CN102496167A - Pseudo-color coding method for phase modulated digital image - Google Patents

Abstract

The invention discloses a pseudo-color coding method for carrying out digital phase modulation on a gray image signal. The pseudo-color coding method comprises the following steps of: adopting a phase grating coding method as a physical model to carry out mathematical modeling, leading an optical path difference to vary with the density of an input gray image, finding an operator relationship between the strength of a pseudo-color image and the gray value of an original gray image, and always assuming that a white light source only contains three colored lights of red, green and blue, i.e. lambda r, lambda g and lambda b, wherein the light intensity on an output plane expresses the non-coherent superposition of the output three colored lights. The invention provides a pseudo-color coding scheme of the phase modulated digital image based on a RGB (Red, Green, Blue) true color display mechanism in the premise of assumption, thereby the mapping relationship between the gray and the color is optimized, and good operator selection is supplied for processing of the images and other signals. The coding method has good flexibility; and diffractive order colorized images obtained by adopting the coding method have excellent effects and have the advantages of rich chromaticity, good color saturation, high definition and the like.

Description

Phase modulation (PM) digital picture pseudo-color coding method

Technical field

The invention belongs to the digital image processing techniques field, be specifically related to a kind ofly gray image signals is carried out the position modulate pseudo-color coding method mutually.

Background technology

With the gray level image pseudo-coloursization, and make the coloured image characteristic distinct, be easy to identification, be an important topic in the Flame Image Process always.This technology is that a kind of visual effect is obvious, but complex image enhancement techniques not too also is a kind of faster image processing techniques of present domestic development.Because human eye can only be distinguished the 4～5bit gray level in the piece image, but can distinguish nearly thousand kinds colour.Therefore be the resolution characteristic of performance human eye to colour, often use the different gray scales of various color representative image, the change gray level image is coloured image, thereby makes the observer can from image, obtain more information.So it is a kind of very effective image enhancement technique that gray level image is carried out the pseudo-colours processing, has application market and technological redevelopment prospect widely.Because development of computer is with universal, what use mostly in the commercial instrument and equipment at present is digitizing pseudo-colours treatment technology.

Gray level image pseudo-colours treatment technology is just being brought into play more and more important effect in the every field of scientific research and practical application, and for example: in medical diagnosis, the digital picture overwhelming majority who obtains is a gray level image, like X line, CT, MRI, B ultrasonic image etc.The application of medical science numerical imaging mainly is the extraction to characteristics of image, and characteristics of image comprises characteristic, local feature, provincial characteristics and global feature a bit.Pseudo color image is handled and will obviously be improved all these Feature Recognition abilities of image.It can make full use of the sensitive characteristics of human eye to colour, improves the visually-perceptible to overview image.Pseudo-colours can the thickness of profile, smooth, sharpening, fuzzy, continuously and regional relation such as distribution show.Nearly all medical science black white image can be faked color processing.In industrial detection, the workpiece image in the industrial furnace is carried out pseudo-colours handle, can obtain better effect, can provide more rational quality analysis and early warning information, finally reach the target of energy-saving and emission-reduction.In material tests, utilize the Electronic Speculum colour picture of pseudo-color coding fabrication techniques, color difference is bigger, and the element colour that especially differs bigger for atomic number differs bigger.Therefore material is analyzed very intuitive and reliablely, remedied with the spectrometer analysis and can only on picture, show X ray point and can not show secondary electron image, can only on a line, be shown as component curve and can not see the weakness of overall distribution situation.Show thereby make tissue topography, the content of material and be distributed on the cromogram, make that material is carried out semi-quantitative analysis is more perfect.

In recent years, the research of gray scale pseudo-colours method receives scientific research personnel's attention always, has researched and developed the pattern of many different pseudo-color codings.Mainly can be divided into two big class methods: one type is the digital pseudo-colours method that adopts computer technology, and digital processing method for example commonly used has: density stratification method and spatial domain gray level-color transformation.

The simplest pseudo-colours disposal route is the density stratification method, also can be called the gray scale top and bottom process.It is that (x y) regards coordinate (x, density function y) as with a width of cloth gray level image f.Be divided into some grades to the gray scale of time image, and give the pseudo-colours processing that various colors realizes image, but the image visual effect after this method is handled is not ideal enough these some gray shade scales; Color is stiff; The not enough mediation, and work as the gray level layering more for a long time, algorithm is very loaded down with trivial details.

