CN103646408A - Image based human foot key part data extraction and measurement method - Google Patents

Abstract

An image-based data extraction and measurement method for key parts of the human foot, the steps are as follows: Step 1: Image acquisition; Step 2: Detect the coordinates of the vertices of the four corners of the A4 paper, and perform geometric correction on the image; Step 3: The target of the front foot Extraction and measurement; step 4: target extraction and measurement of the side foot; the present invention can effectively obtain the data of the key parts of the foot through geometric correction and image processing technology, which can meet the needs of shoe buyers when choosing shoe sizes and shoe manufacturers. requirements, the error is within 2 mm. The method can use the obtained data as a reference in online shoe stores to provide users with more accurate shoe sizes and styles and improve the success rate of online shopping. This data can also be used by shoe manufacturers to provide consumers with customized services, which can help users choose or customize shoes to their satisfaction, and can save merchants the cost of returning and exchanging services in the sales process.

Description

A kind of data of the people's pin key position based on image are extracted and measuring method

(1) technical field:

The data that the present invention relates to a kind of people's pin key position based on image are extracted and measuring method, belong to the technical field of image processing and photography dimensional measurement.

(2) background technology:

People needs walking, and shoes comfort level affects quality of life.The brand of footwear is numerous, and each brand can have indoor design parameter and the streamline of own exclusive footwear.For the definite footwear of a pair of number, the width of footwear and height, the shape of sole and parameter of slope design and shoe tree etc., all can exert an influence to the comfort of pin.The footwear that how meet people's physilogical characteristics according to people's pin type design are very professional problems.The style of footwear is numerous, is not but that every a pair of shoes is all applicable to oneself.Buying footwear is bothersome things, especially all the more so for a bit special people of pin type.In shopping at network today prevailing, rely on merely a footwear code information to be difficult to buy comfortable shoes.If the key position data of pin can be extracted, as businessman, for the reference data that user selects footwear code and style, can improve undoubtedly the success ratio of shopping at network, the expense that minimizing produces because of Returns.

The present invention adopts A4 paper as object of reference (standard size is 210 millimeters * 297 millimeters), and user steps down in pin on an A4 paper, and acquisition of image data is extracted pin target, and according to the proportionate relationship of pin and A4 paper, completes extraction and the measurement of foot's critical data.

(3) summary of the invention:

1, object: the object of the present invention is to provide a kind of data of the people's pin key position based on image to extract and measuring method, to adapt to the needs of current shopping at network.The method can be obtained the data of people's pin key position, and the success ratio of shopping online can by the data that obtain as a reference, for user provides footwear code and style more accurately, improve in online shoes store.Further, these data also can be used for shoemaking manufacturer provides special customize services for consumer.Therefore, this invention can help user to select or be customized to satisfied shoes, can save again the expense that businessman produces because of the service of replacing at sales section.

2, technical scheme: the present invention is achieved through the following technical solutions.

The data of a kind of people's pin key position based on image of the present invention are extracted and measuring method, and the method comprises following four steps:

Step 1: Image Acquisition

This programme is wide by proportionate relationship calculating pin length and pin between people's pin and A4 paper, and according to the proportionate relationship between instep height and the length of pin, calculates the true altitude of instep key position.Therefore, need to take two width images, a width is that (hereinafter to be referred as front, shining) shone in the front of pin, as Fig. 1 (a) is positive, shines as shown in image acquisition mode schematic diagram, requires pin to step down on white A4 paper, and camera is taken vertically downward directly over pin; Another width is that (hereinafter to be referred as side, shining) shone in the side of pin, requires camera, from the inner side of pin, pin is carried out to side projection, if Fig. 1 (b) side is according to image acquisition mode schematic diagram.Specific requirement and operation are as follows:

1. the acquisition method of positive photograph: white A4 paper minor face one side is pasted to wall and place; User steps down in pin on A4 paper, makes the axis of pin align with the axis of A4 paper as far as possible; Heel, by wall, makes the alignment of heel position HeA4 paper edge, and the length direction of pin is consistent with the length direction of A4 paper, and it is inner to guarantee that pin drops on A4 paper completely; Camera directly over pin between 50 centimetres to 70 centimetres, take that angle is perpendicular to the ground carries out imaging, keep A4 paper not crooked in image as far as possible, and guarantee to comprise completely in visual field A4 paper region.

2. the acquisition method of side photograph; Side, according to not needing A4 paper, only needs subscriber station before wall or a pure color baffle plate, and the outside of pin is by wall or baffle plate; Camera lens is from the outside imaging of the interior side direction pin of pin, apart from 30 centimetres to 50 centimetres of the distances of side pin, takes angle and is parallel to ground, and keep same height with instep;

3. in visual field, scene will be tried one's best simply: positive as requested only comprises pin, A4 paper and floor in visual field; The background of side photograph should be simple wall or baffle plate, avoids other chaff interference to occur; Require user to wear black or other dark socks, to guarantee that there is enough large contrast contrast on pin, A4 paper and floor simultaneously.

