CN106056618A - Image threshold segmentation method based on Renyi cross entropy and Gaussian distribution - Google Patents

Abstract

Provided is an image gray histogram threshold segmentation method based on Renyi cross entropy and Gaussian distribution. The method comprises the following steps: 1) initializing Renyi cross entropy index alpha; 2) reading a grayscale image to be segmented and storing the image to a two-dimensional image array I; 3) traversing the image array I and calculating the maximum image gray level L and a gray level set G={0,1,...,L}; 4) supposing t is segmentation threshold value, and based on the t, dividing image pixels into two different kinds of gray level sets C0 and C1; 5) calculating prior probability P0 and P1, gray level mean values M0 and M1 and class variance S0 and S1 with respect to the C0 and C1 through formulas, and class probability P0<i> and P1<i> of each gray level i of the image with respect to the C0 and C1, and normalized posterior probability of each image gray level i obtained through Gaussian fitting; defining a symmetrical information amount formula of the image with respect to Renyi cross entropy; obtaining optimal segmentation threshold value; and finally, outputting an image obtained after segmentation.

Description

Carrying out image threshold segmentation method based on Renyi cross entropy Yu Gauss distribution

Technical field

The invention belongs to technical field of image processing, further relate to the one of technical field of image segmentation based on Renyi cross entropy and the carrying out image threshold segmentation method of Gauss distribution.

Background technology

Image segmentation is a key link in image processing tasks based on machine vision, and it is to realize image object Feature extraction, identify, detect and the basis of graphical analysis and understanding.In numerous image partition methods, due to Threshold segmentation Method succinct effectively and the cutting techniques that is widely adopted in scientific research and application practice of being easily achieved property and becoming.

Threshold sementation can be divided into parametric method and non parametric method.Owing to non parametric method only needs to set when carrying out image segmentation Count a criterion function and the estimating thus bring the minimizing of calculating time of rare quantity of parameters, and effectiveness is from theory and practice Aspect can preferably be verified, research and the application of the most this kind of method are the most active.Famous nonparametric Method is just like maximum variance between clusters (also referred to as Otsu method), maximum entropy (ME) method, minimum cross entropy (MCE) method, Renyi entropy method Deng.

Image is a complicated physical system, does not the most also have a kind of pervasive dividing method to be applicable to own Image segmentation task, so in the face of different segmentation task (segmentation as to NDT image), studying and propose effective Dividing method is presently remaining the work of a great challenge.

Summary of the invention

It is an object of the invention to propose one based on Renyi cross entropy with high for the image that reply is complicated splits task The carrying out image threshold segmentation method of this distribution.

The present invention is achieved through the following technical solutions above-mentioned purpose:

Carrying out image threshold segmentation method based on Renyi cross entropy Yu Gauss distribution, comprises the steps:

(1) Renyi cross entropy index α (α > 0 and α ≠ 1) is initialized；

(2) read gray level image to be split, and be deposited in two dimensional image array I；

(3) traversing graph is as array I, is calculated image maximum gray scale number L and gray level set G={0, and 1 ..., L}, meter Calculate normalized grey level histogram H(H={h₀, h₁, …, h_L)；

(4) supposing that t is segmentation threshold, image pixel is divided into and belongs to two inhomogeneous gray level set C by t₀With C₁, C₀= 0,1,2 ..., t}, C₀={t+1, t+2, …, L}；

(5) with H as the PDF estimation of image gray levels, then can calculate about C by below equation₀With C₁'s Prior probability P₀And P₁, gray level average M₀With M₁；

Formula one:；

Formula two:；

Formula three:；

Formula four:；

(6) in order to by Gauss Distribution Fitting image gray levels probability distribution, calculate about C by below equation₀With C₁Class variance S₀ With S₁；

Formula five:；

Formula six:；

(7) each gray level of image is calculated by below equationiAbout C₀With C₁Class probabilityWith；

Formula seven:；

Formula eight:；

(8) image gray levels is calculated with formula nineiThe normalization posterior probability obtained by Gauss curve fitting；

Formula nine:；

(9) based on assumed above, definition image has symmetric quantity of information formula D about Renyi cross entropy；

Formula ten:；

(10) at G={0,1 ..., in the range of L}, search makes following formula obtain gray level t of minima^*, t^*I.e. optimum segmentation threshold Value；

Formula 11:；

(11) setf (x,y) expression image I coordinate (x,y) grey scale pixel value at place, then can use following formula that image I is implemented segmentation；

Formula 12:；

(12) image after output segmentation.