Spatial domain gray scale-color transformation method is a kind of more commonly used, the more effective pseudo-colours enhancing of specific density top and bottom process method.This pseudo-colours treatment technology can become the continuous multicolor image with multiple gradual change with the black and white gray level image, and realizes simple.Like the principle of Fig. 1 according to colorimetry; Three kinds of different conversion of same gray scale segmentation process red, green, blue with original image; And make three transducer outputs different; Become the three primary colours component, remove to control the red, green, blue electron gun of color monitor then with them respectively, just can on the screen of color monitor, synthesize a width of cloth coloured image.Colored content is decided by the shape of transforming function transformation function.Typical transforming function transformation function is as shown in Figure 2, and wherein (a) and (b), (c) are respectively three kinds of transforming function transformation functions of red, green, blue, and (d) is drawn in three kinds of conversion on same the figure so that see mutual relation clearly among the figure.Visible by (d) among Fig. 2, only, gray scale is blue when being zero, and gray scale is green during for L/2, and gray scale takes on a red color during for L, and gray scale will be mixed into different tones by three primary colours during for other value.

Although that digital image processing method has that amount of image information is big, image information is theoretical is closely related with communication theory, the comprehensive advantage such as strong of image processing techniques; But these methods are all only encoded according to grey level information; Not outstanding edge of image zone, so they only are applicable to the gray level image below 256 grades.Concerning the high-definition picture that is higher than 256 grades of gray scales, can only earlier the gray level compression be hinted obliquely at is 256 grades of gray scales, and then encodes, but the gray level resolution that has been equivalent to reduce the processing image is hinted obliquely in compression.That is to say in shortcomings such as high-resolution gray level image to be carried out will produce when pseudo-colours is handled color sensitivity not high, and gradation is clearly demarcated inadequately.And this two kinds of methods shortages dirigibility, gray level is in case confirm that its corresponding color has just confirmed that also this just causes the only corresponding unique pseudo color image of a width of cloth gray level image.

Another kind of pseudo-colours method is the traditional optical method.For example, shadow tone is shielded method, contrast inversion method, is utilized the emulsion of silver chloride photodichroism to realize density pseudocolor encoding, phase grating compiling method etc.Wherein phase grating compiling method equipment needed thereby is simpler, and treatment step is also uncomplicated.It is that the gray level image that utilizes rectangular raster that desire is handled carries out encoded recording; Doing bleaching again handles; Make density informations different on the image change into phase information; Make a holographic grating that includes gray level image information, this phase grating is placed on carries out white light demodulation by filter processing in the white light information disposal system at last, just can in output face, obtain pseudo color image.In the experiment, the light distribution of thing function (former gray level image) is determining the diffraction characteristic of coded slice, when illumination and observation condition one timing, unique color and brightness that has determined output image.Picture after it is handled is bright-colored, and the efficiency of light energy utilization is higher, is therefore paid attention to very much.This method divides pre-service and two steps of filtering to carry out.At pretreatment stage, pending black and white transparency film images on the film, and has a grating to fit tightly with it before the film, after the development treatment, again this coded slice bleaching, thereby forms the phase coding sheet.Place this phase coding sheet on the input face of White-Light processing system, on frequency spectrum, only let zero level or 1 grade pass through, then in output face, form false color image.

Optical processing method has that equipment is simple, cost is low, and the advantage of handling that capacity is big, rich color is distinct.But because of the needs chemical treatment, its process complicated and time consumption can not modulated in real time, has brought significant limitation for actual application.

Summary of the invention

The present invention for solve that the digital picture pseudo-color coding exists to high-resolution gray level image carry out pseudo-colours when handling color sensitivity not high, gradation is clearly demarcated inadequately, lacks shortcomings such as dirigibility; Proposing new a kind of gray image signals to be carried out the coding method of digitizing phase modulation (PM) pseudo-coloursization, is means with digital image processing techniques, reaches the effect that pure optical means is handled; Brightness and color Adjustable real-time can be handled the gray level image of 1 to 24 multiple common form, and the pseudo color image that obtains is more clear than the gray level image profile before handling; Level is distincter; Color is abundanter, and the details target recognizes to have higher gray scale sensitivity more easily.

Technical scheme of the present invention:

1, phase modulation (PM) digital picture pseudo-color coding method provided by the invention; According to Fourier optical principle the phase grating compiling method is carried out mathematical modeling (in detail modeling process see after literary composition), adopts the pseudo color image intensity that finds to concern as the original coding formula with the operator between the original-gray image gray-scale value:

$I_0(x_3,y_3;\mathrm{\λ})=0.5+0.5\cos \left[\frac{4.27}{\mathrm{\λ}}{D}_i(x_3,y_3)\right]$

$I_m(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})=\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}+\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}\cos [\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\&PlusMinus;\mathrm{\&pi;}]$

Wherein, λ is a lambda1-wavelength, I ₀Be output face Zero-order diffractive light intensity, I _mBe other level time diffraction intensities of output face, D _i(x ₃, y ₃) gray-scale value of gray level image.

