CN105844584A - Method for correcting image distortion of fisheye lens - Google Patents

Abstract

The present invention provides a method for correcting the image distortion of a fisheye lens. According to the method, a main optical axis, the main light of a spatial object point, a virtual projection object plane, a first optical surface, a fisheye lens, an image plane, an i-th optical surface, an i+1-th optical surface and a final optical surface are adopted; the virtual projection object plane is perpendicular to the main optical axis of the fisheye lens; the image plane is the imaging plane of the fisheye lens and is perpendicular to the main optical axis; the main light of the spatial object point passes through the virtual projection object plane, the first optical surface of the fisheye lens, the i-th optical surface and the i+1-th optical surface, and finally arrives at the image plane, wherein the first optical surface is the first optical surface of the first lens of the fisheye lens, and the i-th optical surface and the i+1-th optical surface are the i-th optical surface and the i+1-th optical surface of the fisheye lens respectively; and the main light of the spatial object point passes through the virtual projection object plane and intersects on the virtual projection object plane. With the method adopted, the radial height relation of object images can be obtained, and the image distortion can be corrected through using the radial height relation. The method has the advantages of ideal correction effects, simplicity and clear principles, and can be well applied to many fields.

Description

The method of correction fisheye image distortion

Technical field

The present invention relates to fault image processing technology field, particularly relate to a kind of method correcting fisheye image distortion.

Background technology

In fields such as monitoring, military, medical intelligent navigations, having big the visual field even demand at ultra-large vision field angle, the conventional angle of visual field is Through not meeting the requirement in these fields now, the fish eye lens angle of visual field can reach 180 °, 270 ° even 320 °.But fish The image of eye camera shooting has the most serious distortion, if to utilize these to have the information of gross distortion image, Just the correction of these deformation patterns need to be expanded into the perspective projection image that people are accustomed to.The camera lens of different optical textures is suitable for not Same correction model, the most dissimilar fish eye lens selects the correction model being suitable for relatively difficult, and model is more complicated；Should With the method correction fish eye images distortion demarcated, need to formulate accurate scaling board and the inside and outside portion parameter to camera lens Yu camera Demarcating, process is relatively cumbersome.

Summary of the invention

The technical problem to be solved is to provide a kind of method correcting fisheye image distortion, and it can obtain image Radial height relation, utilizes this relation to be corrected fault image, and calibration result is preferable, and method is simple, and clear principle can It is applied to a lot of field very well.

The present invention solves above-mentioned technical problem by following technical proposals: a kind of side correcting fisheye image distortion Method, it is characterised in that it uses primary optical axis, the chief ray of dimensional target point, virtual projection object plane, first optical surface, fish Glasses head, image planes, i-th optical surface, i+1 optical surface and last optical surface, virtual projection object plane is vertical In fish-eye primary optical axis, image planes are fish-eye imaging surfaces, are perpendicular to primary optical axis, and the chief ray of dimensional target point is through void Intend projection object plane, fish-eye first optical surface, i-th optical surface, i+1 optical surface, finally reach picture Face, first optical surface is first optical surface of fish eye lens first lens, i-th optical surface, i+1 light Learn surface and be respectively fish-eye i-th optical surface and i+1 optical surface；The chief ray of dimensional target point is through virtual projection Object plane, meets on virtual projection object plane, and coordinate is P " and (x ", y "), dimensional target point is after panorama picture of fisheye lens, in image planes x ' o ' y ' Upper corresponding picture point P ' (x ', y ')；General tangential distortion is less than radial distortion to be obtained, and often can ignore tangential distortion to image Impact, the deformation that only research radial distortion brings to fish eye images, therefore, θ₁=θ₂；The chief ray trace utilizing dimensional target point obtains Take h_i=f (h₀) relation, wherein h_iFor picture point radial height O in image planes ' P ', h₀For picture point radial height O in image planes " P "；Profit Carry out Function Fitting by Fourier's sine series, then function of negating tries to achieve h₀=f^-1(h_i), then utilize this relation to carry out pixel seat Mark mapping solves, and image pixel point coordinates after being corrected reaches the purpose of correction, and i is natural number, represents ordinal number.

Preferably, in described virtual projection object plane, dimensional target point is subpoint P on virtual projection object plane " and (x ", y "), virtual In projection object plane, subpoint radial distance is the distance that target is asked for.

