CN1797470A - Quick method for picking up stepped edge in sub pixel level - Google Patents

Abstract

The invention belongs to the machine vision and related image processing techniques, relating to the improvement of an image edge extracting method. The steps of the invention: making smooth filtering processing on the original image; searching a boundary point Ps with steady-state grey scale maximum value and a boundary point Pe with steady-stage grey scale minimum value of a step edge; calculating initial values a0, b0 and c0 of edge model parameters; calculating the optimum values of a, b and c and determining the step edge. The initial value selection of the model parameters is simple, and the step edge extraction has high speed, strong robustness and high accuracy.

Description

One sub pixel level quick method for picking up stepped edge

Technical field

The invention belongs to machine vision and associated picture treatment technology, relate to improvement image edge extraction method.

Background technology

The most basic feature of image is the edge, so-called edge is meant that pixel grey scale in the image has step to change or the set of those pixels that the roof shape changes, it is present between target and background, target and target, zone and the zone, and relevant, thereby show as step edge and line edge with the uncontinuity of the first order derivative of brightness of image or brightness of image.Step edge shows as the pixel gray-scale value of brightness of image on the both sides at discontinuous place evident difference, and this species diversity carries out the transition to dark background for image from the bright field scape from visually apparent, or carries out the transition to dark scene from bright background.Handle for machine vision and associated picture, the Pixel-level step edge extracts and can't meet the demands.The precision that step edge extracts directly influences the order of accuarcy that machine vision and associated picture are handled, thus the step edge of sub-pixel-level to be extracted in a lot of occasions be necessary.At present, sub-pixel-level step edge extracting method mainly contains two classes: a class is to carry out interpolation in certain zone of Pixel-level step edge, and as curve fitting or surface fitting, and the extreme value place of leading with curve or curved surface single order is as the accurate position of step edge.In order to obtain sub-pixel level precision, nonlinear optimization method is adopted in the estimation of curve or surface model parameter, because initial value is selected relatively difficulty, the nonlinear optimization process is longer, and precision is subjected to certain restriction.The another kind of method that the sub-pixel-level step edge extracts is earlier original image to be carried out first derivation, makes it become line edge, and then the first moment or the Hessian matrix in calculating pixel level line edge zone, realizes the edge extracting of sub-pixel-level.The common drawback of these two class methods is to calculate comparatively loaded down with trivial detailsly, and the speed of Flame Image Process is slow, is unsuitable for the requirement in real time fast that machine vision and associated picture are handled.

Summary of the invention

The objective of the invention is: the deficiency at existing method exists, a sub pixel level quick method for picking up stepped edge is proposed, further improve the real-time that machine vision and associated picture are handled.

Technical scheme of the present invention is: a sub pixel level quick method for picking up stepped edge is characterized in that the step edge skeleton pattern is defined as:

$y=\frac{a}{1+e^{\frac{x-b}{\mathrm{\σ}}}}+c---\left[1\right]$

The step of extracting the sub-pixel-level step edge is as follows:

(1) use the Gauss convolution kernel that original image is carried out The disposal of gentle filter;

(2) from top to bottom, from left to right press row/column scan image, if the gray-scale value of current scan point compares the fall of the gray-scale value of analyzing spot＞30 before this, then current point is the stable state gray scale maximum value boundary point P of step edge _sThen at P _sContinue scanning after the point, if the gray-scale value of current scan point is than the amplitude of variation of the gray-scale value of analyzing spot＜5 before this, then current point is the frontier point P of the stable state minimum gray value of step edge _e, the span of gray-scale value is 0～255, so P is arranged _sThe gray-scale value y of point _sWith horizontal ordinate x _s, P _eThe gray-scale value y of point _eWith horizontal ordinate x _eSatisfy following formula:

y _s＝y _max，x _s＝x _min

y _e＝y _min，x _e＝x _max [5]

(3) the initial value a of edge calculation model parameter ₀, b ₀, c ₀The initial value that calculates a, b and c according to following formula is respectively:

a ₀＝y _max-y _min＝y _s-y _e [6]

b ₀＝(x _max+x _min)/2＝(x _s+x _e)/2 [7]

c ₀＝y _min＝y _e [8]

(4) calculate a, b, the optimal value of c is determined step edge, the steps include:

1. at a P _sAnd P _eSearch for gray-scale value y by row or column between the row or column at place _e≤ y _i≤ y _sSome P _i(x _i, y _i), i=1,2 ..., m, wherein m is the number of the point that searches, m 〉=3;

2. by formula [1], make

$f(x,y)=y-\frac{a}{1+e^{\frac{x-b}{\mathrm{\σ}}}}-c---\left[9\right]$

Getting the objective optimization function is following formula: $\min \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{f}^2(x_i,y_i)---\left[10\right]$

3. a P _i(x _i, y _i), i=1,2 ..., m brings formula [10] into, obtain an overdetermination about a, b, the Nonlinear System of Equations of c.Utilize the Levenberg-Marquardt nonlinear optimization algorithm to obtain a, b, the optimal value of c; Then put x=b, $y=\frac{a}{2}+c$ Be the position of step edge point.

