CN109711284A - A kind of test answer sheet system intelligent recognition analysis method - Google Patents
A kind of test answer sheet system intelligent recognition analysis method Download PDFInfo
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Abstract
The invention discloses a kind of test answer sheet system intelligent recognition analysis method, by by the image grayscale in Preprocessing Technique, image binaryzation, image denoising, Morphological scale-space decomposition operation item by item；Using monitoring image gradient and rotation correction technology, independent peak point is formed, image is read and carries out binaryzation；Edge detection technology is continued to use, by constructing the monitoring of edge detection operator to original image differential technology, forms image filtering, image enhancement, image detection, Canny operator, Canny limb recognition algorithm；Data image discriminance analysis is carried out using image recognition point location and affine transformation.The identification of answering card intelligent high-speed can be achieved, the precision of images is higher, and it is high-efficient, do not limit to specific scanning device, to the big data mining analysis of batch scanning result, energy intelligent recognition goes out specific wrong knowledge point and Intelligent statistical is concluded.
Description
Technical field
The present invention relates to a kind of test answer sheet system intelligent recognition analysis methods.
Background technique
Currently, there are picture instabilities for answering card identification at this stage, lack big data analysis, low efficiency, Bu Nengshi
The Current Situations such as not specific wrong knowledge point.It is accustomed to irregular since examinee answers, and test answer sheet pattern is changeable, generates
Error result cannot intervene and monitor in time.
Summary of the invention
The technical problem to be solved by the present invention is to overcome the identification of answering card in the prior art lacking there are picture instability
It falls into, a kind of test answer sheet system intelligent recognition analysis method is provided.
In order to solve the above-mentioned technical problems, the present invention provides the following technical solutions:
The present invention is using image recognition technology, using input equipments such as the relatively inexpensive digital camera of price, scanners
Information on examinee's answering card is acquired, intelligence deposit Computer Database after acquisition, finally using at digital picture
The essential information of examinee and paper answer are carried out intelligent recognition by the technology of reason, are stored in new database.There is real-time prison simultaneously
The characteristic superintended and directed can make a response rapidly, be handled, can also observe and read at any time when paper detection goes wrong
The state of volume, in due course intellectual analysis go out paper items score and total score, and intelligently conclude examinee's mistake knowledge point and summarize.
Specifically includes the following steps:
S1: to image preprocessing
Image gray processing, image binaryzation, image denoising, Morphological scale-space are carried out to the picture of examinee's answering card；
Described image binaryzation, which refers to, reflects image entirety by threshold value appropriate screening for gray level image；
The Morphological scale-space includes expansion and corrosion；
S2: detection image gradient simultaneously carries out rotation correction, forms independent peak point, reads image and carries out binaryzation；
S3: edge detection is extracted
Edge detection extracts the feature of discontinuous section in image, determines specific region according to closure continuous boundary, will
Region division with same characteristic features together, is demarcated between region by edge, and the Edge definition of edge detection is image
Zone boundary jumpy occurs for middle gray value；Variation of image grayscale situation is reacted with image grayscale distribution gradient, by right
Original image differential technology constructs edge detection operator to carry out edge detection, specifically includes image filtering, image enhancement and figure
As detection；Then Canny limb recognition algorithm is carried out；
S4 image recognition
Including identification point location and affine transformation；The identification point location refers to
The point set of largest contours screens, and four points for being capable of forming maximum quadrangle area, as answering card are searched in concentration
Identification point, then the sequence of four anchor points and position are identified with cross product；
The affine transformation is referred to there is the answer card graphic that deformation occurs to be corrected using affine transformation.
The beneficial effects obtained by the present invention are as follows being: the present invention is by by image grayscale, the image in Preprocessing Technique
Binaryzation, image denoising, Morphological scale-space decomposition operation item by item；Using monitoring image gradient and rotation correction technology, formed
Independent peak point reads image and carries out binaryzation；Edge detection technology is continued to use, by constructing side to original image differential technology
Edge monitors operator monitoring, forms image filtering, image enhancement, image detection, Canny operator, Canny limb recognition algorithm；It adopts
Data image discriminance analysis is carried out with image recognition point location and affine transformation.The identification of answering card intelligent high-speed, image can be achieved
Precision is higher, high-efficient, does not limit to specific scanning device, can intelligent recognition to the big data mining analysis of batch scanning result
Specific wrong knowledge point and Intelligent statistical are concluded out.
Detailed description of the invention
Attached drawing is used to provide further understanding of the present invention, and constitutes part of specification, with reality of the invention
It applies example to be used to explain the present invention together, not be construed as limiting the invention.In the accompanying drawings:
Fig. 1 is the result of image expansion and corrosion；
Fig. 2 limb recognition algorithm flow schematic diagram；
The position Fig. 3 algorithm of convex hull schematic diagram；
Fig. 4 affine transformation effect picture.
Specific embodiment
Hereinafter, preferred embodiments of the present invention will be described, it should be understood that preferred embodiment described herein is only used
In the description and interpretation present invention, it is not intended to limit the present invention.
Embodiment
1. Preprocessing Technique
1.1 image gray processing
The color of each pixel of color image is made of red (R), green (G), blue (B) three kinds of color components, RGB
Color mode is that progress mixing color, each color have 255 kinds of gray values that can take from optical principle, and 0 representative is most dark
Black, otherwise 255 indicate white.Gray level image is to set identical rainbow image for tri- component values of R, G, B.Ash
The characteristics of image description of image is spent there is no changing, and brightness and the coloration that still can reflect whole image entirety and part are special
Sign.
Image gray processing is exactly the process for converting color image to gray level image.Since processing color image needs RGB
Three channels, time overhead is bigger, and image gray processing is exactly that the data transmission of triple channel is become single channel, can subtract in this way
Calculation amount in few image processing process.The complexity and information processing degree of image gray processing reduction image.Image gray processing
Several ways have
(1) simple component method is taken
The value of R in triple channel image, G, tri- components of B can take according to actual needs any one component value as gray scale
The gray value of image.Gray processing formula is as follows:
Gray=B；
OR Gray=G；
OR Gray=R；
(2) maximum value process
R, the maximum value in tri- components of G, B, then using the maximum as the result after gray processing are calculated first, it may be assumed that
Gray=max (R, G, B)
(3) mean value method
This method first calculates the average value of three components, and then using average value as the gray value of gray level image, formula is such as
Under:
Gray=(B+G+R)/3
In image gray processing, weighted mean method is most common method.Because weighted mean method is according to human eye pair
The respective different weight of sensitivity distribution of three primary color components, such gray processing result is more true reasonable, more meets reality
Border application.