During the white light source that 2, adopts, the intensity of certain one-level output image can be expressed as with the non-coherent addition of each coloured light

I _m，n(D(i，j))＝∫I _m，n(D(i，j)，λ)dλ

Always suppose and only contain 3 kinds of coloured light λ of red, green, blue r in the white light source, λ g, λ b, the light intensity in the output face then is expressed as the non-coherent addition of these 3 kinds of coloured light outputs

I(D(i，j))＝I(D(i，j)，λ _r)+I(D(i，j)，λ _g)+I(D(i，j)，λ _b)

3, under the prerequisite of above-mentioned hypothesis, adopt the Matlab language to propose a kind of phase modulation (PM) digital picture pseudo-color coding scheme based on RGB RGB display mechanism.Be defined as three input variable m_Red, m_Green, m_Blue to wavelength X respectively to the red, green, blue three primary colours; Its value all changes between 0-255; After the data combination in each variable and the gray level image matrix by the corresponding three primary colours light intensity of phase place operator transformation output; After the two dimensional gray image strengthens computing through three different gray scales of operator; Be combined into light intensity cubical array I, each ties up the electron gun corresponding of all kinds that gray matrix drives the RGB display respectively, output be 24 pseudo color images.

Consider the visual effect of people's eyes to light, i.e. the most responsive only green-yellow light of human eye is according to the weight coefficient of three primary colours in the additive color mixture principle in white light is synthetic; The needed three primary colours approximate representation of white light that produces 1lm (W) is: 1lm (W)=0.30lm (R)+0.59lm (G)+0.11lm (B), and the saturation degree of color mixture is decided by the ratio of 3 kinds of colors, and brightness is the brightness sum of 3 kinds of colors; The three primary colours of output are at last: r=0.30*I (::, 1); G=0.59* (::, 2); B=0.11*I (::, 3).

Handle former gray level image r with the cosine operator, g, the b three primary colours obtain I (::, 1), I (:;:, 2), I (::, 3) strengthen three primary colours, go out public correlative value w according to the weight coefficient proportioning then; W=0.30*I (::, 1)+0.59*I (::, 2)+0.11*I (::; 3), finally export by controlled variable r, g, the adjusted three primary colours I of b (::, 1)=r*W/255; I (::, 1)=g*W/255; I (::, 1)=b*W/255, obtain pseudo color image.The wavelength control district numerical value that the cosine operator is handled all is fixed as 130, then obtains the pseudo color image of single color.

Advantage of the present invention and beneficial effect:

The present invention optimizes the mapping relations that solved between gray scale and the color, selects for image and other signal Processing provide good operator.Owing in coding and bleaching processing procedure, optical path difference is changed with the density of input gray level image, has therefore realized the pseudo-color coding that changes by input image density.Each order of diffraction colorize image effect with this coding method obtains is splendid, has abundant, good, the sharpness advantages of higher of color saturation of colourity.

Description of drawings

Fig. 1 is gray scale-color transformation method schematic diagram.

Fig. 2 is gray scale-color transformation method exemplary process function, (a) is red transforming function transformation function, (b) is green transforming function transformation function, (c) is blue transforming function transformation function, (d) the synthetic transforming function transformation function of redgreenblue.

Fig. 3 is a phase grating compiling method Experimental equipment.Among the figure, 1 is white light source, and 2 is fourier lense, and 3 is diaphragm, and 4 is input face, and 5 is frequency plane, and 6 for receiving optical screen.

Fig. 4 is a phase modulation (PM) digital picture pseudo-color coding theory diagram.

Fig. 5 is the original-gray image before the coding.

Fig. 6 is through the pseudo color image behind scheme one coding.

Fig. 7 is through the pseudo color image behind scheme two codings.

Fig. 8 is through the pseudo color image behind scheme three codings.

Embodiment

Embodiment

Combine Fig. 4 that the specific embodiments of phase modulation (PM) digital picture pseudo-color coding method is described at present:

Phase modulation (PM) digital picture pseudo-color coding method provided by the invention; According to Fourier optical principle the phase grating compiling method is carried out mathematical modeling, adopts the pseudo color image intensity and the operator between the original-gray image gray-scale value that find to concern as the original coding formula:

$I_0(x_3,y_3;\mathrm{\&lambda;})=0.5+0.5\cos \left[\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\right]$

$I_m(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})=\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}+\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}\cos [\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\&PlusMinus;\mathrm{\&pi;}]$

Wherein, λ is a lambda1-wavelength, I ₀Be output face Zero-order diffractive light intensity, I _mBe other level time diffraction intensities of output face, D _i(x ₃, y ₃) (i=1,2,3 ...) be the gray-scale value of gray level image.