Advantage of the present invention is: the model parameter initial value is chosen simply, and the step edge extraction rate is fast, strong robustness, precision height.

Description of drawings

Fig. 1 is a step edge skeleton pattern synoptic diagram.

Fig. 2 is that the inventive method step edge extracts the emulation experiment synoptic diagram.

Fig. 3 is to use the inventive method to carry out the synoptic diagram of edge extracting example.

Embodiment

Below the present invention is described in further details.

Step edge skeleton pattern function such as Fig. 1.According to the step edge shape, the step edge skeleton pattern may be defined as:

$y=-\frac{a}{1+e^{\frac{x-b}{\mathrm{\σ}}}}+c---\left[1\right]$

A wherein, b, c is a location parameter, σ represents variance.The geometric meaning of three parameters is: a represents the height at edge, i.e. the maximum steady state value of curve and the difference between the minimum steady-state value; B represents the horizontal ordinate of the symcenter position at edge; C represents the base value at edge, i.e. the minimum steady-state value of curve.The foundation that proposes this model is that this mathematical function is that the profile characteristics of these characteristics and step edge match about x=b point antisymmetry.

Model parameter estimation.

A, b, nonlinear optimization method is adopted in the estimation of c parameter.Guarantee that nonlinear optimization method converges to global optimum's point, the selection of the initial value of parameter is the key link very.

(1) initial value chooses.

Because the step edge model parameter that proposes previously has tangible geometric meaning, so that choosing of parameter initial value becomes simple.

At first doing theoretical analysis, is that formula [1] has according to model:

$y_{\max }=\underset{x\→-\∞}{\lim },y=a+c,y_{\min }=\underset{x\→\∞}{\lim },y=c---\left[2\right]$

So can obtain the initial value of a and c:

a ₀＝y _max-y _min，c ₀＝y _min。[3]

Find out by model, obvious x=b, $y=\frac{a}{2}+c$ Be the symcenter of step edge, so the initial value of b is optional:

b ₀＝(x _max+x _min)/2， [4]

X wherein _Max, x _MinBe respectively the stable state minimum gray value frontier point and the corresponding horizontal ordinate of maximum value boundary point of step edge.

According to model is formula [1], and the step edge point is defined in the point of step edge Grad maximum, and this point is the first order derivative maximum of points, second derivative zero crossing, i.e. y "=0, solve marginal point at the x=b place.

Real image is by the discrete two-dimensional digital image that changes into of line scanning, is worth with the gray scale (brightness) of each point of numeral image between 0～255.When practical operation, the step of extracting the sub-pixel-level step edge is as follows:

(1) use the Gauss convolution kernel that original image is carried out The disposal of gentle filter.(referring to Ma Songde, Zhang Zhengyou writes, " computer vision-theory of computation and algorithm basis ", Beijing: Science Press, 1998.)

(2) from top to bottom (from left to right) is by row (row) scan image, if when the gray-scale value (span is 0～255) of current scan point has obvious decline than the gray-scale value of analyzing spot before this (drop-out value＞30), then current point is the stable state gray scale maximum value boundary point P of step edge _sThen at P _sContinue scanning after the point, if the gray-scale value of current scan point does not have obvious variation (changing value＜5) than the gray-scale value of analyzing spot before this, then current point is the frontier point P of the stable state minimum gray value of step edge _eSo P is arranged _sThe gray-scale value y of point _sWith horizontal ordinate x _s, P _eThe gray-scale value y of point _eWith horizontal ordinate x _eSatisfy following formula:

y _s＝y _max，x _s＝x _min

y _e＝y _min，x _e＝x _max [5]

(3) the initial value a of edge calculation model parameter ₀, b ₀, c ₀The initial value that calculates a, b and c according to following formula is respectively:

a ₀＝y _max-y _min＝y _s-y _e [6]

b ₀＝(x _max+x _min)/2＝(x _s+x _e)/2 [7]

c ₀＝y _min＝y _e [8]

(4) calculate a, b, the optimal value of c is determined step edge, the steps include:

1. at a P _sAnd P _eSearch for gray-scale value y by row or column between the row or column at place _e≤ y≤y _sSome P _i(x _i, y _i), i=1,2 ..., m, wherein m is the number of the point that searches, m 〉=3;

2. by formula [1], make

$f(x,y)=y-\frac{a}{1+e^{\frac{x-b}{\mathrm{\σ}}}}-c---\left[9\right]$

Getting the objective optimization function is following formula: $\min \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{f}^2(x_i,y_i)---\left[10\right]$

3. a P _i(x _i, y _i), i=1,2 ..., m brings formula (10) into, obtain an overdetermination about a, b, the Nonlinear System of Equations of c.Utilize the Levenberg-Marquardt nonlinear optimization algorithm to obtain a, b, the optimal value of c; Then put x=b, $y=\frac{a}{2}+c$ Be the position of step edge point.