1.2 image binaryzation
The process of image binaryzation is that gray level image is reflected image entirety by threshold value appropriate screening.In image
Set maximum for all gray values greater than threshold value, all gray values less than threshold value are set as minimum.Such processing is whole
Only there are two gray value, that is, black and white for a image.
Wherein g (x, y) indicates output gray level value, and f (x, y) indicates that image input gradation value, T represent threshold value.Above formula indicates
All gray values less than T all take 0, are shown as black and are set as background；All gray values more than or equal to T take 255, for white
It is defaulted as target image.Threshold value is the scale that target image and background image is separated, and the principle that threshold value is chosen is should to save
The key message of image, and the interference of noise can be reduced.
Image binaryzation process more important position of accounting in whole image pretreatment.Global thresholding refers to scheming
As only using a global threshold in binarization, the gray value with this global threshold of each pixel are compared in image
Compared with, if more than it, then extracting waste；Otherwise, it is taken as black.The algorithm of Global thresholding is simple, and the time complexity of algorithm is low, energy
Enough target image and background separation is clear but more dispersed for gray value, target image change rate and noise are all bigger
The case where binaryzation effect it is unobvious.
In order to solve such case, local thresholding method is introduced.The threshold value of local thresholding method is by a certain range of
What gray value determined jointly, the image grayscale mean value of each part is automatically determined into out different thresholds as the threshold value of the block image
Value, self-adaption binaryzation processing.Local threshold selection generally divides an image into several subgraphs, on each sub-image area
Using global threshold method, so as to constitute the local thresholding method of entire image.It on position and gray value simultaneously have compared with
Strong consistency and correlation is generally used for interference than more serious, inferior image, but realizes that speed is slow, in background area
Binaryzation effect is unobvious in the case where being interfered.
Either Global thresholding or local thresholding method, the selection of threshold value also just become most important.Selected threshold has
Many kinds of methods.Three kinds of modes are mainly introduced herein:
(1) average value of all pixels gray value, each pixel value of scan image, if picture average gray value method: are calculated
Element value is greater than average value, then is set as 255 (whites), and pixel is less than average value and is set as 0 (black).But use average value as two
Value threshold value may cause partial objects pixel or background pixel is lost, and binarization result cannot really react source images
Information.
(2) maximum kind differences method (Otsu algorithm): the mainly basic thought of the automatic selection Otsu algorithm of realization threshold value
It is that the gray scale of image is divided into two groups with the gray value of a certain hypothesis, calculates separately this two groups pixel number and gray scale is average
Value, then calculates the inter-class variance of this two groups of data, when inter-class variance maximum, which is exactly image binaryzation
Optimal threshold.Whole image is exactly divided into target image and background two parts by threshold value in fact, when target image class and background classes
Between variance maximum when just represent both foreground and backgrounds difference it is maximum, that is, binaryzation effect it is best when
It waits.Maximum kind differences method is very sensitive to the size of noise and target image, generates preferable segmentation effect to unimodal image, but
It is to be easy to appear large-scale black region when prospect and unconspicuous background gray levels difference, or even whole picture figure can be lost
As information [6].
(3) best threshold method: also referred to as iterative method, is a kind of based on the thought approached.Key step are as follows:
1. the maximum gradation value and minimum gradation value of entire image are found out, using the average value of the two as the threshold value of most initial
T (j), j are the number of iterations, initial value 0.
2. dividing the image into target image foreground and background according to threshold value T (j), a pixel in foreground area is found out respectively
The average gray value of pixel in point and background.
3. finding out new threshold value.
4. if T (j)=T (j+1), gained be threshold value, otherwise repeat 2.~4..
The effect of best threshold method is relatively good, can accurately distinguish out the target and background of image, but slight part is distinguished not
It is careful.Image binaryzation processing can become image simply, background information and the target information in image to be distinguished, allowed
The data volume of image becomes smaller, the target object profile of prominent image.Gray processing and binaryzation operation are that an image reduces dimension
Process, reduce dimension not only the feature of image can be made more obvious the operation of image, can also reduce processing image
When operation times.
1.3 image denoising
Picture signal is easy to be caused the image quality of image unclear by noise pollution during acquiring, storing and transmitting
It is clear, it influences people and the understanding and analysis of image is handled.The origin cause of formation and feature of several frequently seen picture noise are understood below.
(1) additive noise
Additive noise refers to that noise is added with signal, and no matter signal whether there is, and noise can all exist, and can only adopt in practice
It takes measure to reduce the influence of additive noise, and cannot thoroughly eliminate.It is main to make an uproar including what is generated when interchannel noise and scan image
Sound is expressed using formula are as follows:
F (x, y)=g (x, y)+n (x, y)
Wherein f (x, y) indicates noisy image, and g (x, y) indicates picture signal, and n (x, y) indicates interchannel noise.
(2) multiplicative noise
Multiplicative noise is related to signal, and then the change of picture signal and change.Generally caused by channel is undesirable, signal
Just exist in noise, noisy image f (x, y) can generally be indicated are as follows:
F (x, y)=g (x, y)+n (x, y) g (x, y)
(3) salt-pepper noise
Salt-pepper noise refers to that the noise of larger and smaller gray value is presented in some pixel or region.Display in the picture
It is exactly to occur black or white pixel at random, introduces error in transform domain, allows the noise of noise after image inverse transformation.The spiced salt is made an uproar
The corresponding probability density function of sound indicates are as follows:
The probability density of salt-pepper noise in the picture is expressed in formula, if b > a, gray value b is shown as one in image
A bright spot when b < a, is shown as a dim spot.If the gray value of Pa or Pb is zero, become unipolar pulse, other situation pulses
Noise is analogous to the spiced salt particle of random distribution on the image, becomes bipolar pulse, that is, salt-pepper noise.Salt-pepper noise goes out
Present random site, noise spot depth are substantially stationary.
(4) Gaussian noise
Gaussian noise is a kind of noise the most universal, and noise spot is randomly generated, and depth is also random, it general
Rate density function is Gaussian distributed.I.e.
When generating the image superposition of Gaussian noise, the contrast of image is reduced, stereovision is deteriorated, edge seems fuzzy.