In order to find pseudo color image intensity required more than the coding and the operator between original-gray image gray-scale value relation, show following to its concrete process of mathematical modeling analysis:

(1). Grating Modulation

Being that d, seam are wide with an intensity profile slide and cycle is close to uniform exposure on a photographic film for the rectangular raster of a.The transmitance of rectangular raster is:

$t_r\left(x_1\right)=\mathrm{rect}\frac{x_1}{a}*\frac{1}{d}\mathrm{comb}\frac{x_1}{d}---\left(1\right)$

Consider the modulating action of grating, the optical density of egative film after exposure, development, photographic fixing etc. are handled distributes

$D(x_1,y_1)=[D_{10}-{\mathrm{\&gamma;D}}_i(x_1,y_1)]\mathrm{rect}\frac{x_1}{a}*\frac{1}{d}\mathrm{comb}\frac{x_1}{d}+D_0---\left(2\right)$

D wherein ₁₀=γ lgE _i(x ₁, y ₁), just processed the amplitude type coded slice of a rectangular raster modulation thus.

(2). Phase Processing

After above-mentioned amplitude type code film bleached processing, become transparent phase type code film.If bleaching suitably can make the caused light path L of phase place egative film (x ₁, y ₁) approximately linear is proportional to the optical density D (x of photographic film ₁, y ₁), shown in (3) formula.

$L(x_1,y_1)=\left\{\begin{array}{cc}{\mathrm{cD}}_0=L_0& t_r=0\\ \mathrm{cD}(x_1,y_1)=c[D_{10}-{\mathrm{\&gamma;D}}_i(x_1,y_1)]=L_1(x_1,y_1)& t_r=1\end{array}\right.---\left(3\right)$

The complex amplitude transmitance does

$e^{\mathrm{i\&phi;}(x_1,y_1)}=\left\{\begin{array}{cc}{e}^{{\mathrm{i\&phi;}}_0}=e^{i\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{cD}}_0}& t_r=0\\ e^{{\mathrm{i\&phi;}}_1(x_1,y_1)}=e^{i\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}c[D_{10}-{\mathrm{\&gamma;D}}_i(x_1,y_1)]}& t_r=1\end{array}\right.---\left(4\right)$

Like this, the variable density information of image just is converted into phase change information.Again because the variable density speed of gray level image far below the modulated grating spatial frequency, so can think that at a certain regional area, phase delay is constant relatively, under the certain situation of wavelength, the relation of phase differential and optical path difference does

$\mathrm{\&Delta;\&phi;}={\mathrm{\&phi;}}_1(x_1,y_1)-{\mathrm{\&phi;}}_0=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(L_1(x_1,y_1)-L_0)=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{\&Delta;L}---\left(5\right)$

Therefore, can be similar to and result (4) is pressed the rectangle phase grating handle.Consider the grating effect, the complex amplitude transmitance that is got coded slice by (4) formula does

$t(x_1,y_1)=(e^{{\mathrm{i\&phi;}}_1(x_1,y_1)}-e^{{\mathrm{i\&phi;}}_0})\mathrm{rect}\frac{x_1}{a}*\frac{1}{d}\mathrm{comb}\frac{x_1}{d}+t_0=(t_1(x_1,y_1)-t_0)\mathrm{rect}\frac{x_1}{a}*\frac{1}{d}\mathrm{comb}\frac{x_1}{d}+t_0---\left(6\right)$

Wherein $t_0=e^{{\mathrm{I\&phi;}}_0},$ Do not contain the thing optical information; $t_1(x_1,y_1)=e^{{\mathrm{I\&phi;}}_1(x_1,y_1)}$ Carry object and incident light information (gray level image Density Distribution, lambda1-wavelength).

At this moment coded slice is transparent fully, and Modulation and Amplitude Modulation just can be ignored, but when regular variation of its optical thickness or variations in refractive index (thickness is even), just can produce periodic phase modulation (PM) to incident wave or transparent picture.

(3). demodulation by filter

Phase encoded slice is placed on the input plane of 4f optical information processing system, as shown in Figure 3.

