CN103852060B - A kind of based on single visual visible images distance-finding method felt - Google Patents

Abstract

The present invention discloses a kind of based on single visual visible images distance-finding method felt, the present invention is by the image of the camera collection of fixed angle, then, set up in image every adjacent two pixels vertically, the one-to-one relationship of horizontal throw and space actual range, obtain in image the actual range between any two points finally by above-mentioned one-to-one relationship. The present invention adopts single camera to work, and realizes range finding by computer, reduces equipment complexity, effectively reduce equipment cost; By actual height representated by each pixel in computed image and horizontal throw, then measure real standard Distance geometry height, reduce computation complexity.

Description

A kind of based on single visual visible images distance-finding method felt

Technical field:

What the present invention relates to is a kind of based on single visual visible images distance-finding method felt.

Background technology:

Image measurement technology, based on optics, has incorporated the modern science and technology such as photoelectronics, computer technology, laser technology, image processing techniques, forms the Integrated Measurement System of light, mechanical, electrical, calculation and control techniques integration. When image measurement measures tested object exactly, image is used as detection and the means transmitted or the measuring method that is used of carrier, its objective is from image, extract useful signal. The ultimate principle of image measurement is exactly the Edge texture of process testee image and obtains the geometric parameter of object, and therefore image processing techniques becomes basis and the key of image measurement system.

Image measurement system is made up of illumination system, digital image collection system and digital image processing and display three subsystems usually. Analyte character zone is irradiated by the background light source in illumination system, then utilize digital imaging apparatus that it is carried out imaging, and computer of directly image digital signal being passed on a skill of craft to others, complete image collection to utilize in a computer, the digital picture gathered is processed by the software of establishment, obtain the characteristic information of analyte, and by image output device, it is carried out image output.

A pick up camera is only adopted based on single visual visible images ranging technology felt, so structure is simple, accordingly that the demarcation of pick up camera is also comparatively simple, avoid the difficulty of three-dimensional coupling in binocular vision simultaneously. So it is simple to have equipment, the advantages such as cost is lower, measuring process is quick, and good environmental adaptability, take off data are more objective.

Summary of the invention:

It is an object of the invention to overcome the deficiencies in the prior art, it is provided that a kind of based on single visual visible images distance-finding method felt.

In order to solve the problem existing for background technology, the present invention by the following technical solutions:

Based on the single visual visible images distance-finding method felt, it comprises the following steps:

Step one: obtain single order visual pattern that pixel is b �� a by monocular cam, and by obtained Image Saving in computer memory device;

Step 2: the mounting height h measuring camera, camera is installed angle, �� and is got 45 ��, the view angle theta of camera in the vertical direction₁, camera view angle theta in the horizontal direction₂;

Step 3: according to the image-forming principle of monocular cam, the information obtained by step one and step 2 calculates in image on the initial vertical direction of image apex the actual projection distance y [m] between m pixel and the m+1 pixel, calculate the actual projection distance x [m, n] of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image;

Step 4: if what measure is height, then adopting the method for elevation correction, the actual projection distance of adjacent two pixels obtained according to the image-forming principle of monocular cam and step 3 calculates actual height height; If what measure is horizontal throw, then not adopting elevation to correct, the actual projection distance of adjacent two pixels directly obtained according to image-forming principle and the step 3 of monocular cam calculates actual range length.

Wherein, in step 2, the installation angle, �� of camera refers to the sight line axis of camera and the angle being perpendicular to direction, ground; The view angle theta of camera horizontal direction₂Refer to the face, the leftmost side of camera sight line and the angle of these two planes of face, the camera sight line rightmost side; Camera vertical direction view angle theta₁Refer to the angle of the top of camera sight line and camera sight line these two planes bottom.

Further, in step 3, according to the image-forming principle of monocular cam, calculate in image the actual projection distance of often adjacent two pixels in the actual range of often adjacent two pixels on vertical direction and horizontal direction, its detailed process is:

Image-forming principle according to monocular cam, obtains on the initial vertical direction of image apex the actual projection distance between m pixel and the m+1 pixel:

$y\[m\]=h\left(tan\right(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\left(m+1\right))-tan(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}m\left)\right)$

Wherein m=0,1,2 ..., a-1;

Image-forming principle according to monocular cam, obtains the actual projection distance of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image:

$x\[m,n\]=\left\{\begin{array}{cc}\frac{h\·\{tan(\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n+1\left)\right)-tan(\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n\left)\right)\}}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=0,1,2,...\frac{b}{2}-1\\ \frac{h\·\{tan(\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}+1\left)\right)-tan(\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}\left)\right)\}}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=\frac{b}{2},\frac{b}{2}+1,\mathrm{...},b-1\end{array}\right.$

Wherein, m=0,1,2 ..., a-1.