Preferably, the method for described correction fisheye image distortion utilizes dimensional target point P (x₀, y₀) the mode of chief ray trace Obtain image radially relation h_i=f (h₀)。

Preferably, the method for described correction fisheye image distortion utilizes Fourier sinusoidal after obtaining image radial height relation This relation curve of series approaching.

Preferably, the method for described correction fisheye image distortion utilizes function of negating to obtain after obtaining image radial height relation Take target radial height expression formula h₀=f^-1(h_i)。

Preferably, the method for described correction fisheye image distortion utilizes this relation h₀=f^-1(h_i) carry out the correction of pixel.

The most progressive effect of the present invention is: the present invention can obtain image radial height relation, utilizes this relation to distortion figure As being corrected, calibration result is preferable, and method is simple, and clear principle can be applied to a lot of field very well.The present invention utilizes master The mode of ray tracing obtains image radial height relation, thus carries out fisheye image distortion correction.The present invention utilizes key light The mode of line trace obtains virtual projection object plane and image radial height relation in image planes, utilizes Fourier's sine series matching with anti- The method of drilling tries to achieve target orthoscopic image pixel coordinate and fault image pixel coordinate corresponding relation, thus carries out distortion correction. Propose this concept of virtual projection object plane, be further converted to be projected on the object plane of virtual projection by the true spatial location of object Face；The relation of the radial height being so obtained with between virtual projection object plane and image planes；Then above-mentioned relation is utilized to obtain Obtain the corresponding relation between projection plane and image plane pixel coordinate point, then carry out distortion correction.The method has effectiveness, Within the specific limits, shooting projective invariant image can reach preferable calibration result to radial height error control, can promote fish Glasses head is in the application of the field of machine vision such as target recognition, the monitoring of big visual field.

Accompanying drawing explanation

Fig. 1 is the panorama picture of fisheye lens illustraton of model that the present invention corrects the method for fisheye image distortion.

Fig. 2 be the present invention correct fisheye image distortion method in chief ray through i-th with i+1 optical surface signal Figure.

Fig. 3 be the present invention correct fisheye image distortion method in chief ray through first optical surface schematic diagram.

Fig. 4 is that in the method correcting fisheye image distortion for the present invention, chief ray passes through last optical surface schematic diagram.

Fig. 5 is method target orthoscopic image pixel and the fault image pixel correcting fisheye image distortion for the present invention Coordinate correspondence schematic diagram.

Detailed description of the invention

Below in conjunction with the accompanying drawings and specific embodiment, it is further elucidated with the present invention, it should be understood that these embodiments are merely to illustrate the present invention Rather than restriction the scope of the present invention, after having read the present invention, those skilled in the art's shape various of equal value to the present invention The amendment of formula all falls within the application claims limited range.

As Figure 1-Figure 5, the present invention corrects method employing primary optical axis 1, the dimensional target point P (x of fisheye image distortion₀, y₀) chief ray 2,3, first optical surface 4 of virtual projection object plane, fish eye lens 5, image planes 6, i-th optical surface 8, I+1 optical surface 9, virtual projection object plane 3 is perpendicular to the primary optical axis 1 of fish eye lens 5, and image planes 6 are fish-eye one-tenth Image planes and be perpendicular to primary optical axis, dimensional target point P (x₀, y₀) chief ray 2 through 3, first optics of flake virtual projection object plane Surface 4, i-th optical surface 8, i+1 optical surface 9, finally reach image planes 6, and first optical surface 4 is flake First optical surface of camera lens first lens, i-th optical surface 8, i+1 optical surface 9 are respectively fish eye lens The i-th optical surface 8 and i+1 optical surface 9.Dimensional target point P (x₀, y₀) chief ray 2 through virtual projection face, hand over In virtual projection object plane 3 (i.e. x " o " y ") on, coordinate is P " (x ", y "), dimensional target point after panorama picture of fisheye lens, Upper corresponding picture point P of imaging plane x ' o ' y ' ' (x ', y ').General tangential distortion is less than radial distortion to be obtained, and often can ignore tangential The distortion impact on image, the deformation that only research radial distortion brings to fish eye images, θ₁Represent subpoint on virtual projection object plane Polar angle, θ₂Represent the angle of subpoint in image planes, therefore, θ₁=θ₂.Utilize dimensional target point P (x₀, y₀) chief ray 2 Trace obtains h_i=f (h₀) relation, wherein h_iFor picture point radial height O in image planes ' P ', h₀For picture point radial height in image planes O”P”.Utilize Fourier's sine series to carry out Function Fitting, then function of negating tries to achieve h₀=f^-1(h_i), then utilize this relation to enter Row pixel coordinate maps and solves.I is natural number.