Step 2: detect four angular vertex coordinates of A4 paper, image is carried out to geometry correction

Image tends to produce geometric distortion in the process of obtaining or showing.Geometric distortion comprises translation, convergent-divergent, rotation and perspective and more complicated geometric distortion.The equation that arbitrarily geometric distortion all can transform to distorted coordinates system (x', y') by non-distorted coordinates system (x, y) defines.Suppose that f (x, y) is undistorted original image, g (x', y') is the geometric distortion result of f (x, y), can obtain the fundamental relation formula of geometry correction, as follows:

$\left\{\begin{array}{c}g(x^{\′},y^{\′})=f(x,y)\\ x^{\′}=h_1(x,y)\\ y^{\′}=h_2(x,y)\end{array}\right.$

In formula, h ₁(x, y) and h ₂(x, y) is for proofreading and correct transforming function transformation function.In this programme, h ₁(x, y) and h ₂(x, y) is similar to polynomial expression below:

$h_1(x,y)=\frac{a_{0}x+a_{1}y+a_2}{a_{6}x+a_{7}y+1}$

$h_2(x,y)=\frac{a_{3}x+a_{4}y+a_5}{a_{6}x+a_{7}y+1}$

Because the actual relative coordinate of four angular vertexs of standard A 4 paper is known, in this programme using four angular vertexs of A4 paper as reference mark, by image processing techniques, detect the coordinate at four angles of A4 paper in geometric distortion image, and then utilize correction transforming function transformation function and bilinear interpolation method to carry out geometry distrotion correction to distorted image.Specific implementation process is as follows:

1. row rim detection is shone into in front.Utilize Sobel operator according to image, to carry out edge extracting to front, obtain the gradient map of image.In gradient map, the edge of target has become bright band, and target and background region is because grey scale change is more smooth, therefore in gradient map, has formed dark space;

2. to gradient image binaryzation.A4 paper and the formed edge of pin target occupy very little a part of region in image, are made as 0.1 of image area.Gradient map is carried out to statistics with histogram, and the edge pixel gray-scale value of image is higher, will be distributed in histogram position on the right side, but not edge pixel concentrates on the keep left position of side of histogram.The cumulative probability of compute histograms (being the pixels statistics of image border) left from the histogram rightmost side, and be that 0.1 corresponding gray-scale value is set as threshold value by cumulative probability, the pixel that is less than threshold value is set to 255, the pixel that is greater than threshold value is set to 0, thereby extracts the edge that comprises A4 paper and pin target;

3. four of Preliminary detection A4 paper angular vertex position coordinateses.To the aforementioned the bianry image 2. obtaining in step, on transverse axis, in the scope of [5 °, 5 °], take 1 ° image is carried out to Gray Projection as step-length.Because two of the left and right longitudinal edge of A4 paper is the strong edge in image, its can form extreme value on correct projecting direction.And according to priori, A4 paper is in the centre position of image, from image centre position to both sides, detect the extreme value of Gray Projection, just can detect two longitudinal edges in left and right and their deflection.Same way can detect two widthwise edges and their deflection up and down of A4 paper.Calculate the point of crossing between two longitudinal edges in left and right and upper and lower two widthwise edges, can obtain the rough coordinates of four angular vertex positions of A4 paper.

4. accurately detect four angular vertex position coordinateses of A4 paper.3. centered by four the angular vertex position coordinateses of A4 paper that obtain in by step, the subgraph of four 140 * 140 sizes of relevant position intercepting on former gray-scale map.In four subgraphs, the ratio of the shared image area in edge is set to 0.15, repeats step above 1. to 3., can obtain the accurate coordinates of four angular vertex positions of A4 paper.

5. image is carried out to geometry correction.The relative coordinate of actual four angular vertexs of A4 paper is known, utilizes above-mentioned correction transforming function transformation function and bilinear interpolation method to carry out geometry correction to distorted image.

6. intercept A4 paper subgraph, remove useless background.After image rectification, the region at A4 paper place is exactly the rectangle of a standard, and the length breadth ratio of rectangle is exactly the length breadth ratio of A4 paper.We intercept this rectangle from image, remove background.This subgraph inside intercepting is exactly the pin target that we will detect.We carry out for this A4 paper subimage in follow-up processing.

Step 3: the target of front pin is extracted and measured

By step 2, be truncated to A4 paper subimage, we will extract pin length and wide two data of pin from this number of sub images.Specific implementation process is as follows:

(1) detection of toe position

Toe is to drop in the first half region of A4 paper, and heel is to align with the base of A4 paper.Therefore can detect in the first half of A4 paper subgraph the position of toe, and it is long according to the proportionate relationship of pin and A4 paper, to calculate pin.Detailed process is:

1. intercept A4 paper subimage the first half subarea, utilize Sobel operator to carry out rim detection; According to priori, the edge that pin target forms in this subarea accounts for 0.06 of subarea area, and this programme carries out threshold value selection with 0.06 area ratio, and binaryzation is carried out in subarea.

2. in bianry image, have the noise spot being scattered, adopt closing operation of mathematical morphology to carry out filtering to binary map, the size of computing template is 5 * 5

$\left[\begin{array}{ccccc}0& 0& 1& 0& 0\\ 0& 1& 1& 1& 0\\ 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 0\\ 0& 0& 1& 0& 0\end{array}\right]$

3. to the bianry image after denoising, press from the top down each impact point of line search.Centered by this impact point, get 5 * 8 window, by the upper and lower doubling of window, on former gray-scale map, add up the gray scale difference of correspondence position in doubling window, and be averaging.And first meets gray scale difference mean value be greater than 30 impact point be the position of toe, with (x, y), represent.