Further, in step 4, according to the actual projection distance y [m] between m pixel and the m+1 pixel on the initial vertical direction of image apex that step 3 calculates, the actual projection distance x [m of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image, n], calculating the actual height height in image and horizontal throw length, its detailed process is:

During measured altitude, adopting the method for elevation correction, in image, actual height between any two points (pixel coordinate in image is respectively (i, s), (j, t)) is:

$height=tan(\frac{\mathrm{\π}}{2}-\mathrm{\θ}+\frac{{\mathrm{\θ}}_1}{2}-\frac{{\mathrm{\θ}}_1}{a}i)\underset{k=min(s,t)}{\overset{max(s,t)}{\Σ}}y\[k\]$

When measuring horizontal throw, do not adopt elevation correction method to calculate, any two points in image, the pixel coordinate in image is respectively (i, s), (j, t)) between real standard distance be:

$length=\sqrt{{(\underset{k_1=min(i,j)}{\overset{\max (i,j)}{\Σ}}x\[\frac{s+t}{2},k_1\])}^2+{(\underset{k_2=\min (s,t)}{\overset{max(s,t)}{\Σ}}y\[k_2\])}^2}$

Wherein, pixel coordinate (i, s) refers to image from left side i-th, the s pixel from top.

The present invention contrasts prior art, there is following useful effect: the present invention provides a kind of based on single visual visible images ranging technology felt, this technology adopts single camera to work, and realizes range finding by computer, reduce equipment complexity, effectively reduce equipment cost. This technology, by actual height representated by each pixel in computed image and horizontal throw, is then measured real standard Distance geometry height, is reduced computation complexity.

Accompanying drawing illustrates:

Fig. 1 is the workflow diagram based on single visual visible images distance-finding method felt of the present invention.

Fig. 2 is monocular cam imaging schematic diagram.

Fig. 3 is projection plane A₁B₁C₁D₁Schematic diagram.

Fig. 4 is elevation carrection schematic diagram.

Fig. 5 is that horizontal throw measures schematic diagram.

Embodiment:

Below in conjunction with the drawings and specific embodiments, the invention will be further described:

Fig. 1 is the workflow diagram based on single visual visible images distance-finding method felt of the present invention. Based on the single visual visible images distance-finding method felt, it comprises the following steps:

Step one: obtain single order visual pattern that pixel is b �� a by monocular cam, and by obtained Image Saving in computer memory device;

Step 2: the mounting height h measuring camera, camera is installed angle, �� and is got 45 ��, the view angle theta of camera in the vertical direction₁, camera view angle theta in the horizontal direction₂;

Step 3: according to the image-forming principle of monocular cam, the information obtained by step one and step 2 calculates in image on the initial vertical direction of image apex the actual projection distance y [m] between m pixel and the m+1 pixel, calculate the actual projection distance x [m, n] of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image;

Step 4: if what measure is height, then adopting the method for elevation correction, the actual projection distance of adjacent two pixels obtained according to the image-forming principle of monocular cam and step 3 calculates actual height height; If what measure is horizontal throw, then not adopting elevation to correct, the actual projection distance of adjacent two pixels directly obtained according to image-forming principle and the step 3 of monocular cam calculates actual range length.

Wherein, in step 2, the installation angle, �� of camera refers to the sight line axis of camera and the angle being perpendicular to direction, ground; The view angle theta of camera horizontal direction₂Refer to the face, the leftmost side of camera sight line and the angle of these two planes of face, the camera sight line rightmost side; Camera vertical direction view angle theta₁Refer to the angle of the top of camera sight line and camera sight line these two planes bottom.

