CN101943839B - Automatic focusing method for integrated automatic focusing camera device - Google Patents

Abstract

The invention discloses an integrated automatic focusing camera device and a definition evaluation method. The reliable evaluation of the focusing definition is guaranteed by taking the high-frequency component of an image signal as a feature estimation value of the focusing definition and by adopting a spatial domain and frequency domain combined algorithm method. The automatic focusing device realizes the calculation of the definition evaluation value and the control over the back and forth movement of an optical focusing lens by controlling a stepper motor, makes an image formed at a most definite focusing position by adopting a spatial domain and frequency domain multi-feature climbing search strategy and ensures quick focusing by adopting a digital signal processor for acceleration. By combining a communication interface and a control protocol, an integrated camera device is realized.

Description

The auto focusing method of incorporate automatic-focusing camera device

Technical field

The automatic focus technology that the present invention relates to a kind of incorporate electron camera and be applied to this electron camera relates in particular to a kind of incorporate automatic-focusing camera device and sharpness evaluation method.

Background technology

Traditional automatic focus technology is divided into two kinds of active and passive types, and active automatic focus utilizes infrared ray or ultrasound wave to measure the distance between video camera and the object, thus the adjustment focal position; Passive type then is a light of accepting external object through passive, adjusts focal position through the mode that associated electrical detects.

Along with development of digital image, increasing automatic focusing system depends on image processing algorithm, rather than active distance measuring method.The Flame Image Process theory thinks that the focusing system of camera lens is equivalent to a low-pass filter, and the cutoff frequency of wave filter is by current image distance and lens focus decision.Therefore, just can judge through the high fdrequency component of extracting image the sharpness of present image.Compare with the automatic focus of general camera; Video camera, especially video monitoring are higher to focusing speed and accuracy requirement with video camera, and this is because scene changes complicated; It is fast that optics becomes times speed; If focusing speed is slow or precision is low, then the picked-up video image poor visual effect or be blurred picture mostly, be applied to have in the video monitoring very big limitation.

According to the passive focusing algorithm of image definition tolerance, its performance is is mainly evaluated and tested by following parameter:

1, accuracy, promptly the sharpness peak that draws of algorithm must the focal position of reality or near.

2, unimodal scope, promptly the articulation curve that draws of algorithm must be unimodal characteristic in big as far as possible scope.

3, universality, promptly algorithm must show in most of environment well, rather than only is applicable to several kinds of specific occasions.

4, peak value steep, promptly articulation curve need near precipitous rising or decline focal zone, with accurate location focal position.

5, algorithm complex, algorithm complex must adapt to the demand of real-time.

Summary of the invention

The objective of the invention is to deficiency, a kind of incorporate automatic-focusing camera device and sharpness evaluation method are provided to prior art.

The objective of the invention is to realize through following technical scheme:

A kind of incorporate automatic-focusing camera device, it comprises: variable times Zoom optic lens unit, ccd image sensor unit, electric-motor drive unit, camera signal processing unit, DSP graphics processing unit and communication unit.Wherein, Said variable times Zoom optic lens unit, ccd image sensor unit, camera signal processing unit, DSP graphics processing unit, electric-motor drive unit polyphone, electric-motor drive unit successively link to each other with variable times Zoom optic lens unit, and the camera signal processing unit links to each other with communication unit respectively with the DSP graphics processing unit.

A kind of auto focusing method of above-mentioned incorporate automatic-focusing camera device may further comprise the steps:

(1) selects suitable sharpness evaluation region: at first under the prerequisite that not disturbed by neighboring region, select suitable region of search size, select the position of region of search then according to the clear area of present image.

(2) select suitable sharpness evaluation function: at first through frequency domain evaluation function, spatial domain evaluation function, and the optimal evaluation function that combines of frequency domain and spatial domain as sharpness evaluation function, based on DSP algorithm is optimized then.