Beneficial effects of the present invention: the present invention uses has the Renyi cross entropy of solid physics's background as image threshold The criterion function of value segmentation, makes the present invention have physics meaning definitely compared with other method；The present invention uses extensively The probability distribution of the general Gauss Distribution Fitting image gray levels pixel for simulating nature event occurrence rate, makes the present invention have There is more preferable universality；The present invention use the symmetrical Renyi cross entropy of, superior performance relatively strong through a large amount of test universalities as The criterion function of carrying out image threshold segmentation, further increases the segmentation quality of gray level image；When image is carried out Threshold segmentation, The present invention can obtain different segmentation thresholds by adjusting Renyi cross entropy parameter alpha value, and this makes the present invention have more preferable answering Potential to different images segmentation task.

The present invention is a kind of based on the histogrammic cutting techniques of image gray levels.Due to the complexity of natural image, to figure It is a highly difficult job as implementing effective segmentation.Fitted figure is carried out as the probability distribution of gray level histogram by Gauss distribution It is that one is more reasonably estimated, then uses and there is the symmetrical Renyi cross entropy of adjustable entropy parameter to build carrying out image threshold segmentation Criterion function, the core concept of this present invention the most just.

Experiment shows, for having several test images of 8 256 grades of gray scales, is Intel (R) Core at a CPU (TM) 2 Duo CPU T8100@2.10GHz, operating system is Window XP, and programmed environment is the bar of MATLAB R2007b Corresponding image segmentation task is performed under part, the application segmentation image-region inner homogeneous that obtains of the present invention, profile boundary accurate, Segmentation result is better than the traditional methods such as Otsu method, maximum entropy (ME) method, minimum cross entropy (MCE) method, Renyi entropy method；Additionally Also the present invention is made to have more preferable universality by regulation entropy parameter α value.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the present invention.

Fig. 2 is three width NDT image and expert's segmentation results thereof.

Fig. 3 is the 5 kinds of methods the compared segmentation results to NDT image img1.

Fig. 4 is the 5 kinds of methods the compared segmentation results to NDT image img2.

Fig. 5 is the 5 kinds of methods the compared segmentation results to NDT image img3.

Fig. 6 is an an infrared image img4 to be split and width blood cell image img5.

Fig. 7 is the 5 kinds of methods the compared segmentation results to infrared image img4.

Fig. 8 is the 5 kinds of methods the compared segmentation results to blood cell image img5.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.

Step 1. sets Renyi cross entropy index α (α > 0 and α ≠ 1) value, initialisation image minimum Renyi cross entropy MinRE is infinitely great.

Step 2. reads image to be split as shown in Figure 2, and is deposited in two dimensional image array I.

Step 3. traversing graph, as I, obtains image maximum gray scale number L, gray level set G, is calculated normalized ash Degree level rectangular histogram H.

Step 4. supposes that t is a grey level histogram segmentation threshold about image I, and this threshold value is divided into C G₀With C₁Two Part.

Step 5. calculates about C₀With C₁Prior probability P₀With P₁, gray level average M₀With M₁, class variance S₀With S₁。

Step 6. calculates image gray levels according to Gauss distribution principleiAbout C₀With C₁Class probabilityWithAnd normalizing Posterior probability p changed_i。

Step 7. calculates image gray levels rectangular histogram probability vector and Gauss curve fitting probability according to Renyi cross entropy principle The Renyi cross entropy quantity of information D of vector.

Step 8. asks for optimal segmenting threshold t according to minimum Renyi cross entropy principle^*。

Step 9. t^*Image I is implemented Threshold segmentation and exports segmentation image.

Effect of the present invention can be further illustrated by following experiment:

1) experiment condition

Experiment simulation environment is: a CPU is Intel (R) Core (TM) 2 Duo CPU T8100@2.10GHz, operation system System is Window XP, and programmed environment is the PC of MATLAB R2007b；Experimental image is: three width maximum gray scales are 255 NDT image img1, img2, img3 and an a width infrared image img4 and width blood cell image img5.

2) experiment content

2.1) by Otsu method, maximum entropy (ME) method, minimum cross entropy (MCE) method, Renyi entropy method and five kinds of methods of the present invention to three Width NDT image img1, img2, img3 test, and in this experiment, the Renyi cross entropy index in the inventive method is set as 0.8, five kinds of dividing method experimental results are as in Figure 3-5.What Fig. 2 listed is three width NDT original images to be split and specially Family's segmentation result, wherein Fig. 2 (a) be img1 original image, Fig. 2 (b) be img2 original image, Fig. 2 (c) be img3 original image, Fig. 2 (d) be expert's segmentation result of img1 image, Fig. 2 (e) be expert's segmentation result of img2 image, Fig. 2 (f) be img3 image Expert's segmentation result.Fig. 3 is five kinds of methods segmentation results to img1 image, and wherein Fig. 3 (a) is Otsu method result, Fig. 3 (b) Being ME method result, Fig. 3 (c) is MCE method result, and Fig. 3 (d) is Renyi entropy method result, and Fig. 3 (e) is segmentation result of the present invention；Fig. 4 Being five kinds of methods segmentation results to img2 image, wherein Fig. 4 (a) is Otsu method result, and Fig. 4 (b) is ME method result, Fig. 4 (c) Being MCE method result, Fig. 4 (d) is Renyi entropy method result, and Fig. 4 (e) is segmentation result of the present invention；Fig. 5 is that five kinds of methods are to img3 The segmentation result of image, wherein Fig. 5 (a) is Otsu method result, and Fig. 5 (b) is ME method result, and Fig. 5 (c) is MCE method result, Fig. 5 D () is Renyi entropy method result, Fig. 5 (e) is segmentation result of the present invention.