Emulation experiment.

Emulation experiment has been carried out on the edge extracting method limit that the present invention is based on the step edge skeleton pattern, and step is as follows:

(1) produce a desirable step signal, its desirable step edge point is B=1.50, as Fig. 2 (a).

(2), make it to be similar to the true step signal of a real world, as Fig. 2 (b) with level and smooth this step signal of Gaussian function.

(3) additive noise signal of about 37dB of signal to noise ratio (S/N ratio) of generation and Gaussian distributed is superimposed upon real step signal with it and folds, as the edge contour signal, as Fig. 2 (c).

(4) method of employing 5.2 is tried to achieve parameter a, b, and c, wherein b is the step edge point, as Fig. 2 (d).

(5) repeating step (3), (4) 1000 times obtain 1000 b values, and mean value is 1.5056.

(6) deviation (b-B) of 1000 step edge point b of calculating and true step edge point B, obtaining standard deviation is 0.0393.According to 3 σ principles of measuring error, the positional precision of extracting step edge based on the edge extracting method of step edge skeleton pattern should promptly can be accurate to sub-pixel-level at 0.12 below the pixel.It is 55ms that said method extracts each average consuming time of step edge point b.In addition, according to above-mentioned steps (1)～(6), the positional precision of the step edge point that the method that adopts the method for interpolation respectively and ask single order to lead back calculating first moment or Hessian matrix is tried to achieve is respectively 0.31 pixel and 0.22 pixel, average 108ms and 145ms respectively consuming time.Therefore, be significantly improved based on the edge extracting method of step edge skeleton pattern speed than other existing method.

Fig. 3 is that of this algorithm extracts instance graph.On the visual observation just as can be seen this algorithm extracted the position at edge more accurately.

Claims (1)

1, a sub pixel level quick method for picking up stepped edge is characterized in that, the step edge skeleton pattern is defined as:

$y=\frac{a}{1+e^{\frac{x-b}{\mathrm{\σ}}}}+c---\left[1\right]$

The step of extracting the sub-pixel-level step edge is as follows:

(1) use the Gauss convolution kernel that original image is carried out The disposal of gentle filter;

(2) from top to bottom, from left to right press row/column scan image, if the gray-scale value of current scan point compares the fall of the gray-scale value of analyzing spot＞30 before this, then current point is the stable state gray scale maximum value boundary point P of step edge _sThen at P _sContinue scanning after the point, if the gray-scale value of current scan point is than the amplitude of variation of the gray-scale value of analyzing spot＜5 before this, then current point is the frontier point P of the stable state minimum gray value of step edge _e, the span of gray-scale value is 0～255, so P is arranged _sThe gray-scale value y of point _sWith horizontal ordinate x _s, P _eThe gray-scale value y of point _eWith horizontal ordinate x _eSatisfy following formula:

y _s＝y _max，x _s＝x _min

y _e＝y _min，x _e＝x _max [5]

(3) the initial value a of edge calculation model parameter ₀, b ₀, c ₀The initial value that calculates a, b and c according to following formula is respectively:

a ₀＝y _max-y _min＝y _s-y _e [6]

b ₀＝(x _max?+x _min)/2＝(x _s+x _e)/2 [7]

c ₀＝y _min＝y _e [8]

(4) calculate a, b, the optimal value of c is determined step edge, the steps include:

1. at a P _sAnd P _eSearch for gray-scale value y by row or column between the row or column at place _e≤ y _i≤ y _sSome P _i(x _i, y _i), i=1,2 ..., m, wherein m is the number of the point that searches, m 〉=3;

2. by formula [1], make

$f(x,y)=y-\frac{a}{1+e^{\frac{x-b}{\mathrm{\σ}}}}+c---\left[9\right]$

Getting the objective optimization function is following formula: $\min \underset{i=1}{\overset{m}{\mathrm{\Σ}}}{f}^2(x_i,y_i)---\left[10\right]$

3. a P _i(x _i, y _i), i=1,2 ..., m brings formula [10] into, obtain an overdetermination about a, b, the Nonlinear System of Equations of c.Utilize the Levenberg-Marquardt nonlinear optimization algorithm to obtain a, b, the optimal value of c; Then put x=b, $y=\frac{a}{2}+c$ Be the position of step edge point.