculating based on volume coordinate only can be used in the similarity of constraint space position, its similarity mapping graph is isotropic level and smooth decay pattern (as shown in Fig. 4 c), therefore utilize the method for volume coordinate not there is good structure consciousness performance, the present invention utilizes gradient magnitude to carry out the similarity between calculating pixel point for this reason, why using gradient magnitude is mainly to consider that the method can be good at judging border, at boundary, there is larger mould value, and at flat site, there is the mould value that is approximately zero, therefore little by very in its similarity of borderline region, flat site similarity is close to 1, limit weight calculation function based on gradient magnitude is as follows:

$s_{\mathrm{grad}}(i,j)=\exp (-\frac{{\max }_{x\&Element;\mathrm{line}(i,j)}{\left|\right|\mathrm{Grad}\left(x\right)\left|\right|}_2^2}{{\mathrm{\&sigma;}}_{\mathrm{grad}}^2}).$

Wherein line (i, j) represent to connect the straight line between pixel i and j, and x has represented to be positioned at pixel on this straight line, and Grad (x) has represented the gradient magnitude of pixel x, max function representation get the greatest gradient amplitude on this straight line, parameter σ _gradrepresent standard deviation, be used to control the respective degrees of opposite side.Therefore this function positioning boundary position preferably, can be used to the additional penalty item based on gray scale limit weighing computation method.

(3), limit weight mapping function

By the limit weighing computation method of above gray scale and gradient magnitude, final weight mapping function of the present invention is as follows: s (i, j)=s _grad(i, j) * s _int(i, j).Fig. 4 d has provided pixel i that the method calculates and the similarity between j and i and k, wherein color by ash to having represented that to black similarity is very high, more high and low more in vain.Color is more grey, and similarity is higher, and color is more black, and similarity is lower.As seen from the figure, although due to pixel i and the higher gray scale similarity of k, owing to having crossed over border, therefore there is lower limit weighted value, and between pixel i and j gray-scale value close and not crossing the boundary therefore there is higher limit weight.By Fig. 4 d, can also be found, institute's put forward the methods has good corresponding at boundary, therefore can effectively stop thermal diffusion at boundary.

Limit weighing computation method based on proposed, the building method of figure Laplce matrix L is as follows:

$L(i,j)=\left\{\begin{array}{ccc}{\mathrm{\&Sigma;}}_{j\&Element;N\left(i\right)}s(i,j)& \mathrm{if}& i=j\\ -s(i,j)& \mathrm{if}& j\&Element;N\left(i\right)\\ 0& & \mathrm{otherwise}\end{array}\right..$

The coding that this Laplacian Matrix is intrinsic the structural information of image, its dimension is | V| * | V|, | the pixel number in V| presentation video.By matrix L is carried out to spectral factorization, obtain building the local needed eigenwert of small echo of anisotropy and proper vector.

3. the pyramidal divide-and-conquer strategy of thermonuclear

In order to calculate the thermonuclear of whole image block, need to be to dimension | V| * | the Laplacian Matrix of V| carries out spectral factorization, conventionally the complexity of spectral factorization be O (| V| ³), for high-definition picture, because its pixel number magnitude is larger, it is extremely difficult therefore carrying out this spectral factorization operation, or even unpractical.In order to address this problem, the present invention is based on Gauss's attenuation attributes of proposed small echo, propose to use image divide-and-conquer strategy (as shown in Figure 5), image is divided into the image subblock with lap, each image subblock is built respectively to Laplacian Matrix, carry out spectral factorization, thereby avoid the overall spectral factorization of high storage and high time loss, effectively raise the computing velocity of algorithm.Wherein it should be noted that and between each image subblock, need to exist lap, why adopting the method is mainly the time t considering for large, its thermal diffusion may exceed the scope of image subblock, while the image reorganization after being processed by each image subblock being whole image, can avoid the generation of blocking effect simultaneously, the black image sub-block of should be in Fig. 5 introducing between light gray and gray image sub-block, makes image have lap between fast.