2.2) with Otsu method, ME method, MCE method, Renyi entropy method and five kinds of methods of the present invention to a width infrared image img4 and One width blood cell image img5 carries out split-run test, in this experiment, Renyi cross entropy index of the present invention when splitting for img4 Being set as 0.8, when splitting img5, Renyi cross entropy index of the present invention is set as 1.5, five kinds of dividing method experimental results such as figure Shown in 7-8.That Fig. 6 lists is an infrared img4 and a width blood cell image img5 of experiment, and wherein Fig. 6 (a) is img4 Artwork, Fig. 6 (b) is img5 artwork.Fig. 7 is five kinds of methods segmentation results to img4, and wherein Fig. 7 (a) is Otsu method result, figure 7 (b) is ME method result, and Fig. 7 (c) is MCE method result, and Fig. 7 (d) is Renyi entropy method result, and Fig. 7 (e) is that the present invention splits knot Really；Fig. 8 is five kinds of methods segmentation results to img5, and wherein Fig. 8 (a) is Otsu method result, and Fig. 8 (b) is ME method result, Fig. 8 C () is MCE method result, Fig. 8 (d) is Renyi entropy method result, and Fig. 8 (e) is segmentation result of the present invention.

3) interpretation

From the segmentation result of Fig. 3-5 and Fig. 7-8 it can be seen that either Otsu method, ME method, MCE method, or Renyi entropy method, All can not well Target Segmentation to be paid close attention to out also remain more in segmentation result figure in experimental image segmentation Noise spot information, segmentation area concordance is poor, and these phenomenons show particularly evident in the segmentation to NDT image, this Invention performance in this respect is better than control methods.

Table 1 has been born distinct methods and has been compared img1, img2, img3 segmentation result.In table 1, data represent mistake classification picture The percentage ratio that vegetarian refreshments number is total with image slices vegetarian refreshments, i.e. mistake classified pixels point number/total number of image pixels × 100%.At this In using the expert's segmentation result in Fig. 2 as the correct segmentation result of original image, mistake classified pixels point number is by respectively The segmentation result of method and expert's segmentation result compare and obtain.As it can be seen from table 1 the segmentation result that the present invention obtains Point rate is minimum by mistake, closest to expert by splitting the result obtained by hand.

A table 1. NDT image point rate by mistake compares

Claims (1)

1. image grey level histogram threshold segmentation method based on Renyi cross entropy Yu Gauss distribution, it is characterised in that include as Lower step:

(1) Renyi cross entropy index α (α > 0 and α ≠ 1) is initialized；

(2) read gray level image to be split, and be deposited in two dimensional image array I；

(3) traversing graph is as array I, is calculated image maximum gray scale number L and gray level set G={0, and 1 ..., L}, meter Calculate normalized grey level histogram H(H={h₀, h₁, …, h_L)；

(4) supposing that t is segmentation threshold, image pixel is divided into and belongs to two inhomogeneous gray level set C by t₀With C₁, C₀= 0,1,2 ..., t}, C₀={t+1, t+2, …, L}；

(5) with H as the PDF estimation of image gray levels, then can calculate about C by below equation₀With C₁'s Prior probability P₀And P₁, gray level average M₀With M₁；

Formula one:；

Formula two:；

Formula three:；

Formula four:；

(6) in order to by Gauss Distribution Fitting image gray levels probability distribution, calculate about C by below equation₀With C₁Class variance S₀ With S₁；

Formula five:；

Formula six:；

(7) each gray level of image is calculated by below equationiAbout C₀With C₁Class probabilityWith；

Formula seven:；

Formula eight:；

(8) image gray levels is calculated with formula nineiThe normalization posterior probability obtained by Gauss curve fitting；

Formula nine:；

(9) based on assumed above, definition image has symmetric quantity of information formula D about Renyi cross entropy；

Formula ten:；

(10) at G={0,1 ..., in the range of L}, search makes following formula obtain gray level t of minima^*, t^*I.e. optimum segmentation threshold Value；

Formula 11:；

(11) setf (x ,y) expression image I coordinate (x,y) grey scale pixel value at place, then can use following formula that image I is implemented segmentation；

Formula 12:；

(12) image after output segmentation.