Use the collimated white light light illumination, establishing incident intensity is I (λ), and gets I (λ)=1.The wavelength information that contains on white light source and the grating when pseudo-colours is reproduced is identical, and then the complex amplitude on the frequency plane is the amplitude transmittance t (x of encode grating ₁, y ₁) Fourier transform, promptly

$T(\frac{x_2}{\mathrm{\&lambda;f}},\frac{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}{\mathrm{\&lambda;f}})=\frac{a}{d}{T}_1(\frac{x_2}{\mathrm{\&lambda;f}},\frac{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}{\mathrm{\&lambda;f}})*\left[\sin c\left(a\frac{{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">x</figure-callout>}}_2}{\mathrm{\&lambda;f}}\right)\underset{-\&infin;}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(\frac{x_2}{\mathrm{\&lambda;f}}-\frac{m}{d})\right]-t_0\frac{a}{d}\sin c\left(a\frac{{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">x</figure-callout>}}_2}{\mathrm{\&lambda;f}}\right)\underset{-\&infin;}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}(\frac{x_2}{\mathrm{\&lambda;f}}-\frac{m}{d})+t_0\mathrm{\&delta;}\left(\frac{x_2}{\mathrm{\&lambda;f}}\right)---\left(7\right)$

In the formula

Be t ₁(x ₁, y ₁) Fourier transform.

If placement space wave filter on frequency plane lets zero level spectrum or the ± m level spectrum pass through respectively, the output face negate is to coordinate time, and then their COMPLEX AMPLITUDE on output plane are the inverse fourier transform of (7) formula.

$g_0(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3,\mathrm{\&lambda;})=\frac{a}{d}{F}^{-}\left(T_1(\frac{x_2}{\mathrm{\&lambda;f}},\frac{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}{\mathrm{\&lambda;f}})\right)-t_0\frac{a}{d}+t_0=\frac{a}{d}{t}_1(x_3,y_3)-t_0\frac{a}{d}+t_0---\left(8\right)$

$g_m(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3,\mathrm{\&lambda;})=\frac{a}{d}{t}_1(x_3,y_3)[\mathrm{rect}\frac{x_3}{a}*e^{i2\mathrm{\&pi;}\frac{{\mathrm{mx}}_3}{d}}]-\frac{a}{d}{t}_0[\mathrm{rect}\frac{x_3}{a}*e^{i2\mathrm{\&pi;}\frac{{\mathrm{mx}}_3}{d}}]+t_0---\left(9\right)$

T in the formula ₁(x ₃, y ₃) do

Inverse Fourier transform.Because human eye can only be experienced the variation of light intensity, if make d=2a, and will $t_0=e^{{\mathrm{I\&phi;}}_0},$ $t_1(x_1,y_1)=e^{{\mathrm{I\&phi;}}_1(x_1,y_1)},$ And (5) formula substitution (9) formula, omit the constant phase factor that integration produces after, the light intensity that in output face, obtains images at different levels does

$I_0(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})={\left|g_0(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})\right|}^2=\frac{1}{2}(1+\cos \mathrm{\&Delta;\&phi;})=\frac{1}{2}(1+\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{\&Delta;L})---\left(10\right)$

$I_m(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})={\left|g_m(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})\right|}^2=\frac{2}{{\left(\mathrm{m\&pi;}\right)}^2}(1-\cos \mathrm{\&Delta;\&phi;})=\frac{2}{{\left(\mathrm{m\&pi;}\right)}^2}(1-\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{\&Delta;L})---\left(11\right)$

Can find out that by formula the light intensity size that complex amplitudes at different levels are corresponding is only relevant with wavelength X with phase difference L (or optical path difference Δ L).M is an odd number in the formula, and this moment, optical path difference did

ΔL＝L ₁(x ₃，y ₃)-L ₀＝cγ[lgE _i(x ₃，y ₃)-D _i(x ₃，y ₃)]-cD ₀ (12)

In the formula, c=1, γ=0.68, D ₀=0.02, E _i(x ₃, y ₃)=1.5, then

ΔL＝0.68[1g1.5-D _i(x ₃，y ₃)]-0.02 (13)

Further handle, have

ΔL＝0.0997-0.68D _i(x ₃，y ₃) (14)

ΔL＝-0.68D _i(x ₃，y ₃) (15)

$I_0(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})=0.5+0.5\cos \left[\frac{0.63-4.27D_i(x_3,y_3)}{\mathrm{\&lambda;}}\right]=0.5+0.5\cos [\frac{4.27D_i(x_3,y_3)}{\mathrm{\&lambda;}}-\frac{0.63}{\mathrm{\&lambda;}}]---\left(16\right)$

$I_0(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})=0.5+0.5\cos \left[\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\right]---\left(17\right)$