For above image divide-and-conquer strategy, the present invention has utilized Krylov sub-space technique to realize the wavelet transformation of image subblock simultaneously, has further accelerated the realization of algorithm, has improved the actual application value of algorithm.

4. the image of the local small echo of anisotropy is processed application

Proposed by the invention realizes by Matlab based on the pyramidal anisotropy wavelet algorithm of thermonuclear, operates in 64 systems of Windows7.The hardware configuration that experiment is used is Intel i7-3770 processor, 8G internal memory.This small echo can be applied to during the multiple image with structural defence requirement processes; Fig. 6～Fig. 9 has provided that institute's invention algorithm strengthens at one-dimensional signal and two dimensional image smoothing processing, image detail, the experiment effect figure of high-definition image tone operation, and has contrasted recent many algorithms.

The technology contents that the present invention does not elaborate belongs to those skilled in the art's known technology.

Although above the illustrative embodiment of the present invention is described; so that the technician of this technology neck understands the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various variations appended claim limit and definite the spirit and scope of the present invention in, these variations are apparent, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (4)

1. based on the pyramidal anisotropy Wavelet image of a thermonuclear disposal route, it is characterized in that comprising the following steps:

The theory of step (1), anisotropy small echo is derived: the deriving analysis of leading by the negative second order that is Gaussian function to Mexico's hat wavelet, and Gaussian function is the characteristic of the analytical solution of thermal diffusion partial differential equation in Euler space, provided the representation of Mexico's hat wavelet about thermonuclear, it is led about the negative single order of time for thermonuclear, and the discrete representation form of this small echo and Anisotropic Wavelet Transform and inverse transformation thereof have been defined;

Step (2), the anisotropy thermal diffusion based on figure Laplce: utilize limit weight mapping method, by grey scale pixel value and gradient magnitude, calculate similarity degree, image pixel lattice is mapped as to weight non-directed graph, thereby build, there is the figure Laplacian Matrix that structure consciousness is relevant with data, the intrinsic structural information that has slipped into image of this figure Laplce matrix computations method, therefore thermal diffusion is anisotropy, and formed small echo is anisotropic;

Step (3), thermal image are assessed the divide-and-conquer strategy of calculation: by the Laplacian Matrix calculating in step (2), because image dimension is when larger, the dimension of corresponding Laplacian Matrix will increase fast, thereby caused the storage of large-scale matrix and feature decomposition extremely difficult, so Gauss's decay characteristics based on thermonuclear, use image block calculative strategy has been proposed, and each interblock exists overlapping, realize the parallel computation of each image subblock thermonuclear, improved the practical feasibility of the wavelet algorithm proposing; For further accelerating algorithm, with Krylov sub-space technique, realize the quick calculating of wavelet transformation;

Step (4), anisotropy Wavelet image are processed: Fast implementation in the theory derivation based on step (1) and step (2), step (3); the anisotropy small echo proposing can be applied to multiplely having during image that structural defence requires processes, and described image is treated to image smoothing, figure image intensifying, the operation of high-definition image tone and/or image stylization.

2. according to claim 1 a kind of based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route, it is characterized in that: the wavelet method described in step (1) is anisotropic, the various characteristics not only with Mexico's hat wavelet, but also built-in data are relevant and the characteristic of structure consciousness.

3. according to claim 1 a kind of based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route; it is characterized in that: the computing method of the figure Laplacian Matrix described in step (2); pixel gray-scale value and gradient magnitude are mapped as to limit weight, there is good limit and stop and structural defence characteristic.

4. according to claim 1 a kind of based on the pyramidal anisotropy Wavelet image of thermonuclear disposal route, it is characterized in that: the use of passing through image to be divided into image block and the Krylov subspace method with lap described in step (3), while having avoided high, the global characteristics of consumption decomposes, and has strengthened the practical feasibility of the local wavelet algorithm proposing.

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