The invention has the beneficial effects as follows: the present invention serves as the characteristic estimated value that focuses on sharpness with the high fdrequency component of picture signal, and the computing method that adopted spatial domain and frequency domain to combine are guaranteed focusing on the reliable evaluation of sharpness.Automatic focusing system is except that realizing that the sharpness evaluation of estimate is calculated; Through Stepping Motor Control being realized the control that moves forward and backward of optical focusing lens; Adopt the search by hill climbing strategy of spatial domain and the many characteristics of frequency domain, make imaging be in the most clear position of focusing, realize the integrated imaging function of video camera.Compare with existing automatic-focusing camera, can satisfy under the prerequisite of real-time performance, realize more stable focusing.

Description of drawings

Fig. 1 is the block diagram of apparatus of the present invention;

Fig. 2 is the articulation curve figure of search box when too small;

Fig. 3 is the influence synoptic diagram of neighboring region to the region of search;

Fig. 4 is the articulation curve figure of search box when excessive;

Fig. 5 is the sectional view of Hi-pass filter;

Fig. 6 is the computation complexity comparison diagram before and after the algorithm optimization;

Fig. 7 is the optimum articulation curve figure of this algorithm use.

Fig. 8 is the circuit diagram of dsp graphics processing unit

Embodiment

As shown in Figure 1; The incorporate automatic-focusing camera device of the present invention comprises variable times Zoom optic lens unit, ccd image sensor unit, electric-motor drive unit, camera signal processing unit, DSP graphics processing unit and communication unit; Wherein, Variable times Zoom optic lens unit, ccd image sensor unit, camera signal processing unit, DSP graphics processing unit, electric-motor drive unit polyphone, electric-motor drive unit successively link to each other with variable times Zoom optic lens unit, and the camera signal processing unit links to each other with communication unit respectively with the DSP graphics processing unit.Communication unit is responsible for communicating by letter with host computer.

Variable times Zoom optic lens unit, ccd image sensor unit and electric-motor drive unit are formed imaging moiety; Wherein variable times Zoom optic lens unit and electric-motor drive unit can be bought the LM10 camera lens of Shun's space optics science and technology (group) company limited and realize, the ccd image sensor unit can adopt the 4103-227 nest plate group of Sony to realize.

Variable times Zoom optic lens unit comprises focus lens group and the stepper motor that is used to drive lens combination.Simultaneously, also comprise miscellaneous part, for example, be used to stop the infrared filter of infrared incident light, be used to change the adjustable diaphragm and the driving circuit that is used to drive infrared filter and adjustable aperture of incident light quantity.

Electric-motor drive unit is used for the mobile of control step motor-driven focus lens group, the adjusting of aperture, the adjusting of time shutter etc.

The ccd image sensor unit is reached reference object photo-sensitive cell and converted it into the pixel by lens unit is the electronic signal of unit, and exports this vision signal.Different with the cmos imaging principle, all exposures at one time of each pixel during the CCD imaging, temporal correlation is stronger.

The camera signal processing unit is used for the electronic signal that ccd sensor spreads out of is done further processing, improves picture quality.Comprise the electronic signal processing and amplifying of sampling, transform through A/D it is converted into digital signal, to digital signal correct, AWB etc. improves its picture quality, after handling its output format according to digital picture is exported.This element can adopt the 4103-227 nest plate group of Sony to realize

The DSP graphics processing unit is responsible for the realization of automatic focus (AF) algorithm.At first, device is used to analyze the necessary image definition of focusing algorithm.Sharpness is by the decision of the high fdrequency component of present image and contrast, and is more and contrast is high more if the present image high fdrequency component accounts for the ratio of entire image energy, and then image is more near focal zone, otherwise then image is got over away from focal zone.Simultaneously, the DSP module is confirmed the direction that focusing lens moves through to the contrast of image definition, and this signal is passed to motor drive module controls.The schematic diagram of this element is as shown in Figure 8.

Wherein, U1 can adopt the Blackfin series dsp chip of ADI company, and U2 is the camera signal processing unit, can adopt the 4103-227 nest plate group of Sony to realize that U3 can adopt the SP3220EEA chip of SIPEX company.The PPICLK of U1 is connected to the CLK of U2, and the PPID0-7 of U1 is connected to the DATE0-7 of U2 successively, and the SCL of U1 and SDA are connected to SCL and the SDA of U2 respectively.The UART_TX of U1 and UART_RX are connected to DIN and the ROUT port of U3 respectively.1 one of resistance R meet 3.3V; A SCL pin that is connected to U1,2 one of resistance R meet 3.3V, a SDA pin that is connected to U1; Capacitor C 1 connects C1-pin and the C1+ pin of U3 respectively; Capacitor C 2 connects C2-pin and the C2+ pin of U3 respectively, and capacitor C 3 connects ground wire and V+ pin respectively, and capacitor C 4 connects ground wire and V-pin respectively.