Gaussian noise is determined by flattening mean value and two instantaneous covariance functions at that time completely, if noise is stable, average value
It is unrelated with the time, and covariance function then becomes only correlation function related with the difference of two moments considered, it is in the sense
It is equivalent to power spectral density.
Image denoising is important link and step in image procossing, it is therefore an objective to be filtered out various present in real image
Noise, improve picture quality, preferably embody original image entrained by information, reduce the influence of noise.The effect of image denoising
Fruit will have a direct impact on other subsequent processing operations, and it is complete to be able to maintain raw information to the accurate noise reduction process of image progress
Property while, and remove useless information in signal, the final image for obtaining high quality.
1.4 Morphological scale-space
The image that Morphological scale-space grows up primarily directed to bianry image according to the set enumeration tree of mathematical morphology
Processing method.Morphological transformation process nature for process of aggregation is mutual between set and structural element by image shape
Effect shows, and the shape of structural element determines the shape information of the Morphological scale-space signal of being extracted, and general processing is
Target image structural element and background are subjected to the operations such as intersection, union.
Morphological operation operates image exactly based on shape, and most basic is expansion and corrodes, they
It is to be compared pixel each in image and displacement element point by point, is handled accordingly according to comparison result.
Expansion can connect gap smaller in image, and target image is allowed to expand；Corrosion can remove smaller in image
The particular points such as burr, protrusion reduce image.Expansion and etching operation can eliminate noise, by independent pictorial element from background
In separate, adjacent elements are integrated, apparent maximum region and minimum region are found, find out the ladder of image
Degree.The application of expansion and corrosion is quite extensive.
(1) it expands
Simple expansion is the process being merged into all background dots of target image contact in target image.As a result make
The area of target image increases.General expansion is defined as:
Formula represents the result that B expands A.Acquired results be the image of the opposite and own origin of B and by
Based on mobile element z shifts image.A is the set of all displacement z by B expansion and A at least one element is
Overlapping.Process can be divided into:
1. with structural element B, each pixel of scan image A
2. doing with operation with the bianry image that structural element is covered with it
3. the pixel of result images is 0 if being all 0.It otherwise is 1
(2) corrode
Simple corrosion is to eliminate the process of target image peripheral limit point, as a result makes remaining target image along it
The small circle of the original image on periphery.Corrosion is defined as:
A ⊙ B=z | (B)z∈A}
A, B are two set on Z, are corroded using B as structural element to A, Corrosion results are by mobile element z group
At set so that the result of mobile element is still contained in A in B.The whole process that B corrodes A is as follows:
"AND" behaviour is with the bianry image that structural element is covered with it with each pixel of structural element B, scan image A
If making all is 1, the pixel of result images is 1.When otherwise carrying out Image erosion processing by the above process for 0, if structure
All black color dots in element are identical with back vegetarian refreshments, otherwise it is white which, which is black,.
Expansion and corrosion can be converted into the logical operation of set, and algorithm is simple, be suitable for parallel processing, and be easy to hardware reality
It is existing, the operations such as image segmentation, refinement, extraction skeleton, edge extracting, shape analysis are carried out to bianry image.
Such as the skeleton of binary map is white point, then being precisely to white bone to the expansion process of black skeleton binary map
The corrosion treatment of frame binary map.Similarly, expansion process of the corrosion treatment of black skeleton binary map namely to white skeleton.?
Under the different conditions of demand of target image, the selection and processing algorithm of expansion and corrosion be will be different, the selection of structural element
Morphology effect can be all directly affected with size.Fig. 1 is the result of image expansion and corrosion.
2. detection image gradient and rotation correction technology
Answering card may generate image inclination, horizontally or vertically mistake due to various reasons during acquiring image
Position will carry out correctly identification and be corrected firstly the need of to it, and here is for the inclined detection of image and correction.
Answer card graphic is obtained using scanner as shown in Figure 1, there is an apparent black horizontal line in image, therefore can be with
Straight line as correction.
The processing time is reduced in order to compress image information, converts the image into gray level image, then carry out binary conversion treatment.Ash
The data of degree image save as two-dimensional array g (i, j), and bianry image saves as two-dimensional array b (i, j).
If there was only inclined straight line in answering card figure, other straight lines are not present, this straight line is easily detected
Out.Judge whether image tilts using the inclination angle of this straight line in hough change detection image, and with this inclination angle.
If indicating straight line with the inclination angle of the distance of straight line to origin and straight line, this straight line are as follows:
ρ=xcos (θ)+ysin (θ)
Here ρ is distance of the straight line to origin, and the image most upper left corner is exactly some origin, and θ is the inclination angle of straight line, is exactly
The angle of straight line and x-axis.ρ and θ constitutes a parameter space, referred to as ρ θ parameter space.For any one point A on x/y plane
(xi, yi), there is ρ=xi·cos(θ)+yiSin (θ), this is a sine curve in ρ θ parameter space.If in x/y plane
An only line segment 1 shares a point on this line segment, carries out hough transformation to it, just obtain the n item in ρ θ parameter space
Sine curve.Because line segment 1 has identical ρ and θ in xy plane, these sine curves can phase in ρ θ parameter space
It meets at a bit, forms a peak point in parameter space.Coordinate of this peak point in parameter space is exactly straight line in xy
ρ and θ in plane.It is several in corresponding parameter space after hough transformation if there is several straight lines in plane
A peak point.
As soon as carrying out the ρ θ parameter space that Hough transform obtains when there was only a line segment in image to image and forming a peak
Value point.
The inclination angle of straight line and aligning step are as follows in Hough transform detection image:
(1) entire image is read, color image is become into gray level image, and it is inner to be stored in two-dimensional array g (i, j).Wherein
I is rower, and j is column mark, and g (i, j) indicates the gray value of corresponding rower i and column mark j；
(2) image is become into bianry image.It is verified by test of many times, effect is best when binarization threshold is 50, can have
The straight line by black line and other colors in image of effect distinguishes.The data of bianry image are stored in bw (i, j)；
(3) hough transformation is carried out to image.A two-dimensional array A (ρ, θ) is initially set up as the cumulative of parameter space
Device.Here ρ is distance of the straight line to origin, and range is the length from 0 to answering card image diagonal.θ is the inclination angle of straight line, model
Enclose is -90 ° to 90 °.Then the binary image data bw (i, j) that second step obtains is scanned, is by the inner all pixels value of bw (i, j)
The coordinate of 0 point preserves.Point (the bw for being 0 for pixel value in bw (i, j)i, bwj), by (bwi, bwj) substitute into formula (1)
In, enable θ be equal to each of -90 ° to 90 ° values, if obtained ρ value arrives between the length of answering card image diagonal 0,
The value of corresponding A (ρ, θ) is just added 1.Obtained two-dimensional array A (ρ, θ) is exactly ρ θ parameter space.