(2) position probing of first metatarsal bone and fifth metatarsal bone

From professional angle, the width of sole refers to the distance between the first metatarsal bone of pin (inner side of pin) and fifth metatarsal bone (outside of pin).And first metatarsal bone is positioned at 69.5% position from heel to toe, fifth metatarsal bone is positioned at 62.5% position from heel to toe.Because first metatarsal bone and fifth metatarsal bone lay respectively at the both sides of sole, we detect this position of 2 by following process:

1. rim detection filtering are carried out in the subarea at forefoot place.Similar with the process of toe position probing, rim detection is carried out in the region, edge at the wide place of pin, and use closing operation of mathematical morphology filtering;

2. determine the horizontal ordinate position of first metatarsal bone.On A4 paper subgraph, the ordinate of corresponding 69.5% position from heel to toe, with 1 * 16 window, search for from right to left, by the right left doubling of window, on former gray-scale map, add up the gray scale difference of correspondence position in doubling window, it is exactly first metatarsal bone position that the average of gray scale difference is greater than 25 position, and the horizontal ordinate at this some place is designated as to x _inner.

3. determine the horizontal ordinate position of fifth metatarsal bone.2. similar with step, at heel, to 62.5% position of toe, with 1 * 16 window, to search for from left to right, first meets window left and right doubling gray scale difference mean value, and to be greater than 25 position be exactly the position of fifth metatarsal bone, and the horizontal ordinate at this some place is designated as to x _outer.

(3) pin length and the wide calculating of pin

The normal size of A4 paper is 210 millimeters * 297 millimeters.Suppose that A4 paper subgraph is the capable N row of M, making the A4 paper subimage lower left corner is true origin, if the coordinate of toe position in subimage is (x, y), the physical length of pin is 297 * y/M millimeter.Suppose that the sole width number of pixels of extracting is c on A4 paper subimage, by the abscissa value of first metatarsal bone and fifth metatarsal bone, can obtain c=x _inner-x _outer, and the developed width of pin is 210 * c/N millimeter.

Step 4: the target of side pin is extracted and measured

The side of pin is for extracting the height of key position instep according to image.From heel to toe 2/5,1/2 and 3/4, the instep height at these positions is shoe last designing important parameters used.While selecting footwear code, the people that instep is high can select than the footwear code of large one of normal foot, or in customization shoes, can suitably increase the height of shoe tree.Side is according in image, and heel to the distance of toe is exactly that pin is long, and from vola to instep just correspondence the pin of relevant position high.Suppose side according in heel in the left side of image, toe is on right side, the instep of key position detect and height measurement method as follows:

(1) detect heel and toe

Heel and toe be in the latter half of image, and in the image left and right sides, formed two edges longitudinally.Therefore at image in 1/2 interval from bottom to height, edge longitudinally in detected image, can navigate to the position of heel and toe.Detailed process is as follows:

1. adopt the gradient template of horizontal direction to carry out rim detection to image, the longitudinal edge of outstanding toe and heel.The template that adopts as follows:

$\left[\begin{array}{ccc}1& 0& -1\\ 3& 0& -3\\ 1& 0& -1\end{array}\right]$

2. the edge of heel and toe area occupied ratio in image is 0.1, with this area ratio as threshold value to image binaryzation, obtain edge binary map;

3. use 5 * 8 windows from left to right by row search, suppose that in window, impact point number is n, first window position that meets (n/ (5 * 8)) >0.9 is exactly the rough position of heel, with (x' ₀, y' ₀) expression, wherein x' ₀for the horizontal ordinate of heel rough position, y' ₀for ordinate.

4. with heel position coordinates (x' ₀, y' ₀) centered by, the subwindow of intercepting 20 * 20 carries out fine searching to heel position in window.Adopt gradient template [1-1] the calculation window inside gradient of x direction, the greatest gradient position of every row in search window, horizontal ordinate statistics is carried out in greatest gradient position to all row, has the accurate horizontal ordinate that maximum horizontal ordinates is heel position, and we use (x ₀, y ₀) represent the accurate coordinates position of heel.

5. same process, when starting left by row search from image right side, can obtain the coordinate position (x of toe ₁, y ₁).

(2) detect vola

Vola is positioned at the below of toe and heel ordinate, contacts with floor, has formed horizontal edge.But because there is radian at the arch of foot place of pin, so the edge that the bottom of pin becomes on image is not straight line.Thus, we using the bottom position of forefoot and as position, vola, detect the height at 1/2 and 3/4 place, and the bottom position of hind paw of usining detects 2/5 height as position, vola.Forefoot is generally 1/3 of pin length, and its horizontal ordinate is at [x ₀-(x ₁-x ₀) * 2/3, x ₁] in interval, the vola testing process of this position is:

1. with the gradient template of vertical direction, image is carried out to rim detection, outstanding transverse edge, template is;

$\left[\begin{array}{ccc}1& 3& 1\\ 0& 0& 0\\ -1& 3& -1\end{array}\right]$

2. on transverse edge image, horizontal ordinate is [x ₀-(x ₁-x ₀) * 2/3, x ₁], ordinate is [0, min (y ₀, y ₁)] interval in, the gray-level projection of calculated level direction, the ordinate at the row place of integrated value maximum is the ordinate in vola, is designated as y ₂.

Hind paw vola detection method is similar.