Video camera with above equipment disposition can form vision signal clearly with extraneous scenery, and it is exported in the external display screen or storage medium.

Auto focusing method of the present invention may further comprise the steps

1, select suitable sharpness evaluation region, comprising: suitable region of search size is selected in (1) under the prerequisite that not disturbed by neighboring region, the position of region of search is selected in (2) according to the clear area of present image.

2, select suitable sharpness evaluation function, comprising: (1) through frequency domain evaluation function, spatial domain evaluation function, and the optimal evaluation function that combines of frequency domain and spatial domain as sharpness evaluation function, (2) are optimized algorithm based on DSP.

1, selects suitable sharpness evaluation region

The selection of sharpness evaluation region can directly have influence on the computation complexity and the focusing accuracy of focusing algorithm.On the one hand, the selection of focal zone size directly has influence on the computation complexity of focusing algorithm, accelerates focusing speed.On the other hand, pick out interesting areas through certain algorithm and focus on, reject background parts, can effectively improve the unimodal performance of articulation curve, improve focusing accuracy.

The invention provides the method for a kind of definite sharpness evaluation region size and position.

1.1 under the prerequisite that not disturbed by neighboring region, select suitable region of search size

Excessive or the too small unimodality that all can destroy focusing curve in region of search.Fig. 3 explains that image can blur under defocus condition, and image boundary has expansion to a certain extent.Fig. 2 is if the evaluation region of choosing is too little, and image can make articulation curve forfeiture unimodality owing near the interference of the expansion image zone.Fig. 4 has explained that evaluation region is excessive, then can make articulation curve unimodality variation because of the scenery of having sneaked into too much different depth.Therefore, the upper limit of evaluation region and lower limit must satisfy above-mentioned 2 conditions.Through the test to above-mentioned 2 conditions, the present invention gets the size of the M * N of original image as evaluation region.Wherein, M, N get 1/3 to 1/2 of picturedeep and columns.

1.2 select the position of region of search according to the clear area of present image.

The position of evaluation region directly influences the precision of focusing.The present invention adopts the image gradient method to judge the position of evaluation region.Concrete; Through type (1) is tried to achieve present image level and VG (vertical gradient); Try to achieve the gradient magnitude of current pixel point by formula (2); Try to achieve regional inside gradient size sum respectively as the criterion of judging each regional sharpness size in N preset zone, the zone that sharpness is maximum is as the focused search zone.

$\▿\stackrel{\→}{f}=[G_X,G_Y]=[\∂\stackrel{\→}{f}/\∂x,\∂\stackrel{\→}{f}/\∂y]---\left(1\right)$

$\▿f=\mathrm{mag}(\▿\stackrel{\→}{f})=[{(\∂\stackrel{\→}{f}/\∂x)}^2+{(\∂\stackrel{\→}{f}/\∂y)}^2]---\left(2\right)$

Wherein

Be (x, Grad y), G _XG _YBe respectively the direction gradient value of xy direction.▽ f is the size of

2 select suitable sharpness evaluation function

2.1 through frequency domain evaluation function, spatial domain evaluation function, and the optimal evaluation function that combines of frequency domain and spatial domain as sharpness evaluation function

Image definition is by the high fdrequency component and the contrast decision of present image.

Below be the test mode that the present invention proposes based on the sharpness of frequency domain filtering:

2.1.1 through type (3) adopts 2 dimension Fourier transforms that picture signal is converted to frequency domain by the spatial domain.

$F(u,v)=\frac{1}{\mathrm{MN}}\underset{x=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{y=0}{\overset{N-1}{\mathrm{\&Sigma;}}}f(x,y)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000177581400042.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(\mathrm{ux}/M+\mathrm{vy}/N)}---\left(3\right)$

X wherein, y has represented the coordinate position of image.(x y) is the gray scale function of image to f, MN representative image wide and high.