(4) obvious three peak values of its parameter space, wherein only one is target line, it is in addition answering card there are also two
The peak value of many squares formation on the right of image and below, it is therefore desirable to the peak value detected in next step be differentiated, be
The no straight line in image.
(5) it is a two-dimensional array that hough, which converts domain space, finds the peak value of hough transformation domain space, that is, this
The maximum value of two-dimensional array, and its position is write down, it is denoted as (ρ ', θ ').And the peak value (ρ ', θ ') found and its neighborhood
In hough converter unit be set as zero, Size of Neighborhood is 8 × 8.
It (6) whether is straight line in answer card graphic corresponding to the peak value (ρ ', θ ') that finds of judgement.Method of discrimination are as follows:
By 90 ° of-θ ' of image rotation, it is located at this straight line probably on a vertical line.Here θ ' is that the peak value institute that second step detects is right
The straight line inclination angle answered.Detect the longest line segment length on this straight line.If a threshold value T, if the longest on this straight line
Line segment length is greater than threshold value T, just illustrate this peak value it is corresponding be straight line in answer card graphic.
(7) second step is repeated to the 4th step, until finding out the straight line in answer card graphic.The inclination angle of this straight line is exactly institute
The inclination angle theta for the answer card graphic asked '.Figure is rotated into θ ' counterclockwise, two in image straight lines is horizontally situated, just completes
Detection image gradient and rotation correction.
3. edge detecting technology
Edge refers to surrounding pixel gray value set jumpy, is the essential characteristic of image, and edge is being image
The important evidence of segmentation.
The feature that edge detection extracts discontinuous section in image determines specific region according to closure continuous boundary, will have
The region division for having same characteristic features together, is demarcated between region by edge.Edge detection is greatly reduced in image
The removal of irrelevant information is only retained the important feature attribute in image by data volume.
If the edge in edge detection is considered the changed place of certain amount point brightness, then edge detection can
To regard the derivative for calculating brightness change as.The essence of edge detection is to extract target image and back in image using appropriate algorithm
Boundary between scape.The Edge definition of edge detection is that zone boundary jumpy occurs for gray value in image.
Variation of image grayscale situation can be reacted with image grayscale distribution gradient, so edge detection method is exactly to pass through pair
Original image differential technology constructs edge detection operator to carry out edge detection.Edge detection general step be filtering, enhancing and
Detection.
3.1 image filtering
Image filtering inhibits noise in the case where retaining image detail as far as possible, is necessary behaviour in edge detection
Make, eliminates low frequency and Mid Frequency that the noise contribution in image can make picture signal be largely focused on amplitude spectrum, useful letter
Breath may be covered in high band.
Image filtering can distinguish the feature mode of target image, also adapt to image processing requirements, eliminate institute in image
Mixed noise.Filtering processing retains the important informations such as image outline and edge, can finally obtain clear good visual effect
Image.
Gaussian filtering belongs to linear filter, linear filter be frequently used for rejecting in input signal undesired frequency or
Person selects one from many frequencies.Gaussian filtering is typical linear smoothing filtering, can eliminate Gaussian noise, is widely applied
In the denoising process of image procossing.
Gaussian filtering is exactly to be weighted and averaged process to entire image, and each pixel point value is by pixel itself and surrounding
What pixel was weighted and averaged.The process of gaussian filtering is with each pixel in a convolution scan image, benefit
It is weighted and averaged with the neighborhood territory pixel point value that convolution determines, replaces convolution central point pixel value.Gaussian filter is for inhibiting
The noise of Normal Distribution is highly effective, and one-dimensional Gaussian function is as follows:
For image procossing, it is frequently utilized that two-dimensional discrete Gaussian function avoids ringing.Two-dimensional Gaussian function tool
Have rotational symmetry, be in each smoothness it is identical, a direction will not be biased in edge detection；Gaussian filter is used
Neighborhood of pixels weighted mean replaces the pixel value, and each neighborhood territory pixel point weight is dull at random at a distance from central point
Successively decrease；Gaussian function, which is formed by smoothed image, to be polluted by HF noise signal, and useful signal can be only retained；Gaussian filtering
The smoothness of device is determined by parameter adjustment；Two-dimensional Gaussian function convolution can carry out step by step, first with one-dimensional Gaussian function
Number carries out convolution, by result identical one-dimensional Gaussian function convolution vertical with direction, therefore the calculation amount of 2-d gaussian filters with
The width linearity of filtering increases, two-dimensional Gaussian function are as follows:
3.2 image enhancement
While image enhancement is prominent image important information, weaken irrelevant information.Shown in being classified as follows.
Clearly show that image enhancement can be divided into spatial domain enhancing, frequency domain enhancing, colored enhancing and figure in structural formula
As algebraic operation.Image enchancing method mainly introduces spatial domain enhancing and frequency domain enhancing from humidification domain here.
Spatial domain enhancing is directly handled gray value of image to weaken noise.It includes point in algorithm that spatial domain, which enhances,
Mathematical algorithm and local mathematical algorithm, point processing algorithm are exactly the correction of gray level, greyscale transformation and histogram modification, allow image
Imagewise uniform, expanded contrast.Point processing mainly has greyscale transformation and histogram equalization processing, and the principle of greyscale transformation is exactly
By changing the dynamic range or picture contrast of gray scale, reach the method for enhancing gray value of image.Histogram equalization is
A kind of most widely used method in spatial domain image enhancement, the basic principle is that allow the grey value profile of image uniform, most
Reach image enhancement effects eventually.It is to be uniformly distributed that original image is obtained a secondary grey level histogram by certain transformation by histogram equalization
New images.It is efficiently used for image enhancement, is easy to calculate.Histogram equalization realizes enhancing part by extension brightness
Contrast does not influence overall contrast.