(3) key position of instep detects

This sentences 1/2 is example from heel to toe, and the key position of introducing instep detects.Based on experience value, 1/2 place's instep height of people's pin is approximately 1/3 long left and right of pin, and therefore, the horizontal ordinate of 1/2 place's instep is (x ₀+ x ₁)/2, ordinate are approximately y ₂+ (x ₁-x ₀)/3.Intercept the subarea window at 1/2 instep place, place, adopt region-growing method to cut apart this window area, in region, be divided into target and background two parts.Instep is the separatrix of target and background, and horizontal ordinate is (x ₀+ x ₁the separation at place)/2 is exactly people's pin 1/2 instep position, place, and we use y ₃the ordinate that represents this point.

Same process, we can extract the instep position at 2/5 place and 3/4 place.

(4) the key position true altitude of instep is calculated

By above step, the distance between the toe of side photograph and sufficient heel is x ₁-x ₀individual pixel, 1/2 place's instep height is y ₃-y ₁individual pixel.According to pin, the long and pin proportionate relationship between high, can show that the true altitude of 1/2 place's instep is

we can calculate the instep height at 3/4 place and 2/5 place the same manner.

3, advantage and effect

Advantage of the present invention is: by standard A 4 paper as a reference, can effectively obtain the data of the key position of pin by geometry correction, image processing techniques.In 50 groups of view data that gather, pin is long, pin is wide and the height measurement results error of instep key position all within 2 millimeters.

According to footwear code and the long general computing formula of pin

According to half yardage error of calculation, can obtain the long error of pin within 2.5 millimeters, the error that and pin wide in conjunction with pin is high again and shoemaker's shoemaking standard used, pin is long, pin is wide and the measurement result maximum error of crucial instep height fixes on 2 millimeters, demand in the time of can meeting the person that purchases footwear and selecting footwear code and shoemaker's shoemaking, and methods experiment resultant error of the present invention is all within 2 millimeters.

(4) accompanying drawing explanation

Fig. 1 (a) is positive according to image acquisition mode schematic diagram

Fig. 1 (b) side is according to image acquisition mode schematic diagram

Positive, the pin wide measurement procedure figure long according to pin of Fig. 2 (a)

Fig. 2 (b) side is according to instep key position height measurement procedure figure

(5) embodiment

In order to understand better technical scheme of the present invention, below in conjunction with accompanying drawing, embodiments of the present invention are further described:

The present invention realizes in conjunction with opencv1.0 under Microsoft Visual C++6.0 programmed environment.Positive, pin wide measurement procedure long according to pin is as shown in Fig. 2 (a), and process flow diagram 2 (b) is seen according to the measurement of instep key position height in side.Allocation of computer adopts: Intel Core i2E7300 processor, and dominant frequency 2.66GHz, internal memory 3GB, operating system is 32-bit Windows XP professional version.The data of this people's pin key position are extracted with measuring method and are comprised the following steps:

Step 1: press Fig. 1 (a), Fig. 1 (b), the form of image acquisition mode schematic diagram gathers positive photograph and side photograph, and concrete acquisition method is as follows:

1. the acquisition method of positive photograph: white A4 paper minor face one side is pasted to wall and place; User steps down in pin on A4 paper, makes the axis of pin align with the axis of A4 paper as far as possible; Heel, by wall, makes the alignment of heel position HeA4 paper edge, and the length direction of pin is consistent with the length direction of A4 paper, and it is inner to guarantee that pin drops on A4 paper completely; Camera directly over pin between 50 centimetres to 70 centimetres, take that angle is perpendicular to the ground carries out imaging, keep A4 paper not crooked in image as far as possible, and guarantee to comprise completely in visual field A4 paper region.

2. the acquisition method of side photograph; Side, according to not needing A4 paper, only needs subscriber station before wall or a pure color baffle plate, and the outside of pin is by wall or baffle plate; Camera lens is from the outside imaging of the interior side direction pin of pin, apart from 30 centimetres to 50 centimetres of the distances of side pin, takes angle and is parallel to ground, and keep same height with instep;

3. in visual field, scene will be tried one's best simply: positive as requested only comprises pin, A4 paper and floor in visual field; The background of side photograph should be simple wall or baffle plate, avoids other chaff interference to occur; Require user to wear black or other dark socks, to guarantee that there is enough large contrast contrast on pin, A4 paper and floor simultaneously.

Step 2: detect four angular vertex coordinates of A4 paper, image is carried out to geometry correction;

Specific implementation process is as follows:

1. Sobel operator is 3 * 3 the field based on gradient operator.The convolution mask of Sobel operator is by detection level direction gradient template

$\left[\begin{array}{ccc}1& 2& 1\\ 0& 0& 0\\ -1& -2& -1\end{array}\right]$

With detection of vertical direction gradient template

$\left[\begin{array}{ccc}1& 0& -1\\ 2& 0& -2\\ 1& 0& -1\end{array}\right]$

Form.Two templates are applied to respectively the positive image that shines, and root is opened in the horizontal direction of each pixel and square summation of the Grad of vertical direction again, can obtain the positive gradient map according to image;

2. rule of thumb, the area ratio of place, edge gradient map image accounts for 0.1.So, this method is by the histogram of statistical gradient figure, from gray-scale value, be 255 to start to calculate cumulative probability, by cumulative probability, be that 0.1 corresponding gray-scale value is set as threshold value, the pixel that is less than threshold value is set to 255, the pixel that is greater than threshold value is set to 0, thereby extracts the binary image that comprises A4 paper and pin object edge;

3. bianry image step being obtained in 2., on transverse axis, in the scope of [5 °, 5 °], take 1 ° image is carried out to Gray Projection as step-length.A4 paper is in the centre position of image, from image centre position to both sides, detects the extreme value of Gray Projection, detects two longitudinal edges in left and right and their deflection.Same way can detect two widthwise edges and their deflection up and down of A4 paper.Calculate the point of crossing between two longitudinal edges in left and right and upper and lower two widthwise edges, can obtain the rough coordinates of four angular vertex positions of A4 paper.