$I_m(x_3,{\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="HDA0000117084870000013.png"\; state="\{\{state\}\}">y</figure-callout>}}_3;\mathrm{\&lambda;})=\frac{0.2}{m^2}-\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}\cos \left[\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\right]=\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}+\frac{0.2}{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000117084870000012.png,HDA0000117084870000013.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}\cos [\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)+\mathrm{\&pi;}]---\left(18\right)$

Gray level image for original input; It is confirmed in certain any transmitance; After above-mentioned three steps handle, because the light intensity at this place size is only relevant with phase difference L and wavelength X, so the phasic difference of different wave length is different; Change the relative composition of various wavelength energy like this with regard to the white light that makes incident along with the transmissivity difference of changing the time, the corresponding color mixture of confirming occurred.So just accomplished the pseudo-coloursization of image by transmitance (being density).Because gray level image density is encoded according to wavelength, so its color sensitivity has very big raising compared to digital image processing method.Owing in coding and bleaching processing procedure, optical path difference is changed with the density of input gray level image, has therefore realized the pseudo-color coding that changes by input image density.Each order of diffraction colorize image effect with this coding method obtains is splendid, has abundant, good, the sharpness advantages of higher of color saturation of colourity.

Owing to all with the said prerequisite that is assumed to be of step 2, carry hypothesis is done following explanation in the cataloged procedure at present:

Can find out the gray-scale value D of gray level image by (17) in the The above results, (18) formula _i(x ₃, y ₃) be modulated signals, cosine function is a modulation signal, the intensity I that obtains is a modulated signal, is non-linear modulation.For each order of diffraction time, (i j) changes the intensity distributions I of pseudo color image, has realized that phase modulation (PM) digital picture pseudo-colours strengthens with the matrix D of wavelength X and former gray level image through the cosine operator function.In the corresponding relation formula, zero level spectrum light intensity is positive [+cos ()], and the light intensity of other spectrums at different levels all is negative [cos ()].Two types of difference of composing certain some intensity on the corresponding output image only are that the coefficient before constant term and the cosine function is different.

When adopting white light source, the intensity of certain one-level output image can be expressed as with the non-coherent addition of each coloured light:

I _m，n(D(i，j))＝∫I _m，n(D(i，j)，λ)dλ

But in Digital Image Processing, the meaning that all wavelengths is carried out the light intensity integration only is the limited stack of each color shade, both loses time like this, expends system resource again, and the pseudo-coloursization of gray level image is not had the essence contribution.And the demonstration of one 24 bit-plane image is realized by the relevant interface that 3 color component planes of RGB drive display device respectively always.So we always suppose only contains 3 kinds of coloured light λ of red, green, blue in the white light source _r, λ _g, λ _b, the light intensity in the output face then is expressed as the non-coherent addition of these 3 kinds of coloured light outputs:

I(D(i，j))＝I(D(i，j)，λ _r)+I(D(i，j)，λ _g)+I(D(i，j)，λ _b)

Gray-scale value D (i, the pseudo-colours that j) changes output have finally been obtained with input picture.

Based on above-mentioned hypothesis and result of calculation, adopt Matlab original gray-scale map (like Fig. 5) to be carried out the concrete processing scheme of coding key phase modulation (PM) digital picture pseudo-color coding here:

Scheme one: in the concrete programming operation of 24 pseudo-colours display systems, can be defined as three input variable m_Red, m_Green, m_Blue to wavelength X respectively to the red, green, blue three primary colours, its value all changes between 0-255; After the data combination in each variable and the gray level image matrix by the corresponding three primary colours light intensity of phase place operator transformation output, the intensity I r of red wavelength value correspondence as red color component value I (::; 1), the corresponding intensity I g of green wavelength value as green component values I (::; 2), the corresponding intensity I b of blue light wavelength value as blue sub value I (::; 3); Can also monitor each gray component reinforced effects this moment, after the two dimensional gray image strengthens computing through three different gray scales of operator like this, is combined into light intensity cubical array I; Each ties up the electron gun corresponding of all kinds that gray matrix drives the RGB display respectively, output be 24 pseudo color images.This scheme physical significance is the clearest, and effect is good again, has really reached through phase modulation (PM) digital picture pseudo-colours effect, specifies r=90 in the instance, g=80, and the b=117 effect is as shown in Figure 6.