Further, in step 3, according to the image-forming principle of monocular cam, calculate in image the actual projection distance of often adjacent two pixels in the actual range of often adjacent two pixels on vertical direction and horizontal direction, its detailed process is:

Image-forming principle according to monocular cam, obtains on the initial vertical direction of image apex the actual projection distance between m pixel and the m+1 pixel:

$y\[m\]=h\left(tan\right(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}(m+1))-tan(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}m))$

Wherein m=0,1,2 ..., a-1;

Image-forming principle according to monocular cam, obtains the actual projection distance of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image:

$x\[m,n\]=\left\{\begin{array}{cc}\frac{h\·\{tan(\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n+1\left)\right)-tan(\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n\left)\right)\}}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=0,1,2,...\frac{b}{2}-1\\ \frac{h\·\{tan(\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}+1\left)\right)-tan(\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}\left)\right)\}}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=\frac{b}{2},\frac{b}{2}+1,\mathrm{...},b-1\end{array}\right.$

Wherein, m=0,1,2 ..., a-1.

Further, in step 4, according to the actual projection distance y [m] between m pixel and the m+1 pixel on the initial vertical direction of image apex that step 3 calculates, the actual projection distance x [m of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image, n], calculating the actual height height in image and horizontal throw length, its detailed process is:

During measured altitude, adopting the method for elevation correction, in image, actual height between any two points (pixel coordinate in image is respectively (i, s), (j, t)) is:

$height=tan(\frac{\mathrm{\π}}{2}-\mathrm{\θ}+\frac{{\mathrm{\θ}}_1}{2}-\frac{{\mathrm{\θ}}_1}{a}i)\underset{k=min(s,t)}{\overset{max(s,t)}{\Σ}}y\[k\]$

When measuring horizontal throw, not adopting elevation correction method to calculate, in image, real standard distance between any two points (pixel coordinate in image is respectively (i, s), (j, t)) is:

$length=\sqrt{{(\underset{k_1=min(i,j)}{\overset{\max (i,j)}{\Σ}}x\[\frac{s+t}{2},k_1\])}^2+{(\underset{k_2=\min (s,t)}{\overset{max(s,t)}{\Σ}}y\[k_2\])}^2}.$

Wherein, pixel coordinate (i, s) refers to image from left side i-th, the s pixel from top.

The principle of the present invention:

Fig. 2 is monocular cam imaging schematic diagram, and S is monocular cam position, and ABCD is the ground scenery taken by camera, A₁B₁C₁D₁For the projection plane of ground ABCD in camera. A₁B₁C₁D₁For rectangle, with monocular cam captured by the equal proportion of digital picture. Wherein, ABCD plane and A₁B₁C₁D₁Intersect at dotted line PQ, O shown in figure for projection plane A₁B₁C₁D₁Central point, be also simultaneously the central point of camera sight line.

Get camera sight line central line SO and vertical direction ST angle is ��=45 ��. Camera distance floor level ST=h, planar S AD and plane SBC angle is camera vertical direction view angle theta₁, planar S AB and plane SCD angle are camera horizontal direction view angle theta₂��

Now, on the ABCD of ground the object EF of vertical direction at plane A₁B₁C₁D₁On be projected as E₁F₁, the object GH that horizontal direction is placed is at plane A₁B₁C₁D₁On be projected as G₁H₁, as shown in heavy line in Fig. 2.

The Pixel of Digital Image that monocular cam obtains is b �� a, correspondingly, with the projection plane A of digital picture equal proportion₁B₁C₁D₁B �� a pixel can also be divided into, as shown in Fig. 3 below. Fig. 3 is projection plane A₁B₁C₁D₁Schematic diagram.

As seen from Figure 2, plane A₁B₁C₁D₁The actual range representated by each pixel be inequal, through calculating, the the actual projection distance y [m] between m pixel and the m+1 pixel (thinking, the capable actual projection of the capable m+1 of m of the projection each row of plane is apart from equal) can be obtained calculating in image on the initial vertical direction of image apex here approximately

$y\[m\]=h\left(tan\right(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}(m+1))-tan(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}m))$

Wherein m=0,1,2 ..., a-1.

With reason, it is possible to obtain the actual projection distance x [m, n] of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image

$x\[m,n\]=\left\{\begin{array}{cc}\frac{h\·\{tan(\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n+1\left)\right)-tan(\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n\left)\right)\}}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=0,1,2,...\frac{b}{2}-1\\ \frac{h\·\{tan(\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}+1\left)\right)-tan(\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}\left)\right)\}}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=\frac{b}{2},\frac{b}{2}+1,\mathrm{...},b-1\end{array}\right.$

Wherein, m=0,1,2 ..., a-1.