4. centered by four the angular vertex position coordinateses of A4 paper that obtain in 3. by step, the subgraph of four 140 * 140 sizes of relevant position intercepting on former gray-scale map.In four subgraphs, the ratio of the shared image area in edge is set to 0.15, repeats step above 1. to 3., can obtain the accurate coordinates of four angular vertex positions of A4 paper.

5. the relative coordinate of actual four angular vertexs of A4 paper is known, and transformation for mula is proofreaied and correct in the coordinate figure by four angular vertexs of A4 paper on correcting image and the substitution of actual coordinate value:

${x^{\′}=h}_1(x,y)=\frac{a_{0}x+a_{1}y+a_2}{a_{6}x+a_{7}y+1}$

${y^{\′}=h}_2(x,y)=\frac{a_{3}x+a_{4}y+a_5}{a_{6}x+a_{7}y+1}$

Wherein, x is the abscissa value on the summit on correcting image, and x' is corresponding actual abscissa value, and y is the abscissa value on the summit on correcting image, and y' is corresponding actual abscissa value.8 unknown numbers of 8 equations, solve a _i(i=0,1,2,3,4,5,6,7), obtain the correction transforming function transformation function of image.

Utilize above-mentioned the correction transforming function transformation function solving and bilinear interpolation method to carry out geometry correction to distorted image.

6. in the image from proofreading and correct, intercept rectangular area, A4 paper place, remove background.Obtain the A4 paper subimage with pin target.

Step 3: the target of front pin is extracted and measured;

By step 2, be truncated to A4 paper subimage, from this number of sub images, extract pin length and wide two data of pin.Specific implementation process is as follows:

(1) detection of toe position

Toe is to drop in the first half region of A4 paper, and sufficient heel is to align with the base of A4 paper.Therefore can detect in the first half of A4 paper subgraph the position of toe, and it is long according to the proportionate relationship of pin and A4 paper, to calculate pin.Detailed process is:

1. intercept A4 paper subimage the first half subarea, utilize Sobel operator to carry out rim detection, the area ratio with 0.06 carries out threshold value selection, and binaryzation is carried out in subarea.

2. in bianry image, have the noise spot being scattered, adopt closing operation of mathematical morphology to carry out filtering to binary map, the size of computing template is 5 * 5

$\left[\begin{array}{ccccc}0& 0& 1& 0& 0\\ 0& 1& 1& 1& 0\\ 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 0\\ 0& 0& 1& 0& 0\end{array}\right]$

3. to the bianry image after denoising, press from the top down each impact point of line search.Centered by this impact point, get 5 * 8 window, by the upper and lower doubling of window, on former gray-scale map, add up the gray scale difference of correspondence position in doubling window, and be averaging.And first meets gray scale difference mean value be greater than 30 impact point be the position of toe, with (x, y), represent.

(2) position probing of first metatarsal bone and fifth metatarsal bone

Because first metatarsal bone and fifth metatarsal bone lay respectively at the both sides of sole, by following process, detect this position of 2:

1. rim detection filtering are carried out in the subarea at forefoot place.Similar with the process of toe position probing, to the region, edge at the wide place of pin, utilize the longitudinal template of Sobel operator to carry out longitudinal edge detection, and use closing operation of mathematical morphology filtering;

2. determine the horizontal ordinate position of first metatarsal bone.On A4 paper subgraph, the ordinate of corresponding 69.5% position from heel to toe, with 1 * 16 window, search for from right to left, by the right left doubling of window, on former gray-scale map, add up the gray scale difference of correspondence position in doubling window, it is exactly first metatarsal bone position that the average of gray scale difference is greater than 25 position, and the horizontal ordinate at this some place is designated as to x _inner.

3. determine the horizontal ordinate position of fifth metatarsal bone.2. similar with step, at heel, to 62.5% position of toe, with 1 * 16 window, to search for from left to right, first meets window left and right doubling gray scale difference mean value, and to be greater than 25 position be exactly the position of fifth metatarsal bone, and the horizontal ordinate at this some place is designated as to x _outer.

(3) pin length and the wide calculating of pin

The size of A4 paper subimage is M * N, and its actual size is 210 millimeters * 297 millimeters.Toe coordinate is (x, y), and the physical length of pin is 297 * y/M millimeter, and the developed width of pin is 210 * (x _inner-x _outer)/N millimeter.

Step 4: the target of side pin is extracted and measured;

Suppose side according to mesopodium heel in the left side of image, toe is on right side, the detection of instep key position and height measurement method are as follows:

(1) detect heel and toe

In 1/2 interval at image from bottom to height, edge longitudinally in detected image, can navigate to the position of heel and toe.Detailed process is as follows:

1. adopt the gradient template of vertical direction to carry out rim detection to image, the longitudinal edge of outstanding toe and heel.The template that adopts as follows:

$\left[\begin{array}{ccc}1& 0& -1\\ 3& 0& -3\\ 1& 0& -0\end{array}\right]$

2. the edge of heel and toe area occupied ratio in image is 0.1, with this area ratio as threshold value to image binaryzation, obtain edge binary map;

3. use 5 * 8 window from left to right by row search, suppose that in window, impact point number is n, the position rough position (x' that first window position that meets n/ (5 * 8) >25 is exactly sufficient heel ₀, y' ₀).With (x' ₀, y' ₀) centered by 20 * 20 windows in fine searching, determine the exact position (x of heel ₀, y ₀).