2.1.2 extract image high fdrequency component (Fig. 5) through an ideal highpass filter, calculate the evaluation function of the number percent of high fdrequency component in entire image as sharpness by formula (4).

Wherein P is whole search box, and Q is by the set of frequency with interior pixel in the search box.(u v) is a frequency-domain function to F.

2.1.3 the computed image gradient magnitude is as the sharpness evaluation function of image.

$\mathrm{Def}\_\mathrm{Gra}\left(t\right)=\underset{(x,y)\&Element;P}{\mathrm{\&Sigma;}}{[g(x,y)-g(x-1,y)]}^2+{[g(x,y)-g(x,y-1)]}^2$

Wherein (x y) is (x, gray-scale value y) to g.

2.1.4 two kinds of evaluation functions are combined, obtain a kind of optimal evaluation function:

Def(t)＝Def_Gra(t)*α+Def_Fre(t)*(1-α)；

Wherein Def_Gra (t) is the image gradient valuation functions, and Def_Fre (t) is the image frequency domain valuation functions,

$\mathrm{\&alpha;}=\frac{\mathrm{Def}\_\mathrm{Gra}\left(t\right)-\mathrm{Def}\_\mathrm{Gra}(t-1)}{\mathrm{Def}\_\mathrm{Fre}\left(t\right)-\mathrm{Def}\_\mathrm{Fre}(t-1)+\mathrm{Def}\_\mathrm{Gra}\left(t\right)-\mathrm{Def}\_\mathrm{Gra}(t-1)}$

As shown in Figure 7, final evaluation function has good peak value steepness and unimodal scope, is easy to realize the focused search algorithm based on climbing method.

2.2 based on DSP algorithm is optimized.

Because frequency domain filtering method computation complexity is very high, and the increase fast along with the increase of sharpness evaluation region of its complexity, therefore can not satisfy the requirement of real-time.

Below be the method for the present invention in order to the optimization frequency domain filtering:

2.2.1 the formula of utilization (5) utilizes FFT FFT to replace DFT the stack that 2 dimension DFT are converted into 2 times 1 dimension DFT again.

$F(u,v)=\frac{1}{M}\underset{x=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000177581400042.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ux}/M}\frac{1}{N}\underset{y=0}{\overset{N-1}{\mathrm{\&Sigma;}}}f(x,y)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000177581400042.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;vy}/N}$

$=\frac{1}{M}\underset{x=0}{\overset{M-1}{\mathrm{\&Sigma;}}}F(x,v)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000177581400042.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;vy}/N}---\left(5\right)$

Wherein

Wherein x, y are image space territory coordinate, and u, v are the image frequency domain coordinate, and M, N are the wide and high of image

2.2.2 2 row real number FFT are merged into the plural number FFT of delegation, calculated amount are reduced half the.Specific as follows:

Make x ₁(n) and x ₂(n) be the real sequence of N point, its DFT is DFT (x ₁(n))=X ₁(k) DFT (x ₂(n))=X ₂(k).

Earlier 2 real sequences are synthesized a complex sequences:

w(n)＝x ₁(n)+jx ₂(n)

Re [w (n)]=x then ₁(n), Im [w (n)]=x ₂(n)

$\mathrm{DFT}\left(x_1\left(n\right)\right)=\mathrm{DFT}\left(\mathrm{Re}\right[w\left(n\right)\left]\right)$

$=\frac{1}{2}\left\{\mathrm{DFT}\left[w\left(n\right)\right]+\mathrm{DFT}\left[w^{*}\left(n\right)\right]\right\}$

$=\frac{1}{2}[W\left(k\right)+W^{*}{(N-k)}_N{R}_N\left(k\right)]$

$=\frac{1}{2}[W{\left(k\right)}_N+W^{*}{(N-k)}_N]R_N\left(k\right)---\left(6\right)$

Wherein W (k) is the frequency-domain function of w (n),

In like manner

$=\frac{1}{2j}[W{\left(k\right)}_N-W^{*}{(N-k)}_N]R_N\left(k\right)---\left(7\right)$

Calculate W (k) back and can calculate X according to (6) (7) two formulas ₁(k) X ₂(k)

2.2.3 utilize the Pa Saiwaer law to reduce the FFT calculating number

According to Pa Saiwaer theorem (formula (8)), picture signal is constantly equal to each frequency component energy sum of frequency domain at the energy of spatial domain.