During measured altitude, in image, actual height between any two points (pixel coordinate in image is respectively (i, s), (j, t)) is:

$height=tan(\frac{\mathrm{\π}}{2}-\mathrm{\θ}+\frac{{\mathrm{\θ}}_1}{2}-\frac{{\mathrm{\θ}}_1}{a}i)\underset{k=min(s,t)}{\overset{max(s,t)}{\Σ}}y\[k\]$

When measuring horizontal throw, in image, real standard distance between any two points (pixel coordinate in image is respectively (i, s), (j, t)) is:

$length=\sqrt{{(\underset{k_1=min(i,j)}{\overset{\max (i,j)}{\Σ}}x\[\frac{s+t}{2},k_1\])}^2+{(\underset{k_2=\min (s,t)}{\overset{max(s,t)}{\Σ}}y\[k_2\])}^2}$

About elevation carrection:

Getting SEF place planar cross-sectional in Fig. 2 is that example is described, and is illustrated in fig. 4 shown below, and MN is ground, M₁N₁For projection plane. Fig. 4 is elevation carrection schematic diagram.

Often the real space point at adjacent two pixel places and the angle of camera on image vertical direction:

����₁=��₁/a

Thus can calculate on the initial vertical direction of image apex the actual projection distance between m pixel and the m+1 pixel:

$y\[m\]=h\left(tan\right(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+{\mathrm{\Δ\θ}}_1(m+1))-tan(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+{\mathrm{\Δ\θ}}_{1}m))$

Wherein m=0,1,2 ..., a-1.

During measured altitude, in image between any two points (pixel coordinate in image is respectively (i, s), (j, t)) vertical direction projection distance E₁F₁For:

$\mathrm{\Δ}height=\underset{k=min(s,t)}{\overset{max(s,t)}{\Σ}}y\[k\]$

By ray cast principle, through elevation correction, the actual height EF that can obtain between these 2 is:

$height=\mathrm{\Δ}height\·tan(\frac{\mathrm{\π}}{2}-\mathrm{\θ}+\frac{{\mathrm{\θ}}_1}{2}-\frac{{\mathrm{\θ}}_1}{a}\·i)$

Note: EF and horizontal plane (namely with i=j in E, F 2 corresponding pixel coordinates) in this example, in fact as EF and horizontal plane non-vertical, can also go out height by correct measurement by same method.

Measure about horizontal throw:

Getting SGH place planar cross-sectional in Fig. 2 is that example is described, and is illustrated in fig. 5 shown below, and KL is ground, K₁L₁For projection plane. Fig. 5 is that horizontal throw measures schematic diagram.

The angle of often adjacent two pixel place real space points and camera on image vertical direction:

����₂=��₂/b

In image, coordinate is the distance of point to camera of (m, n):

$l\[m,n\]=\frac{h}{cos(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+{\mathrm{\Δ\θ}}_1(m+1\left)\right)}$

Wherein m=0,1,2 ..., a-1.n=0,1,2 ..., b-1.

In image, coordinate is the point of (m, n), and to be the actual projection distance of the point of (m, n+1) to pixel coordinate be:

$x\[m,n\]=\left\{\begin{array}{cc}l\[m,n\]\{\tan ({\mathrm{\Δ\θ}}_2\·(\frac{b}{2}-n+1\left)\right)-\tan ({\mathrm{\Δ\θ}}_2\·(\frac{b}{2}-n\left)\right)\},& n=0,1,2,\mathrm{...}\frac{b}{2}-1\\ l\[m,n\]\{\tan ({\mathrm{\Δ\θ}}_2\·(n-\frac{b}{2}+1\left)\right)-\tan ({\mathrm{\Δ\θ}}_2\·(n-\frac{b}{2}\left)\right)\},& n=\frac{b}{2},\frac{b}{2}1,\mathrm{...},b-1\end{array}\right.$

When measuring horizontal throw, in image, real standard distance GH between any two points (pixel coordinate in image is respectively (i, s), (j, t)) is:

$length=\sqrt{{(\underset{k_1=min(i,j)}{\overset{\max (i,j)}{\Σ}}x\[\frac{s+t}{2},k_1\])}^2+{(\underset{k_2=\min (s,t)}{\overset{max(s,t)}{\Σ}}y\[k_2\])}^2}.$

Note: GH and projection plane parallel (namely with s=t in G, H 2 corresponding pixel coordinates) in this example, in fact when GH is not parallel with projection plane, can also go out horizontal throw by correct measurement by same method.