The derivation that implement image pixel coordinate relation be presented herein below:

In fig. 2, chief ray M_i-1O_iO_i+1Hand over i-th face in O_i, i+1 face is in O_i+1；Light O_iO_i+1Reversely prolong Long line hands over optical axis in M_iPoint.Wherein C_iFor the center of curvature of i-th optical surface, D_iFor i-th face and axis of symmetry intersection point.O_iM_i It is ω with the angle of optical axis_i, optical axis rotates counterclockwise to O_iM_iAngle sign convention is just, otherwise is negative.I-th optical surface Angle of incidence and refraction angle are respectively α_iAnd β_i, normal when forwarding light counterclockwise to, angle block gauge is just set to, otherwise is negative.Optical system The radius r in i-th face in system_iRepresent, the center of curvature when the right side on optical surface summit, r_iJust it is defined as, otherwise is negative.

At the △ M shown in Fig. 2_iO_iC_iIn, such as following formula (1) and (2):

$\stackrel{\‾}{M_i{C}_{i+1}}=r_{i+1}+d_i-r_i+\frac{{\mathrm{sin\β}}_i}{{\mathrm{sin\ω}}_i}{r}_i---\left(1\right)$

${\mathrm{sin\α}}_{i+1}=\frac{\stackrel{\‾}{M_i{C}_{i+1}}}{r_{i+1}}{\mathrm{sin\ω}}_i---\left(2\right)$

Formula (1) is updated to formula (2), after abbreviation, i.e. can get the angle transmission equation of chief ray, such as following formula (3) and (4):

${\mathrm{sin\α}}_{i+1}=\frac{r_{i+1}+d_i-r_i}{r_{i+1}}{\mathrm{sin\ω}}_i+\frac{r}{r_{i+1}}{\mathrm{sin\β}}_i---\left(3\right)$

${\mathrm{\ω}}_i={\mathrm{\ω}}_{i-1}+{\mathrm{\β}}_i-{\mathrm{\α}}_i,{\mathrm{\β}}_i=arcsin\left(\frac{n_{i-1}{\mathrm{sin\α}}_i}{n_i}\right)---\left(4\right)$

Beat when first optical surface for chief ray, i.e. i=0, such as following formula (5):

$\stackrel{\‾}{M_{-1}{D}_0}=d_0,{\mathrm{sin\α}}_1=\frac{r_1+d_0}{r_1}{\mathrm{sin\ω}}_0---\left(5\right)$

From the beginning of first optical surface, application chief ray transmission equation expression formula (3)-(5) to the optical surface in fish eye lens system by Individual calculate, until obtaining the field angle of image ω of last optical surface_l, result can be obtained by ω_lWith ω₀、β_lWith ω₀Between Relation, such as following formula (6):

ω_l=f₁(ω₀), β₁=f₂(ω₀) (6)

If the distance on first optical surface summit of virtual object plan range is d₀, virtual object point P " distance optical axis radial position be h₀, As it is shown on figure 3, such as following formula (7):

h₀=(L_p(ω₀)+d₀)tanω₀ (7)

L_p(ω0)It is that to define the angle of visual field be ω₀Time chief ray original incident position, chief ray can be by light path mesoporous diaphragm The heart, general L_p(ω0)The process of reverse trace chief ray at aperture diaphragm can be applied to determine.

Fig. 4 represents that chief ray passes through the last optical surface of fish eye lens, and intersects at picture point P in image planes ', wherein d_lFor image distance, h_iFor image height, the radius of curvature of last optical surface is r_l, C_lIt is its center of curvature, D_lIt it is the intersection point of it and optical axis.At △ M_lO_lC_l In, just like following formula (8):

$M_l{C}_l=\frac{{\mathrm{sin\β}}_l}{{\mathrm{sin\ω}}_l}{r}_l---\left(8\right)$

The radial position h of picture point_iCalculation expression such as following formula (9):

$h_i={\mathrm{tan\ω}}_l(\frac{r_l{\mathrm{sin\β}}_l}{{\mathrm{sin\ω}}_l}-r_l+d_l)---\left(9\right)$