Scheme two: on the basis of the first string, consider the visual effect of people's eyes to light, i.e. the most responsive only green-yellow light of human eye is according to the weight coefficient of three primary colours in the additive color mixture principle in white light is synthetic; The needed three primary colours approximate representation of white light that produces 1lm (W) is: 1lm (W)=0.30lm (R)+0.59lm (G)+0.11lm (B), and the saturation degree of color mixture is decided by the ratio of 3 kinds of colors, and brightness is the brightness sum of 3 kinds of colors, and the three primary colours of output are at last: r=0.30*I (:;:, 1), g=0.59*I (::; 2), b=0.11*I (::, 3); Specify r=90 in the instance, g=50, the b=200 effect is as shown in Figure 7.

Scheme three: with reference to preceding two schemes, handle former gray level image r with the cosine operator, g, the b three primary colours obtain I (::, 1); I (::, 2), I (::, 3) strengthen three primary colours, go out public correlative value w according to the weight coefficient proportioning then; W=0.30*I (::, 1)+0.59*I (::, 2)+0.11*I (::; 3), finally export by controlled variable r, g, the adjusted three primary colours I of b (::, 1)=r*W/255; I (::, 1)=g*W/255; I (::, 1)=b*W/55, obtain pseudo color image.If the wavelength control district numerical value that the cosine operator is handled all is fixed as 130, then obtain the pseudo color image of single color, specify rwavelength=60 in the instance, rwavelength=70, rwavelength=120; R=90, g=50, the b=200 effect is as shown in Figure 8.

Following pseudo-colours simulator program can be handled the image of 1,4,8,24 various common type, like * .BMP, * .GIF, * .GIF, * .PNG, * .JPEG etc. handle that picture is not limited to gray level image, but filename must with program in read in consistent.R in the program, g, b had both represented the three primary colours color value, represented the wavelength value of three kinds of colors again.

Scheme 1:

d＝imread(′input.bmp′)；

imshow(d)；title(′Original?Image′)；

[m?n?p]＝size(d)；d＝double(d)；

i＝1:m；j＝1:n；

r＝input(′Please?input?color?value(0-255):r＝′)；

Ir(i，j)＝0.5+0.5*cos(4.27*d(i，j)/r)；

imwrite(Ir，′Ir.bmp′)；

figure；imshow(Ir)；title(′Red?Enhancement′)；

g＝input(′Please?input?color?value(0-255):g＝′)；Ig(i，j)＝0.5+0.5*cos(4.27*d(i，j)/g)；

imwrite(Ig，′Ig.bmp′)；

figure；imshow(Ig)；title(′Green?Enhancement′)；

b＝input(′Please?input?color?value(0-255):b＝′)；

Ib(i，j)＝0.5+0.5*cos(4.27*d(i，j)/b)；

imwrite(Ib，′Ib.bmp′)；

figure；imshow(Ib)；title(′Blue?Enhancement′)；

I(：，：，1)＝Ir；I(：，：，2)＝Ig；I(：，：，3)＝Ib；

imwrite(I，′output.bmp′)；

figure；imshow(′output.bmp′)；title(′Pseudo-color?Image′)；

Scheme 2:

d＝imread(′input.bmp′)；

[m?n?p]＝size(d)；d＝double(d)；

i＝1:m；j＝1:n；

r＝input(′Please?input?red?color?value(0-255):r＝′)；

Ir(i，j)＝0.6+0.5*cos(4.27*d(i，j)/r)；

imwrite(Ir，′Ir.bmp′)；

figure；imshow(Ir)；title(′Red?Enhancement′)；

g＝input(′Please?input?green?color?value(0-255):g＝′)；

Ig(i，j)＝0.6+0.5*cos(4.27*d(i，j)/g)；

imwrite(Ig，′Ig.bmp′)；

figure；imshow(Ig)；title(′Green?Enhancement′)；

b＝input(′Please?input?blue?color?value(0-255):b＝′)；

Ib(i，j)＝0.6+0.5*cos(4.27*d(i，j)/b)；

imwrite(Ib，′Ib.bmp′)；

figure；imshow(Ib)；title(′Blue?Enhancement′)；

I(：，：，1)＝0.30*Ir；I(：，：，2)＝0.59*Ig；I(：，：，3)＝0.11*Ib；

imwrite(I，′output.bmp′)；

figure；imshow(′output.bmp′)；title(′Pseudo-color?Image′)；

Scheme 3:

d＝imread(′input.bmp′)；

Imshow (d); Title (' original image ');