4. same process, when starting left by row search from image right side, navigates to the exact position (x of toe ₁, y ₁).

(2) detect vola

The bottom position of forefoot of usining detects as position, vola.Forefoot is generally 1/3 of pin length, and its horizontal ordinate is positioned at (x ₀-(x ₁-x ₀) * 2/3, x ₁), the vola testing process of this position is:

1. with the gradient template of horizontal direction, image is carried out to rim detection, outstanding transverse edge, template is;

$\left[\begin{array}{ccc}1& 3& 1\\ 0& 0& 0\\ -1& 3& -1\end{array}\right]$

2. on transverse edge image, horizontal ordinate is (x ₀-(x ₁-x ₀) * 2/3, x ₁), ordinate is (0, min (y ₀, y ₁)) interval in, the gray-level projection of calculated level direction, the ordinate at the row place of integrated value maximum is the ordinate in vola, is designated as y ₂.

(3) detection of instep key position

The instep height of 2/5,1/2,3/4 position from heel to toe is the critical data of pin.This sentences 1/2 is example from sufficient heel to toe, introduces the detection of instep key position.

The horizontal ordinate of 1/2 place's instep is (x ₀+ x ₁)/2, ordinate are approximately y ₂+ (x ₁-x ₀)/3.Intercept the subarea window at 1/2 instep place, place, adopt region-growing method to cut apart this window area, in region, be divided into target and background two parts.Instep is the separatrix of target and background, and horizontal ordinate is (x ₀+ x ₁the separation at place)/2 is exactly people's pin 1/2 instep position, place, uses y ₃represent.

Same process, we can extract the instep position at 2/5 place and 3/4 place.Wherein, the instep height at 2/5 place is usingd hind paw bottom and is calculated as vola.

(4) true altitude of instep key position is calculated

According to pin, the long and pin proportionate relationship between high, can show that the true altitude of 1/2 place's instep is

we can calculate the instep height at 3/4 and 3/5 place the same manner.

Claims (5)