By expression formula (6), (7) and (9), it is possible to obtain the radial position h of picture point_iWith the radial position h of object point on virtual object plane₀Letter Number relational expression such as following formula (10):

h_i=f (h₀) (10)

Obtain the radial position h of above-mentioned picture point_iRadial position h with virtual object plane object point₀Functional relation (10) after, try to achieve it Inverse function be such as following formula (11):

h₀=f^-1(h_i) (11)

Thus restore true object point on virtual object plane radial distribution.In FIG, after limited far plane image objects, anti- Drill image plane x ' the upper a certain imaging point P ' of o ' y ' (x ', y '), first rectangular coordinate is converted to polar coordinate, such as following formula (12):

$h_i=\sqrt{x^{\′2}+y^{\′2}},{\mathrm{\θ}}_2=arctan(y^{\′}/x^{\′})---\left(12\right)$

Obtained corresponding virtual object point P by expression formula (11) " at virtual object plane x " o " y " radial coordinate h₀, its rectangular coordinate projection coordinate P " and (x ", y ") it is such as following formula (13):

$x^{\′\′}=h_0{\mathrm{sin\θ}}_2=\frac{h_0{x}^{\′}}{\sqrt{x^{\′2}+y^{\′2}}},y^{\′\′}=h_0{\mathrm{cos\θ}}_2=\frac{h_0{y}^{\′}}{\sqrt{x^{\′2}+y^{\′2}}}---\left(13\right)$

Coordinate points on virtual object plane is the Target Acquisition point of correction chart picture, coordinate points P ' (x ', y ') and P " (x ", y ") correspondence distortion respectively The value of image slices vegetarian refreshments after image and correction.P after correction " value of (x ", y ") pixel be mapped to by expression formula (13) the most right The pixel P ' that answers (x ', y ') assignment, it is achieved the filling of correction image pixel.

In Figure 5, the inverse process of distortion process is exactly pixel trimming process, the P after correction " value of (x ", y ") pixel passes through Expression formula (13) is mapped to corresponding pixel P ' (x ', y ') assignment, it is achieved the filling of correction image pixel.Between radial height Functional relationship be the emphasis studied herein all the time.Purpose is exactly to find the radial position h of picture point_iRadial direction with virtual object plane object point Position h₀Functional relationship, h_i=f (h₀), spy can be obtained by numerical fitting, and wherein numerical fitting needs according to picture point Radial position h_iRadial position h with virtual object plane object point₀Functional relationship, h_i=f (h₀), depending on the distribution situation of image curve, Its purpose reduces error exactly.

In described virtual projection object plane, object point P (x₀,y₀) some P in the above " (x ", y "), its radial distance is that target is asked for Distance.

The method of described correction fisheye image distortion utilizes the mode of chief ray trace to obtain image radially relation h_i=f (h₀)。

The method of described correction fisheye image distortion obtains image radial height relation h_i=f (h₀Utilize Fourier just after) String series approaching.

The method of described correction fisheye image distortion obtains h after image radial height relation_i=f (h₀) utilize function of negating Obtain target radial height expression formula h₀=f^-1(h_i)。

The method of described correction fisheye image distortion utilizes the correction that this relation carries out pixel.