Local operation's method is divided into two kinds of image smoothing and sharpening, the former easily causes edge for eliminating picture noise
It is fuzzy；The latter is used to protrude the edge contour of object, is convenient for target identification.Mainly introduce median filtering calculation in image smoothing part
Method, it is a kind of nonlinear smoothing technology, sets the gray value of each pixel to the intermediate value of gray value around, in this way can be with
Solve the problems, such as that being carried out image detail due to cake resistancet is obscured.Median filtering has good removal to act on impulsive noise, but also
Energy Protect edge information signal is not blurred.Median filtering algorithm description are as follows:
1. obtaining the first address and picture size of original image.
2. opening up one piece of core buffer, buffered results image is simultaneously initialized.
3. the gray value of each element around it is ranked up from small to large, acquires by the pixel in scan image one by one
Pixel corresponding with current point is assigned in target image to median.
4. step before recycling, whole pixels until having handled original image.
5. result to be copied to the data field of image from core buffer.
Image sharpening is exactly to pass through differential to keep image border prominent, clear, commonly uses gradient method to carry out.Image smoothing be through
Crossing integral allows image border to thicken.Frequency domain enhancing is to regard image as 2D signal, to after Fourier transformation
Spectrum component is handled, so that signal enhancing.
Principle is as follows:
--- --- --- --- --- -- frequency domain inverse transformation --- --- exports image to frequency-domain transform to original image for filtering enhancing
Frequency domain enhancing is modified to the transform coefficient values of image, and the algorithm enhanced indirectly is belonged to.Utilize low pass filtered
Wave removes noise, and high-pass filtering enhances edge high-frequency signal.Frequency low pass wave inhibit high frequency in noise contribution, by low frequency at
Point, it then carries out inverse Fourier transform and obtains filtering image, achieve the purpose that image smoothing removes noise.The relationship of frequency domain filtering
Formula are as follows:
G (u, v)=H (u, v) F (u, v)
F (u, v) is the transformation for needing the image f (x, y) of smoothing processing in formula, makes F's (u, v) by function H (u, v)
High fdrequency component decaying, exports G (u, v), G (u, v) is inverse transformed to obtain smoothed image g (x, y).Since filtering eliminates high frequency division
Amount, low-frequency information is lossless to be passed through.Common frequency domain low filter has ideal low-pass filter, Butterworth low-pass filtering
Device, exponential lowpass filtering, trapezoidal lowpass filtering device etc..Part and the high fdrequency component of its frequency spectrum of cataclysm occur for gray scale in image
Corresponding, radio-frequency component existing for the edge of image, details is weaker, and frequency domain high pass filtering eliminates fuzzy, projecting edge, makes height
Frequency signal passes through, and weakens low-frequency component, is sharpened processing to image.Common frequency domain high pass filter has ideal high pass
Filter, Butterworth high-pass filter and exponential highpass filtering device.
Pre-processing of the image enhancement as image recognition improves the effect of image by a series of technologies, so that image
Analysis carries out more convenient.The basis of image enhancement is the changing value of each vertex neighborhood intensity of determining image, by image grayscale point
The point that neighborhood intensity value has significant change highlights, and when specific programming is realized, is determined by calculating gradient magnitude,
Various methods are recycled to be finally reached the effect of image enhancement.
3.3 image detection
It will appear the bigger pixel of many gradient values by image enhancement, but these points are not sometimes needed for image
It wants, so carrying out the marginal point really needed in detection image usually using thresholding method to be accepted or rejected.Choose a ratio
More reasonable threshold value determines the background and target image in image.
Thresholding is a kind of method for coming out our the desired region segmentations analyzed in the picture, we are each gray scale
Value is all made comparisons with a preset threshold value, adjusts pixel value further according to comparison result.If only examined with a threshold value
Survey is called single threshold method；It is called multi-threshold method with multiple threshold values.No matter the method for single threshold or multi-threshold is likely to occur
Different zones have the case where same zone thresholding, only considered pixel itself when this is because taking threshold value, do not account for picture
The spatial position of element, so a kind of pixel possible position is divided into disconnected region according to pixel value, so
It should need to determine target area by some priori knowledges before image detection.
3.4 Canny operators
Canny edge detection algorithm is one of common edge detection method, is substantially that the maximum of signal function is asked
The pixel for determining image border, is then assembled into profile for independent candidate pixel.
The purpose of Canny operator is to find an optimal edge detection.Three primary evaluations of optimal edge detection algorithm
Standard is respectively as follows:
(1) actual edge as much as possible, reduction noise wrong report as few as possible, critical parameter low error rate: are identified
Signal to Noise Ratio (SNR) is bigger, and expression edge extracting quality is better.
G (- x) indicates image border function, and f (x) is the filter function in region, indicates the square of Gaussian noise
Difference.
(2) high polarization: the edge identified will with the actual edge in image as close possible to.The function of positioning accuracy
Value is bigger, and positioning accuracy is bigger.
In formula, f ' (x) and G ' (- x) are the first derivative of f (x) He G (- x) respectively.
(3) minimum response: the edge in image uniquely responds, and guarantees that impulse response derivative average distance meets:
Gradient value maximum of points approximation after Gaussian smoothing meets criterion it is ensured that only one response of single edges.
3.5 Canny limb recognition algorithms
Canny operator function admirable, is widely used, and it is first to original image that the basic thought of marginal point is sought using Canny operator
As carrying out smothing filtering, the image after smoothing processing is then applied into " non-extreme value inhibition " technology, side required for obtaining to the end
Edge image.Canny limb recognition algorithm both effectively inhibits noise, identifies edge again.Canny limb recognition algorithmic procedure can
To indicate are as follows:
Finally, it should be noted that the foregoing is only a preferred embodiment of the present invention, it is not intended to restrict the invention,
Although the present invention is described in detail referring to the foregoing embodiments, for those skilled in the art, still may be used
To modify the technical solutions described in the foregoing embodiments or equivalent replacement of some of the technical features.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Canny limb recognition algorithmic procedure is as shown in Figure 2.
According to the requirement of the above evaluation criterion and detailed process, the specific steps of general Canny edge detection algorithm are as follows:
(1) gaussian filtering smoothed image
Under normal circumstances, Gaussian filter convolution noise reduction is used in Canny limb recognition algorithm, i.e., by pixel
And the gray value of neighborhood point is weighted and averaged according to certain parameter rule, effectively filters the fuzzy edge of image.Image
Gaussian filtering can be by weighting one-dimensional Gaussian kernel realization twice, can also a dimensional Gaussian nuclear convolution realization.One-dimensional Gauss
Function representation are as follows:
μ is the stochastic variable mean value of Normal Distribution in formula, influences the position of normal distribution.