1. a kind of data extraction and measuring method of key parts of people's foot based on image, it is characterized in that: the method concrete steps are as follows: Step 1: Image Acquisition Calculate the foot length and foot width through the proportional relationship between the human foot and the A4 paper, and calculate the actual height of the key parts of the instep according to the proportional relationship between the height of the instep and the length of the foot; therefore, two images need to be taken, one is The frontal photo of the feet is stepped on white A4 paper, and the camera shoots vertically from above the feet; the other is the side view of the feet. The camera projects the feet from the inside of the feet; Step 2: Detect the coordinates of the vertices of the four corners of the A4 paper, and perform geometric correction on the image Geometric distortions often occur in the process of image acquisition and display. Geometric distortions include translation, scaling, rotation and perspective, as well as more complex geometric distortions; any geometric distortion can be transformed from a non-distorted coordinate system (x, y) to a distortion The equation of the coordinate system (x', y') is defined; assuming f(x, y) is the original image without distortion, and g(x', y') is the geometric distortion result of f(x, y), then we get The basic relationship of geometric correction is as follows: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$ In the formula, h ₁ (x, y) and h ₂ (x, y) are correction transformation functions, and h ₁ (x, y) and h ₂ (x, y) are approximated by the following polynomials: ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$ ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$ Since the actual relative coordinates of the four corner vertices of the standard A4 paper are known, the four corner vertices of the A4 paper are used as control points, and the coordinates of the four corners of the A4 paper in the geometrically distorted image are detected by image processing technology, and then used The correction transformation function and the bilinear interpolation method perform geometric distortion correction on the distorted image; Step 3: Target extraction and measurement of frontal feet The A4 paper image is intercepted in step 2. We need to extract the two data of foot length and foot width from this image. The specific implementation process is as follows: (1) Detection of toe position The toe falls in the upper half of the A4 paper, and the heel is aligned with the bottom edge of the A4 paper. Therefore, the position of the toe is detected in the upper half of the A4 paper sub-graph, and according to the foot and the A4 paper The proportional relationship calculates the foot length; (2) Position detection of the first metatarsal and the fifth metatarsal Since the first metatarsal and the fifth metatarsal are located on both sides of the sole of the foot, we use the following process to detect the positions of these two points: ① Perform edge detection and filtering on the sub-area where the forefoot is located; similar to the process of toe position detection, perform edge detection on the area where the edge of the foot width is located, and use morphological closed operation to filter; ②Determine the abscissa position of the first metatarsal; on the A4 paper submap, corresponding to the ordinate at 69.5% of the position from the heel to the toe, use a 1×16 window to search from right to left, fold the window in half from right to left, and in the original The grayscale difference of the corresponding position in the half-fold window is counted on the grayscale image, and the position where the average value of the grayscale difference is greater than 25 is the position of the first metatarsal bone, and the abscissa at this point is marked as x _inner ; ③Determine the abscissa position of the fifth metatarsal; similar to step ②, at the 62.5% position from the heel to the toe, use a 1×16 window to search from left to right, and the first one that satisfies the average gray level difference between the left and right folds of the window The position where the value is greater than 25 is the position of the fifth metatarsal, and the abscissa at this point is marked as x _outer ; (3) Calculation of foot length and foot width The standard size of A4 paper is 210 mm × 297 mm. Assume that the A4 paper sub-image has M rows and N columns. Let the lower left corner of the A4 paper sub-image be the coordinate origin. If the coordinates of the toe position in the sub-image are (x, y ), the actual length of the foot is 297×y/M mm; assuming that the number of pixels of the width of the sole extracted on the A4 paper image is c, the abscissa values of the first metatarsal and the fifth metatarsal can be obtained as c=x _inner -x _outer , while the actual width of the foot is 210×c/N mm; Step 4: Target extraction and measurement of lateral feet The side photo image of the foot is used to extract the height of the key parts of the foot, from the heel to the 2/5, 1/2 and 3/4 of the toe, the height of these parts is used in the design of the shoe last Important parameters, when choosing a shoe size, people with tall feet should choose a shoe size that is one size larger than normal feet, or increase the height of the shoe tree appropriately when customizing shoes; in the side photo image, the distance from the heel to the toe is the length of the foot , and from the bottom of the foot to the top of the foot corresponds to the height of the foot at the corresponding position; assuming that the heel is on the left side of the image and the toe is on the right side of the image in the side view, the detection and height measurement methods of the key parts of the foot are as follows: (1) Detect heel and toe The heel and toe are in the lower half of the image, and two vertical edges are formed on the left and right sides of the image. Therefore, within the 1/2 interval from the bottom to the height of the image, the vertical edge in the image can be detected to locate To the position of the heel and toe; detect the sole of the foot The bottom of the foot is located below the vertical coordinates of the toe and heel, and is in contact with the floor, forming a horizontal edge; however, due to the curvature of the arch of the foot, the edge formed by the bottom of the foot on the image is not a straight line. Therefore, we use the bottom position of the front sole as the sole position to detect the height of 1/2 and 3/4, and the bottom position of the rear sole is used as the sole position to detect the height of 2/5; the forefoot is generally the length of the foot 1/3, its abscissa is in the interval [x ₀ -(x ₁ -x ₀ )×2/3,x ₁ ], then the sole detection process at this position is: ① Use the gradient template in the vertical direction to detect the edge of the image, highlight the horizontal edge, and the template is; $\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 3</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 3</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ ② On the horizontal edge image, the abscissa is [x ₀ -(x ₁ -x ₀ )×2/3,x ₁ ], and the ordinate is [0,min(y ₀ ,y ₁ )], calculate In the gray integral projection in the horizontal direction, the ordinate of the line with the largest integral value is the ordinate of the sole of the foot, which is recorded as y ₂ ; The detection method of the sole of the rear foot is similar; (2) Detection of key parts of the instep Here we take the 1/2 part from the heel to the toe as an example to introduce the detection of key parts of the instep; according to experience, the height of the 1/2 part of the human foot is about 1/3 of the length of the foot. Therefore, 1/2 The abscissa of the instep is (x ₀ +x ₁ )/2, and the ordinate is y ₂ +(x ₁ -x ₀ )/3; intercept the sub-area window where the instep is at 1/2, and use the region growing method to The window area is divided, and the area is divided into two parts, the target and the background; the instep is the dividing line between the target and the background, and the abscissa is (x ₀ +x ₁ )/2 the demarcation point is the position of the human foot at 1/2 , we use y ₃ to represent the ordinate of the point; In the same process, we extract the instep positions at 2/5 and 3/4; (3) Calculation of the actual height of the key parts of the instep From the above steps, the distance between the toe and the heel of the side view is x ₁ -x ₀ pixels, and the height of the foot at 1/2 is y ₃ -y ₁ pixel; according to the ratio between the length of the foot and the height of the foot relationship, the actual height of the instep at 1/2 is