The method of the correction fisheye image distortion of the present invention solves to obtain important information part from flake fault image, by abnormal Become partial correction to become to meet the image of eye-observation.Reducing the algorithm complex of correction to greatest extent, the open one of the present invention utilizes The mode of chief ray trace obtains virtual projection object plane and image radial height relation in image planes, and method is simple, it is only necessary to each light Learn the distance between the radius on surface, optical element and these parameters of refractive index of object distance image distance and each optical element, profit Obtain image radial height relation curve by the mode of chief ray trace, utilize Fourier's sine series matching to try to achieve with inversion method Target orthoscopic image pixel coordinate and fault image pixel coordinate corresponding relation, thus carry out distortion correction.The method has Having effectiveness, within the specific limits, shooting projective invariant image can reach preferable calibration result to radial height error control. Can promote that fish eye lens is in the application of the field of machine vision such as target recognition, the monitoring of big visual field.The present invention can obtain image radially Height relationships, utilizes this relation to be corrected fault image, and calibration result is preferable, and method is simple, and clear principle can be fine It is applied to a lot of field.The present invention is directed to the problem and shortage that prior art exists, solution obtains important from flake fault image Message part, becomes to meet the image of eye-observation by distortion partial correction.Reduce the algorithm complex of correction to greatest extent, this Bright open one utilizes dimensional target point P (x₀,y₀) dimensional target point P (x₀,y₀) the mode of chief ray trace obtain virtual projection thing Face and image radial height relation in image planes, utilize Fourier's sine series matching and inversion method to try to achieve target orthoscopic image picture Vegetarian refreshments coordinate and fault image pixel coordinate corresponding relation, thus carry out distortion correction, method is simple, it is only necessary to each optics Distance between the radius on surface, optical element and these parameters of refractive index of object distance image distance and each optical element, utilize Dimensional target point P (x₀,y₀) chief ray trace just can obtain image radial height relation, good calibration result can be obtained.Existing The image of problem mainly fish eye lens video camera shooting has the most serious distortion, if to utilize these to have gross distortion The information of image, just need to expand into, by the correction of these deformation patterns, the perspective projection image that people are accustomed to.Different optical textures Camera lens is suitable for different correction models, and the most dissimilar fish eye lens selects the correction model being suitable for relatively difficult, mould Type is more complicated, the method correction fish eye images distortion that application is demarcated, and needs to formulate accurate scaling board and to camera lens and camera Inside and outside portion parameter is demarcated, and process is relatively cumbersome.

Those skilled in the art can carry out various remodeling and change to the present invention.Therefore, present invention covers fall into appended Various remodeling in the range of claims and equivalent thereof and change.

Claims (6)

1. the method correcting fisheye image distortion, it is characterized in that, it uses primary optical axis, the chief ray of dimensional target point, virtual projection object plane, first optical surface, fish eye lens, image planes, i-th optical surface, i+1 optical surface and last optical surface, virtual projection object plane is perpendicular to fish-eye primary optical axis, image planes are fish-eye imaging surfaces, it is perpendicular to primary optical axis, the chief ray of dimensional target point is through virtual projection object plane, fish-eye first optical surface, i-th optical surface, i+1 optical surface, finally reach image planes, first optical surface is first optical surface of fish eye lens first lens, i-th optical surface, i+1 optical surface is respectively fish-eye i-th optical surface and i+1 optical surface；The chief ray of dimensional target point, through virtual projection object plane, meets on virtual projection object plane, and coordinate is P ' ' (x ' ', y ' '), and dimensional target point is after panorama picture of fisheye lens, in image planes x ' upper corresponding picture point P of o ' y ' ' (x ', y ')；General tangential distortion is less than radial distortion to be obtained, and often can ignore the tangential distortion impact on image, only study the deformation that radial distortion brings to fish eye images, therefore, θ₁=θ₂；The chief ray trace utilizing dimensional target point obtains h_i =f (h₀) relation, wherein h_iFor picture point radial height O in image planes ' P ', h₀For picture point radial height O in image planes ' ' P ' '；Utilize Fourier's sine series to carry out Function Fitting, then function of negating tries to achieve h₀ =f^-1(h_i), then utilize this relation to carry out the mapping of pixel coordinate and solve, image pixel point coordinates after being corrected, reach the purpose of correction, i is natural number, represents ordinal number.

The method of correction fisheye image the most according to claim 1 distortion, it is characterized in that, in described virtual projection object plane, dimensional target point on virtual projection object plane subpoint P ' ' (x ' ', y ' '), on virtual projection object plane, subpoint radial distance is the distance that target is asked for.

The method of correction fisheye image the most according to claim 1 distortion, it is characterised in that the method for described correction fisheye image distortion utilizes the mode of the chief ray trace of dimensional target point to obtain image radially relation h_i =f (h₀)。

The method of correction fisheye image the most according to claim 1 distortion, it is characterised in that the method for described correction fisheye image distortion utilizes Fourier's this relation curve of sine series matching after obtaining image radial height relation.

The method of correction fisheye image the most according to claim 1 distortion, it is characterised in that the method for described correction fisheye image distortion utilizes function of negating to obtain target radial height expression formula h after obtaining image radial height relation₀ =f^-1(h_i)。

The method of correction fisheye image the most according to claim 1 distortion, it is characterised in that the method for described correction fisheye image distortion utilizes this relation h₀ =f^-1(h_i) carry out the correction of pixel.