σ is standard deviation, definition be normal distribution data dispersion degree, σ value is bigger, and data distribution is more dispersed, normal state
Distribution curve is more flat, and the frequency band of Gaussian filter is wider, and smoothness is better；σ is smaller, and data distribution is more concentrated, and curve is got over
The frequency band of height, Gaussian filter is narrower, and smoothness is poorer.
Two-dimensional Gaussian function are as follows:
Two-dimensional Gaussian function has rotational symmetry, indicate filter smoothness in all directions be it is identical,
So Gaussian filter will not be biased to any one direction in edge detection process.Under the same terms, Gaussian convolution core
Size it is bigger, the effect of image smoothing is better, image appearance be it is relatively fuzzy, the part details at edge is easier to lose；Phase
Instead, core size is smaller, and smooth effect is weaker, and image is relatively clear, and details is not easy to lose.
(2) gradient magnitude and direction are calculated
Image can be calculated on the direction x and y using differential operator using convolution operator by obtaining gradient according to gray value of image
Partial derivative.
Convolution operator are as follows:
The matrix of x Yu y partial derivative are calculated using above-mentioned convolution operator.
Gradient magnitude and direction are calculated using following equation:
M [x, y] reacts image edge strength, and [x, y] reacts the direction of image border.
(3) non-maxima suppression is carried out to gradient magnitude
The point at doubtful edge can be obtained roughly according to element value in image gradient amplitude matrix, but cannot illustrate these
Point must be just edge, it should retain the maximum value of partial gradient, inhibit non-maximum.Inhibit non-maximum, needs to utilize
Gradient direction determines whether the gray value of pixel is maximum in its eight values neighborhood, by each pixel local derviation value and adjacent picture
Element relatively, is maximized as marginal point, and non-edge point gray value is set as 0.Edge pixel can be excluded in this way, only retained thin
Line.But testing result is possible to comprising noise as caused by other reasons etc., so also needing further to handle.
(4) edge is detected and connected with dual threashold value-based algorithm
Two threshold values of image selection height after non-maxima suppression operate image, if a certain location of pixels
Amplitude is more than high threshold, which is left edge pixel；If the amplitude of a certain location of pixels is less than Low threshold, the pixel
It is excluded；If the amplitude of a certain location of pixels is between two thresholds, which is only being connected to one higher than high threshold
Pixel when be retained.
The testing result of high threshold can also lose effective marginal information in addition to largely removing noise；It is sharp again
It is detected to obtain image reservation marginal information with Low threshold, the image that edge is not closed connects into complete profile, so needing
Two images are compared into application, supplement the information of loss, connect the edge of image, keep image border complete.Process is
The point that it is 0 that scanning, which finds pixel not, in high threshold image result, tracking is the contour line started with the pixel, until finding
Terminal；The final position compared with Low threshold image is then included repeating above-mentioned step into final result image if it exists
Suddenly, it being recycled to and compares and cannot be further continued for, a connection marginal operation completes that lookup contour line can be repeated labeled as accessing,
Until can not find new contour line.
4. image recognition technology
4.1 identification point locations
Identify that point location is the point set comprising largest contours in image to be screened first with algorithm of convex hull, in point set
It is middle to search four points for being capable of forming maximum quadrangle area, the as identification point of answering card, then positioning four with cross product
The sequence and position of point are identified.
Convex closure can express the mode of the one-dimensional attribute information of image.The convex closure in one region can be used in some cases
Description in region, so, one can be had to image early period, post-processing and image retrieval and feature extraction by calculating image convex closure
Fixed help.Convex closure is to give any two point on its boundary or internal for a simple polygon, connect the two points
Line segment on all the points be contained on the boundary of the polygon or if inside, then the polygon be convex polygon.Letter
It is exactly that the point in given area is enclosed in inside, the smallest convex polygon of area for list.
In solving the problems, such as convex closure, two kinds of algorithms are introduced:
(1) Graham scanning algorithm
Graham scanning algorithm removes influential salient point, is formed last by the way that new salient point is constantly added in convex closure
Convex closure.Algorithm first sorts to be scanned afterwards, is arranged using sequence to mixed and disorderly point set, and the sequence of polar angle coordinate is common side
It is as a reference point first to find the smallest point of an abscissa for formula, then takes the smallest point of ordinate, and points all so all concentrates on
Angle formed by surface, any two points and reference point is acute angle.
The core concept of scanning process is to sequentially add salient point to obtain new chimb according to the sequence of sequence, according to salient point
With angle formed by reference point, then positive direction is carried out pretreatment using cross product judgement and is iterated to each point.With storehouse
Thought, if chimb is according to counter clockwise direction by convex closure, vertex should turn left, and pop down continues, just popped up if turning right,
Until the side with stack top two o'clock becomes left-hand rotation relationship.
Assuming that there are 8 points in plane, makees a polygon by certain points, this polygon all wraps all the points
It fences up.When this polygon is convex polygon, as " convex closure ".
Concrete principle is as shown in 3 figures:
Graham scanning algorithm specific steps are as follows:
1. all the points are placed in two-dimensional coordinate system, then the smallest point of ordinate must be the point on convex closure, i.e., in figure
P0。
2. calculating angle α of each point relative to P0, sort by sequence from small to large to each point.When α is identical, away from
Closer from P0 comes front.
3. first by convex closure first point P0 and second point P1 be placed on inside stack.Now P2 is made reference a little, looks for third
A point.
4. connecting that point of P0 and stack top, straight line L is obtained.See that reference point is on the right or the left side of straight line L.If
Step 5 is carried out on the right of straight line；If on straight line, or on the left side of straight line being carried out step 6.
5. stack top element is popped if on the right, that element of stack top is not the point on convex closure.Execute step 4.
6. current point is the point on convex closure, it is pressed into stack, executes step 7.
7. checking that current point P2 is the last one element of that result of step 3.Then if the last one element
End loop.Otherwise P3 is as a reference point, return step 4.
(2) Jarvis step-by-step method
Jarvis step-by-step method calculates the convex closure of a point set using packaging technique, and core concept is to find the vertical seat of a concentration
The smallest point P0 is marked, determines that the point is a vertex of convex closure, does ray based on the point, look for one by one counterclockwise convex
The point wrapped often takes a step forward and finds a point, compared by cross product, the point with minimum angle is found, if angle is identical
It is found out again apart from farthest point.Circulation is exited when the point found is starting point.