In the same way we can calculate the height of the instep at 3/4 and 2/5. 2. the data extraction and measuring method of a kind of image-based people's foot key parts according to claim 1, is characterized in that: described in step 1 needs to take two images, one is the frontal photo of pin, The other is a side view of the foot, and its specific requirements and operations are as follows: ①Collecting the frontal photo of the feet: Place the short side of the white A4 paper against the wall; the user steps on the A4 paper so that the central axis of the foot is aligned with the central axis of the A4 paper; the heel is placed against the wall so that the foot Align with the position and the edge of the A4 paper, the length direction of the feet is consistent with the length direction of the A4 paper, and ensure that the feet are completely inside the A4 paper; the camera is between 50 cm and 70 cm directly above the feet, and the shooting angle is perpendicular to the ground For imaging, try to keep the A4 paper from being skewed in the image, and ensure that the A4 paper area is completely included in the field of view; ②The collection method of the side photo of the foot; the side photo does not need A4 paper, only the user needs to stand in front of a wall or a solid color baffle, and the outside of the foot is against the wall or baffle; the lens takes an image from the inside of the foot to the outside of the foot, The distance from the side foot is 30cm to 50cm, and the shooting angle is parallel to the ground and kept at the same height as the foot; ③The scene in the field of view should be as simple as possible: the front view requires only feet, A4 paper and the floor; the background of the side view should be a simple wall or baffle to avoid other distracting objects; at the same time, the user is required to wear black or other Dark colored socks to ensure sufficient contrast between the feet, the A4 paper and the floor. 3. The data extraction and measurement method of a kind of image-based key parts of the human foot according to claim 1, characterized in that: in the step 2, "detect the A4 paper in the geometrically distorted image by image processing technology" The coordinates of each corner, and then use the correction transformation function and bilinear interpolation method to correct the geometric distortion of the distorted image", the specific implementation process is as follows: ①Edge detection on the frontal photo of the feet: Use the Sobel operator to extract the edge of the frontal photo image to obtain the gradient map of the image; The change is relatively flat, so dark areas are formed in the gradient map; ②Binarize the gradient image: the edge formed by the A4 paper and the foot target occupies a small part of the image, which is set to 0.1 of the image area; the histogram statistics are performed on the gradient image, and the gray value of the edge pixel of the image is relatively small. High, the distribution will be on the right side of the histogram, and the non-edge pixels will be concentrated on the left side of the histogram. The cumulative probability of the histogram is calculated from the rightmost side of the histogram to the left, that is, the pixel statistics on the edge of the image. And the gray value corresponding to the cumulative probability of 0.1 is set as the threshold value, the pixels smaller than the threshold value are set to 255, and the pixels greater than the threshold value are set to 0, thereby extracting the edge including the A4 paper and the foot target; ③ Preliminary detection of the position coordinates of the four corner vertices of the A4 paper. For the binary image obtained in the aforementioned step ②, the image is grayed out within the range of [-5°, 5°] on the horizontal axis with a step size of 1°. degree projection; since the left and right longitudinal sides of the A4 paper are strong edges in the image, it will form an extremum in the correct projection direction, and according to prior knowledge, the A4 paper is in the middle of the image, and from the middle of the image To both sides, detect the extreme value of the grayscale projection, you can detect the left and right vertical sides and their direction angle; the same method can detect the upper and lower two horizontal sides of A4 paper and their direction angle; calculate the left and right vertical sides The intersection point between the side and the upper and lower horizontal sides, that is, the rough coordinates of the four corner vertex positions of the A4 paper; ④Precisely detect the position coordinates of the four corner vertices of the A4 paper: Take the position coordinates of the four corner vertices of the A4 paper obtained in step ③ as the center, intercept four 140×140 sub-images at the corresponding positions on the original gray scale image, and The ratio of the image area occupied by the edges of the four sub-images is set to 0.15, and the above steps ① to ③ are repeated to obtain the precise coordinates of the four corner vertex positions of the A4 paper; ⑤ Perform geometric correction on the image: the relative coordinates of the actual four corner vertices of the A4 paper are known, and use the above-mentioned correction transformation function and bilinear interpolation method to perform geometric correction on the distorted image; ⑥Intercept the A4 paper sub-picture and remove the useless background: After the image is corrected, the area where the A4 paper is located is a standard rectangle, and the aspect ratio of the rectangle is the aspect ratio of the A4 paper; intercept the rectangle from the image and remove the background, then The inside of the intercepted sub-image is the foot target we want to detect. 4. the data extraction and measuring method of a kind of image-based people's foot key parts according to claim 1, is characterized in that: in step 3 described in " the detection of tiptoe position ", its specific process is: ①Intercept the sub-area in the upper half of the A4 paper image, and use the Sobel operator to perform edge detection; according to prior knowledge, the edge formed by the foot target in this sub-area accounts for about 0.06 of the area of the sub-area. This scheme uses an area ratio of 0.06 Perform threshold selection and binarize the sub-areas; ②There are scattered noise points in the binary image, and the binary image is filtered by morphological closed operation, and the size of the operation template is 5×5 $\left[\begin{array}{ccccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]$ ③For the denoised binary image, search for each target point by row from top to bottom, take a 5×8 window centered on the target point, fold the window in half up and down, and count the corresponding points in the folded window on the original grayscale image The gray level difference of the position is calculated and averaged, and the first target point that meets the average value of the gray level difference greater than 30 is the position of the toe, represented by (x, y). 5. the data extraction and measuring method of a kind of image-based people's foot key parts according to claim 1, is characterized in that: " detect heel and toe " described in step 4, its concrete process is as follows: ① Use the gradient template in the horizontal direction to detect the edge of the image, and highlight the longitudinal edge of the toe and heel. The template used is as follows: $\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 3</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ ② The area ratio of the edge of the heel and toe in the image is 0.1, and the image is binarized using this area ratio as a threshold to obtain a binary image of the edge; ③Use the 5×8 window to search by column from left to right. Assuming that the number of target points in the window is n, the position of the first window satisfying (n/(5×8))>0.9 is the rough position of the heel , represented by (x' ₀ ,y' ₀ ), where x' ₀ is the abscissa of the rough position of the heel, and y' ₀ is the ordinate; ④ Take the heel position coordinates (x' ₀ , y' ₀ ) as the center, intercept a 20×20 sub-window, and perform a fine search for the heel position in the window; use the gradient template in the x direction [1 -1] to calculate the window Inner gradient, the position of the maximum gradient of each line in the search window, the abscissa statistics of the maximum gradient position of all lines, the most abscissa is the exact abscissa of the heel position, we use (x ₀ ,y ₀ ) represents the precise coordinate position of the heel; ⑤ In the same process, when searching from the right side of the image to the left by column, the coordinate position (x ₁ , y ₁ ) of the toe is obtained.

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