[m?n?p]＝size(d)；d＝double(d)；

i＝1:m；j＝1:n；

r＝input(′Please?input?red?wavelength?value(50-200):rwavelength＝′)；

R(i，j)＝0.5+0.5*cos(4.27*d(i，j)/rwavelength)；

g＝input(′Please?input?green?wavelength?value(50-200):gwavelength＝′)；

G(i，j)＝0.5+0.5*cos(4.27*d(i，j)/gwavelength)；

b＝input(′Please?input?blue?wavelength?value(50-200):bwavelength＝′)；

B(i，j)＝0.5+0.5*cos(4.27*d(i，j)/bwavelength)；

I(：，：，1)＝R；I(：，：，2)＝G；I(：，：，3)＝B；

W＝I(：，：，1)*0.30+I(：，：，2)*0.59+I(：，：，3)*0.11；

r＝input(′Please?input?red?color?value(0-255)：r＝′)；I(：，：，1)＝r*W/255；

g＝input(′Please?input?green?color?value(0-255)：g＝′)；I(：，：，2)＝g*W/255；

b＝input(′Please?input?blue?color?value(0-255):b＝′)；I(：，：，3)＝b*W/255；

imwrite(I，′output.bmp′)；

Figure; Imshow (' output.bmp '); Imfinfo (' output.bmp '); Title (' pseudo-colours ').

Claims (5)

1. phase modulation (PM) digital picture pseudo-color coding method is characterized in that it may further comprise the steps:

(1) according to Fourier optical principle the phase grating compiling method is carried out mathematical modeling, adopts the pseudo color image intensity and the operator between the original-gray image gray-scale value that find to concern as the original coding formula:

$I_0(x_3,y_3;\mathrm{\&lambda;})=0.5+0.5\cos \left[\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\right]$

$I_m(x_3,y_3;\mathrm{\&lambda;})=\frac{0.2}{m^2}+\frac{0.2}{m^2}\cos [\frac{4.27}{\mathrm{\&lambda;}}{D}_i(x_3,y_3)\&PlusMinus;\mathrm{\&pi;}]$

Wherein, λ is a lambda1-wavelength, I ₀Be output face Zero-order diffractive light intensity, I _mBe other level time diffraction intensities of output face, D _i(x ₃, y ₃) be the gray-scale value of gray level image, i=1,2,3

(2) adopt the Matlab language to the realization of programming of the white light reconstruction process in the phase grating compiling method; Concrete scheme is following: can be defined as three input variable m_Red, m_Green, m_Blue to wavelength X respectively to the red, green, blue three primary colours; After the data combination in each variable and the gray level image matrix by the corresponding three primary colours light intensity of phase place operator transformation output; After the two dimensional gray image strengthens computing through three different gray scales of operator; Be combined into light intensity cubical array I, each ties up the electron gun corresponding of all kinds that gray matrix drives the RGB display respectively, output be 24 pseudo color images; Consider the visual effect of people's eyes to light, promptly the most responsive only green-yellow light of human eye according to the additive color mixture principle, is revised the weight coefficient of three primary colours in white light is synthetic; For obtaining the pseudo color image of single color, handle former gray level image r with the cosine operator, g, the b three primary colours, obtain I (:;:, 1), I (::, 2); I (::, 3) strengthen three primary colours, go out public correlative value w according to the weight coefficient proportioning then; Finally export by controlled variable r, g, the adjusted three primary colours of b can all be fixed the wavelength control district numerical value that the cosine operator is handled.

2. method according to claim 1 is characterized in that, always supposes in the described white light source of (2) step only to contain 3 kinds of coloured light λ of red, green, blue r, and λ g, λ b, the light intensity in the output face then is expressed as the non-coherent addition of these 3 kinds of coloured light outputs

I(D(i，j))＝I(D(i，j)，λ _r)+I(D(i，j)，λ _g)+I(D(i，j)，λ _b)。

3. method according to claim 1; It is characterized in that; Can be defined as three input variable m_Red, m_Green, m_Blue to wavelength X respectively to the red, green, blue three primary colours; Its value all changes between 0-255, after the data combination in each variable and the gray level image matrix by the corresponding three primary colours light intensity of phase place operator transformation output.

4. method according to claim 1 is characterized in that, behind the weight coefficient of correction three primary colours in white light is synthetic, the three primary colours of output are at last: r=0.30*I (::, 1), g=0.59*I (::, 2), b=0.11*I (::, 3).

5. method according to claim 4 is characterized in that, is the pseudo color image of output single color, public correlative value w=0.30*I (:;:, 1)+0.59*I (::, 2)+0.11*I (:;:, 3), finally export by controlled variable r, g; The adjusted three primary colours of b are: I (::, 1)=r*W/255; I (::, 1)=g*W/255; I (::, 1)=b*W/255, the wavelength control district numerical value that the cosine operator is handled all is fixed as 130.

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