The foregoing is only the better embodiment of the present invention, not in order to limit the present invention, all any amendment, equivalent replacement and improvement etc. done within the spirit and principles in the present invention, all should be included within protection scope of the present invention.

Claims (1)

1. the visible images distance-finding method based on single visual feel, it is characterised in that, it comprises the following steps:

Step one: obtain single order visual pattern that pixel is b �� a by monocular cam, and by obtained Image Saving in computer memory device;

Step 2: the mounting height h measuring camera, camera is installed angle, �� and is got 45 ��, the view angle theta of camera in the vertical direction₁, camera view angle theta in the horizontal direction₂;

Step 3: according to the image-forming principle of monocular cam, the information obtained by step one and step 2 calculates in image on the initial vertical direction of image apex the actual projection distance y [m] between m pixel and the m+1 pixel, calculate the actual projection distance x [m, n] of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image;

Step 4: if what measure is height, then adopting the method for elevation correction, the actual projection distance of adjacent two pixels obtained according to the image-forming principle of monocular cam and step 3 calculates actual height height; If what measure is horizontal throw, then not adopting elevation to correct, the actual projection distance of adjacent two pixels directly obtained according to image-forming principle and the step 3 of monocular cam calculates actual range length;

In step 2, the installation angle, �� of camera refers to the sight line axis of camera and the angle being perpendicular to direction, ground; The view angle theta of camera horizontal direction₂Refer to the face, the leftmost side of camera sight line and the angle of these two planes of face, the camera sight line rightmost side; Camera vertical direction view angle theta₁Refer to the angle of the top of camera sight line and camera sight line these two planes bottom;

In step 3, according to the image-forming principle of monocular cam, calculating in image the actual projection distance of often adjacent two pixels in the actual range of often adjacent two pixels on vertical direction and horizontal direction, its detailed process is:

Image-forming principle according to monocular cam, obtains on the initial vertical direction of image apex the actual projection distance between m pixel and the m+1 pixel:

$y\[m\]=h\left(tan\right(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\left(m+1\right))-tan(\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}m\left)\right)$

Wherein m=0,1,2 ..., a-1;

Image-forming principle according to monocular cam, obtains the actual projection distance of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image:

$x\[m,n\]=\left\{\begin{array}{cc}\frac{h\·\{\tan (\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n+1\left)\right)-\tan (\frac{{\mathrm{\θ}}_2}{b}\·(\frac{b}{2}-n\left)\right)\}}{\cos (\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=0,1,2,\mathrm{...}\frac{b}{2}-1\\ \frac{h\·\{\tan (\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}+1\left)\right)-\tan (\frac{{\mathrm{\θ}}_2}{b}\·(n-\frac{b}{2}\left)\right)\}}{\cos (\mathrm{\θ}-\frac{{\mathrm{\θ}}_1}{2}+\frac{{\mathrm{\θ}}_1}{a}\·(m+1\left)\right)},& n=\frac{b}{2},\frac{b}{2}+1,\mathrm{...},b-1\end{array}\right.$

Wherein, m=0,1,2 ..., a-1;

In step 4, according to the actual projection distance y [m] between m pixel and the m+1 pixel on the initial vertical direction of image apex that step 3 calculates, the actual projection distance x [m of the capable pixel of m initial n-th pixel and (n+1)th pixel on the left of image in image, n], calculating the actual height height in image and horizontal throw length, its detailed process is:

During measured altitude, adopting the method for elevation correction, in image, actual height between any two points is that wherein, the pixel coordinate that in image, any two points is specially in image is respectively (i, s), (j, t):

$height=tan(\frac{\mathrm{\π}}{2}-\mathrm{\θ}+\frac{{\mathrm{\θ}}_1}{2}-\frac{{\mathrm{\θ}}_1}{a}i)\underset{k=\min (s,t)}{\overset{\max (s,t)}{\Σ}}y\[k\]$

When measuring horizontal throw, not adopting elevation correction method to calculate, in image, real standard distance between any two points is that wherein, the pixel coordinate that in image, any two points is specially in image is respectively (i, s), (j, t):

$length=\sqrt{{(\underset{k_1=\min (i,j)}{\overset{\max (i,j)}{\Σ}}x\[\frac{s+t}{2},k_1\])}^2+{(\underset{k_2=\min (s,t)}{\overset{\max (s,t)}{\Σ}}y\[k_2\])}^2},$

Wherein, pixel coordinate (i, s) refers to image from left side i-th, the s pixel from top.