$\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|x\left(n\right)\right|}^2=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|X\left(k\right)\right|}^2---\left(8\right)$

Therefore, can release the value of sharpness evaluation function and reduce nearly half FFT calculated amount by formula (9).

$=1-\underset{(u,v)\&Element;Q}{\mathrm{\&Sigma;}}F{(u,v)}^2/\underset{(u,v)\&Element;P}{\mathrm{\&Sigma;}}F{(u,v)}^2$

$=1-\underset{(u,v)\&Element;Q}{\mathrm{\&Sigma;}}F{(u,v)}^2/{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000177581400042.png"\; state="\{\{state\}\}">N</figure-callout>}}^2\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|f(x,y)\right|}^2---\left(9\right)$

Wherein PP is whole search box, and Q is by the set of frequency with interior pixel in the search box.X, y are image space territory coordinate, and u, v are the image frequency domain coordinate.

Fig. 6 has shown that the algorithm complex after optimizing has tangible reduction.

4103 CCD nest plates with Sony are that example is specifically listed the self-focusing method of the present invention below.

1. at first confirm the size of sharpness evaluation region, because the digital signal resolution of nest plate output is 704 * 576, according to the principle of step 1.1, we are decided to be 256 * 128 to sharpness evaluation region size.Be divided into 9 to picture in its entirety, every block size is 256 * 128 (allowing overlapping), and every basis (4) formula is calculated its sharpness, with the maximum zone of sharpness as final region of search.

2. for requirement of real time, evaluation function is optimized according to the step of method 2.2.Optimal evaluation function after the optimization is a standard, searches for to confirm accurate focal position through climbing method.

Be the preferred embodiments of the present invention more than, be not limited to the present invention.Concerning the technician who is engaged in this field, the present invention can have change or conversion, but within spirit of the present invention and principle, any change or conversion all should be within protection scope of the present invention.

Claims (1)

1. the auto focusing method of the automatic-focusing camera device of an application continuum, incorporate automatic-focusing camera device comprises: variable times Zoom optic lens unit, ccd image sensor unit, electric-motor drive unit, camera signal processing unit, DSP graphics processing unit and communication unit; Wherein, Said variable times Zoom optic lens unit, ccd image sensor unit, camera signal processing unit, DSP graphics processing unit, electric-motor drive unit polyphone, electric-motor drive unit successively link to each other with variable times Zoom optic lens unit, and the camera signal processing unit links to each other with communication unit respectively with the DSP graphics processing unit; It is characterized in that, may further comprise the steps:

(1) selects suitable sharpness evaluation region: at first under the prerequisite that not disturbed by neighboring region, select suitable region of search size, select the position of region of search then according to the clear area of present image;

(2) select suitable sharpness evaluation function: at first through frequency domain evaluation function, spatial domain evaluation function, and the optimal evaluation function that combines of frequency domain and spatial domain as sharpness evaluation function, based on DSP algorithm is optimized then;

Said through frequency domain evaluation function, spatial domain evaluation function, and the optimal evaluation function that combines of frequency domain and spatial domain specific as follows as sharpness evaluation function:

(A) adopt 2 dimension Fourier transforms that picture signal is converted to frequency domain by the spatial domain through following formula:

$F(u,v)=\frac{1}{\mathrm{MN}}\underset{x=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{y=0}{\overset{N-1}{\mathrm{\&Sigma;}}}f(x,y)e^{-j2\mathrm{\&pi;}(\mathrm{ux}/M+\mathrm{vy}/N)},$

X wherein, y has represented the coordinate position of image; F (x y) is the gray scale function of image, MN representative image wide and high, and u, v are the image frequency domain coordinate;

(B) extract the image high fdrequency component through an ideal highpass filter, draw the evaluation function of the number percent of high fdrequency component in entire image as sharpness by computes:

Wherein, P is whole search box, and Q is by the set of frequency with interior pixel in the search box; F (u v) is a frequency-domain function;

(C) the computed image gradient magnitude is as the sharpness evaluation function of image:

$\mathrm{Def}\_\mathrm{Gra}\left(t\right)=\underset{(x,y)\&Element;P}{\mathrm{\&Sigma;}}{[g(x,y)-g(x-1,y)]}^2+{[g(x,y)-g(x,y-1)]}^2,$

Wherein, (x y) is (x, gray-scale value y) to g;

(D) two kinds of evaluation functions are combined, obtain a kind of optimal evaluation function:

Def(t)＝Def_Gra(t)*α+Def_Fre(t)*(1-α)；

Wherein, Def_Gra (t) is the image gradient valuation functions, and Def_Fre (t) is the image frequency domain valuation functions,

$\mathrm{\&alpha;}=\frac{\mathrm{Def}\_\mathrm{Gra}\left(t\right)-\mathrm{Def}\_\mathrm{Gra}(t-1)}{\mathrm{Der}\_\mathrm{Fre}\left(t\right)-\mathrm{Def}\_\mathrm{Fre}(t-1)+\mathrm{Def}\_\mathrm{Gra}\left(t\right)-\mathrm{Def}\_\mathrm{Gra}(t-1)};$

Said algorithm being optimized based on DSP is specially:

(a) utilize following formula with the stack that 2 dimension DFT are converted into 2 times 1 dimension DFT, utilize FFT FFT to replace DFT again;

$F(u,v)=\frac{1}{M}\underset{x=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{e}^{-j2\mathrm{\&pi;ux}/M}\frac{1}{N}\underset{y=0}{\overset{N-1}{\mathrm{\&Sigma;}}}f(x,y)e^{-j2\mathrm{\&pi;vy}/N}$

$=\frac{1}{M}\underset{x=0}{\overset{M-1}{\mathrm{\&Sigma;}}}F(x,v)e^{-j2\mathrm{\&pi;vy}/N},$

Wherein,

x, y are image space territory coordinate; U, v are the image frequency domain coordinate; M, N are the wide and high of image, and (x y) is the gray scale function of image to f;

(b) 2 row real number FFT are merged into the plural number FFT of delegation, calculated amount is reduced half the; Specific as follows:

Make x ₁(n) and x ₂(n) be the real sequence of N point, its DFT is DFT (x ₁(n))=X ₁(k) DFT (x ₂(n))=X ₂(k);

Earlier 2 real sequences are synthesized a complex sequences:

w(n)＝x ₁(n)+jx ₂(n)

Re [w (n)]=x then ₁(n), Im [w (n)]=x ₂(n)

$\mathrm{DFT}\left(x_1\left(n\right)\right)=\mathrm{DFT}\left(\mathrm{Re}\right[w\left(n\right)\left]\right)$

$=\frac{1}{2}\left\{\mathrm{DFT}\right[w\left(n\right)]+\mathrm{DFT}[w^{*}\left(n\right)\left]\right\}$

$=\frac{1}{2}[W\left(k\right)+W^{*}{(N-k)}_N{R}_N\left(k\right)]$

$=\frac{1}{2}[W{\left(k\right)}_N+W^{*}{(N-k)}_N]R_N\left(k\right)$

Wherein W (k) is the frequency-domain function of w (n),

In like manner $\mathrm{DFT}\left(x_2\left(n\right)\right)=\mathrm{DFT}\left(\mathrm{Im}\right[w\left(n\right)\left]\right)$

$=\frac{1}{2j}[W{\left(k\right)}_N-W^{*}{(N-k)}_N]R_N\left(k\right)---\left(7\right)$

Calculate W (k) back and can calculate X according to (6) (7) two formulas ₁(k) X ₂(k)

(c) utilize the Pa Saiwaer law to reduce the FFT calculating number: according to the Pa Saiwaer theorem, picture signal is constantly equal to each frequency component energy sum of frequency domain at the energy of spatial domain:

$\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|x\left(n\right)\right|}^2=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|X\left(k\right)\right|}^2,$

Therefore, can release the value of sharpness evaluation function and reduce nearly half FFT calculated amount by following formula;

Wherein, PP is whole search box, and Q is by the set of frequency with interior pixel in the search box; X, y are image space territory coordinate, and u, v are the image frequency domain coordinate.

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