Graham scanning algorithm is that each step obtains an interim convex closure, and time complexity is O (nlogn).
Jarvis step-by-step method is that each step finds out a line on convex closure, and time complexity is O (nh).Wherein n is represented a little
The total number of collection, what h was represented is the number put on convex closure.
Cross product is denoted asIf enablingThenDirection beAnd meet right hand rule,Another kind defines
What the geometric meaning of cross product indicated be withWithFor the directed area of the parallelogram on side, operation result is one
A vector, the symbology Vector rotation direction of the cross product of vector.IfFor positive number, then for origin,?
Clockwise；IfFor negative, then for origin,?Counter clockwise direction on；If it is 0, that
Illustrate that two vectors are conllinear on boundary, direction is equidirectional or opposite direction.
4.2 affine transformation
To there is the answer card graphic that deformation occurs to correct using affine transformation.Affine transformation is to pass through two-dimensional coordinate system
To the transformation of two-dimensional coordinate system, the relative positional relationship between X-Y scheme in image is constant, and parallel lines are still parallel lines,
But the angle of intersecting straight lines is possible to convert under the angle of affine transformation.It is characterized in that a shear deformation all will not failure line
Item it is linear, deformation after both horizontally and vertically on length ratio can change, but in coordinate system each point transformation
It is all uniformly, the case where there is no the distortion of part and collapsing.Affine transformation mainly passes through variable and is multiplied with transformation matrix
It realizes, specific formula expression are as follows:
Determine the affine transformation between two coordinate planes, it is only necessary to determine transformation matrix.Not conllinear three pairs
Corresponding points determine unique affine transformation.Respectively by m1, m2, m3 point are done to be mapped one by one, is found out by this two groups 3 points affine
After transformation matrix, all the points inside region can be converted according to this matrix.
Claims (10)
1. a kind of test answer sheet system intelligent recognition analysis method, which comprises the following steps:
S1: to image preprocessing
Image gray processing, image binaryzation, image denoising, Morphological scale-space are carried out to the picture of examinee's answering card；
Described image binaryzation, which refers to, reflects image entirety by threshold value appropriate screening for gray level image；
The Morphological scale-space includes expansion and corrosion；
S2: detection image gradient simultaneously carries out rotation correction, forms independent peak point, reads image and carries out binaryzation；
S3: edge detection is extracted
Edge detection extracts the feature of discontinuous section in image, determines specific region according to closure continuous boundary, will have
The region division of same characteristic features together, is demarcated between region by edge, and the Edge definition of edge detection is ash in image
Zone boundary jumpy occurs for angle value；Variation of image grayscale situation is reacted with image grayscale distribution gradient, by original
Image differentiation technical construction edge detection operator carries out edge detection, specifically includes image filtering, image enhancement and image inspection
It surveys；Then Canny limb recognition algorithm is carried out；
S4 image recognition
Including identification point location and affine transformation；The identification point location refer to first with algorithm of convex hull by image comprising maximum
The point set of profile screens, and four points for being capable of forming maximum quadrangle area, the as knowledge of answering card are searched in concentration
It is other, then be identified the sequence of four anchor points and position with cross product；
The affine transformation is referred to there is the answer card graphic that deformation occurs to be corrected using affine transformation.
2. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that in the step 1)
Image gray processing is carried out using mean value method, that is, the average value of tri- components of R, G, B is calculated, then using average value as grayscale image
The gray value of picture, formula are as follows: Gray=(B+G+R)/3.
3. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that when image binaryzation
The selection of threshold value uses average gray value method, maximum kind differences method or best threshold method；
The average gray value method refers to the average value for calculating all pixels gray value, each pixel value of scan image, if pixel
Value is greater than average value, then is set as 255 (whites), and pixel is less than average value and is set as 0 (black)；
The maximum kind differences method refers to is divided into two groups for the gray scale of image for the gray value of a certain hypothesis, calculates separately this two groups
Then pixel number and average gray calculate the inter-class variance of this two groups of data, when inter-class variance maximum, the gray scale
Value is exactly the optimal threshold of image binaryzation；
The best threshold method the following steps are included:
1) maximum gradation value and minimum gradation value for, finding out entire image, using the average value of the two as the threshold value T of most initial
(j), j is the number of iterations, initial value 0；
2) target image foreground and background, is divided the image into according to threshold value T (j), finds out a pixel in foreground area respectively
With the average gray value of in background pixel
3) new threshold value, is found out；
If 4), T (j)=T (j+1), gained be threshold value, otherwise repeat 2.~4..
4. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that the detection figure
As gradient and carries out rotation correction and specifically comprise the following steps:
(1) entire image is read, color image is become into gray level image, and it is inner to be stored in two-dimensional array g (i, j)；Wherein i is capable
Mark, j are column marks, and g (i, j) indicates the gray value of corresponding rower i and column mark j；
(2) image is become into bianry image；
The data of bianry image are stored in bw (i, j)；
(3) hough transformation is carried out to image
Initially set up accumulator of the two-dimensional array A (ρ, θ) as parameter space；ρ is distance of the straight line to origin, and range is
From 0 to answering card image diagonal length；θ is the inclination angle of straight line, and range is -90 ° to 90 °；Then scanning second step obtains
Binary image data bw (i, j), the coordinate of point that the inner all pixels value of bw (i, j) is 0 is preserved；For bw (i, j)
Point (the bw that middle pixel value is 0i, bwj), by (bwi, bwj) substitute into formula (1), enable θ be equal to each of -90 ° to 90 ° values,
If the value of corresponding A (ρ, θ) is just added 1, two obtained between 0 to answering card image diagonal length by obtained ρ value
Dimension group A (ρ, θ) is exactly ρ θ parameter space；
(4), the peak value detected is differentiated, if for the straight line in image；It is a two-dimemsional number that hough, which converts domain space,
Group, finds the maximum value of two-dimensional array, and writes down its position, is denoted as (ρ ', θ '), and the peak value (ρ ', θ ') found and
Hough converter unit in its neighborhood is set as zero, and Size of Neighborhood is 8 × 8；
It is straight line inclination angle corresponding to peak value by 90 ° of-θ ' of image rotation, θ ', detects the longest line segment length on this straight line,
If a threshold value T, if longest line segment length on this straight line is greater than threshold value T, just illustrate this peak value it is corresponding be answer
Straight line in card graphic；Otherwise the step (4) is repeated, until finding out the straight line in answer card graphic；The inclination angle of this straight line is just
Be required answer card graphic inclination angle theta '；
(5), θ ' will be rotated counterclockwise, be horizontally situated two in image straight lines, just be completed detection image gradient
And rotation correction, then the answer card graphic progress binaryzation that transformation is obtained.
5. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that in the S3
Image detection, which refers to, to be carried out when after image enhancement carrying out the marginal point really needed in detection image using thresholding method
It accepts or rejects；The thresholding method refers to that the region segmentation analyzed in the image by target comes out, each gray value and one
A preset threshold value is made comparisons, and adjusts pixel value further according to comparison result.
6. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that the Canny
The evaluation criterion of the optimal edge detection of limb recognition algorithm are as follows:
(1) actual edge as much as possible, reduction noise wrong report as few as possible, critical parameter noise low error rate: are identified
Expression edge extracting quality bigger than SNR is better.
G (- x) indicates image border function, and f (x) is the filter function in region, indicates the mean square deviation of Gaussian noise.
(2) high polarization: the edge identified will with the actual edge in image as close possible to；The functional value of positioning accuracy is got over
Greatly, positioning accuracy is bigger.
In formula, f ' (x) and G ' (- x) are the first derivative of f (x) He G (- x) respectively；
(3) minimum response: the edge in image uniquely responds, and guarantees that impulse response derivative average distance meets:
7. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that
8. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that in the S3
Canny limb recognition algorithm the following steps are included:
1) gaussian filtering smoothed image
The gray value of pixel and neighborhood point is weighted and averaged according to certain parameter rule, effectively filters the fuzzy of image
Edge；The gaussian filtering of image can be by weighting one-dimensional Gaussian kernel realization twice, can also a dimensional Gaussian nuclear convolution reality
It is existing；One-dimensional Gaussian function expression are as follows:
μ is the stochastic variable mean value of Normal Distribution in formula, influences the position of normal distribution.
σ is standard deviation, definition be normal distribution data dispersion degree, σ value is bigger, and data distribution is more dispersed, normal distribution
Curve is more flat, and the frequency band of Gaussian filter is wider, and smoothness is better；σ is smaller, and data distribution is more concentrated, and curve is higher, high
The frequency band of this filter is narrower, and smoothness is poorer；
Two-dimensional Gaussian function are as follows:
Two-dimensional Gaussian function has rotational symmetry, indicates that the smoothness of filter in all directions is identical, so
Gaussian filter will not be biased to any one direction in edge detection process；Under the same terms, the ruler of Gaussian convolution core
Very little bigger, the effect of image smoothing is better, and image appearance is relatively to obscure, and the part details at edge is easier to lose；On the contrary, core
Size is smaller, and smooth effect is weaker, and image is relatively clear, and details is not easy to lose；
(2) gradient magnitude and direction are calculated
Image in the x and y direction inclined can be calculated using differential operator using convolution operator by obtaining gradient according to gray value of image
Derivative.
Convolution operator are as follows:
The matrix of x Yu y partial derivative are calculated using above-mentioned convolution operator.
Gradient magnitude and direction are calculated using following equation:
M [x, y] reacts image edge strength, and [x, y] reacts the direction of image border；
(3) non-maxima suppression is carried out to gradient magnitude
The point at doubtful edge can be obtained roughly according to element value in image gradient amplitude matrix, but cannot illustrate these points just
It must be edge, it should retain the maximum value of partial gradient, inhibit non-maximum；Inhibit non-maximum, needs to utilize gradient
Direction determines whether the gray value of pixel is maximum in its eight values neighborhood, by each pixel local derviation value and adjacent pixel ratio
Compared with being maximized as marginal point, non-edge point gray value is set as 0；
(4) edge is detected and connected with dual threashold value-based algorithm
Two threshold values of image selection height after non-maxima suppression operate image, if the amplitude of a certain location of pixels
More than high threshold, which is left edge pixel；If the amplitude of a certain location of pixels is less than Low threshold, which is arranged
It removes；If the amplitude of a certain location of pixels is between two thresholds, which is only being connected to the picture for being higher than high threshold
It is retained when plain.
The point that it is 0 that scanning, which finds pixel not, in high threshold image result, tracking are the contour line started with the pixel, until
Find terminal；The final position compared with Low threshold image is then included repeating above-mentioned into final result image if it exists
Step is recycled to and compares and cannot be further continued for, and a connection marginal operation completes that lookup profile can be repeated labeled as accessing
Line, until can not find new contour line.
9. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that convex in the S4
Packet passes through Graham scanning algorithm or Jarvis step-by-step method；
The specific steps of the Graham scanning algorithm are as follows:
(1) all the points are placed in two-dimensional coordinate system, then the smallest point of ordinate must be the point on convex closure, i.e. P0 in figure；
(2) angle α of each point relative to P0 is calculated, is sorted by sequence from small to large to each point；When α is identical, distance
P0 it is closer come front；
(3) first by convex closure first point P0 and second point P1 be placed on inside stack；Now P2 is made reference a little, looks for third
Point；
(4) that point for connecting P0 and stack top, obtains straight line L；See reference point be on the right or the left side of straight line L, if
Step 5 is carried out on the right of straight line；If on straight line, or on the left side of straight line being carried out step 6；
(5) if on the right, that element of stack top is not the point on convex closure, stack top element is popped, and executes step 4；
(6) current point is the point on convex closure, it is pressed into stack, executes step 7；
(7) check that current point P2 is the last one element of that result of step 3；Then terminate if the last one element
Circulation, otherwise that P3 is as a reference point, return step 4；
The Jarvis step-by-step method is that each step finds out a line on convex closure, and time complexity is O (nh)；Wherein n is represented a little
The total number of collection, what h was represented is the number put on convex closure；
Cross product is denoted asIf enablingThenDirection beAnd meet right hand rule,Another kind defines
What the geometric meaning of cross product indicated be withWithFor the directed area of the parallelogram on side, operation result be one to
Amount, the symbology Vector rotation direction of the cross product of vector；IfFor positive number, then for origin,?It is suitable
On clockwise；IfFor negative, then for origin,?Counter clockwise direction on；If it is 0, then saying
Bright two vectors are conllinear on boundary, and direction is equidirectional or opposite direction.
10. test answer sheet system intelligent recognition analysis method as described in claim 1, which is characterized in that the step S4
In affine transformation is multiplied with transformation matrix realization by variable, specific formula is expressed are as follows:
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