Summary of the invention
The technical problem to be solved in the present invention provides a kind of Intelligentized method that generates high-definition full views based on soft-shelled turtle eye or drum shaft images automatically, fast, it is simple and easy to use, can be automatically, amalgamation generates the high-quality panoramic picture fast, the panorama that can either solve 3 and 3 above soft-shelled turtle eye pattern pictures generates problem, the panorama that can solve 4 and 4 above drum shaft images again generates problem, and finish automatically to the whole process that generates panoramic picture from importing original image, do not need manual intervention.
For solving the problems of the technologies described above, of the present inventionly generate the Intelligentized method of high-definition full views fast based on soft-shelled turtle eye or drum shaft images, comprise the steps:
At first, regional according to soft-shelled turtle eye or drum shaft images at the optimum envelope circle that boundary brightness variation relation calculates them;
Above-mentioned optimum envelope circle region projection is transformed to a specific spherical interior surface;
Then, utilization feature point extraction algorithm carries out feature point extraction to above-mentioned spherical interior surface, and utilization Feature Points Matching algorithm, and the Optimum Matching unique point that calculates adjacent spherical interior surface is right;
Set up the complete space model, the utilization iterative algorithm is calculated model parameter based on above-mentioned Optimum Matching unique point;
At last, based on above-mentioned model and parameter thereof, amalgamation generates panoramic picture.
The present invention's beneficial effect compared with prior art is:
Amalgamation algorithm of the present invention is not subjected to the photographic images numerical limitations, as long as satisfy certain photographing request during user's photographic images, can use the present invention to carry out amalgamation, and the automatic amalgamation algorithm of present fish eye images can only solve the automatic amalgamation problem of two and three soft-shelled turtle eye pattern pictures.
The present invention can solve the automatic amalgamation problem of soft-shelled turtle eye pattern picture and drum shaft images simultaneously, has very strong universality.
Amalgamation process automation degree height of the present invention, the user only need import original image, can generate panorama sketch automatically.
The present invention decreases to the requirement of image taking, during photographic images, only needs adjacent image to have certain coincidence zone to get final product, and the angle between adjacent camera lens is axial does not need to equate that therefore the requirement to pan and tilt head also decreases.
Amalgamation speed of the present invention is fast, and at AMD Athlon (tm) XP 2800+, on the loom of 1.024G internal memory, 6 resolution of amalgamation are that 3072 * 2048 drum shaft images are panoramic picture, and whole amalgamation process is no more than 2 minutes.
The present invention can generate the high-definition full views image.With fov is that 183 two soft-shelled turtle eye patterns of fish eye lens gained of spending are made comparisons as four sheets of drum shaft images amalgamations among amalgamation and the present invention, it is that 3000 * 6000 panoramas generate figure for generating resolution that its digital camera ccd resolution all is 3072 * 2048., the former effect is obviously not as the latter, this is because about 1/2 zone is that 3000 * 3000 pixels are to calculate from about 50% * 3072 * 2048 pixel interpolation in the panorama sketch that the former generates, and the latter about 1/3 zone is 3000 * 2000th, calculates from about 90% * 3072 * 2048 pixel interpolation.This shows that the latter's clear effect will be apparently higher than the former.In addition, because camera lens is for the non-linear distortion influence of light, the closer to the part at center, it is more little distort, the present invention can amalgamation the characteristic of many images arbitrarily, undoubtedly to the amalgamation effect generation positive impact of panoramic picture.
The user only need be when taking, by shooting tripod head, guarantee to be in same plane substantially at the axial place straight line of different shooting direction camera lenses, the center of camera lens is substantially in same point, captured adjacent image has certain coincidence zone simultaneously, promptly can use the panoramic picture that this method generates high definition fast.
Embodiment
The present invention is further detailed explanation below in conjunction with accompanying drawing.
Concrete set forth of the present invention generate the Intelligentized method of high-definition full views fast based on soft-shelled turtle eye or drum shaft images before, earlier the specific requirement of taking is described.Concerning most of full shots, need four kinds of hardware devices: fish eye lens (sigma camera lens or full frame camera lens), digital camera, special-purpose pan-shot The Cloud Terrace, the tripod of support cameras, the framework relation between them is as shown in Figure 2.The shooting condition that method of the present invention need satisfy mainly contains 3 points:
1, in different shootings constantly, the center of camera lens is substantially in same point.
2, in different shootings constantly, the axial place straight line of camera lens is similar on the same plane, the value of pitching and rotation less (referring to Fig. 3).
3, between the shooting gained adjacent image certain coincidence zone is arranged, and every width of cloth image is adjacent with two width of cloth images front and back.Above-mentioned coincidence zone has guaranteed that the adjacent spherical interior surface of its correspondence has certain coincidence zone each other.
More than 3 shooting conditions, under the assistance of special-purpose pan-shot The Cloud Terrace, be easy to accomplish.
Panorama image generation method based on soft-shelled turtle eye or drum shaft images of the present invention, mainly by the image pre-service, original image is to spherical coordinate transformation, adjacent image feature point extraction and coupling, set up the complete space model, determine model parameter, generate five parts of panoramic picture and form.Wherein, the image preprocessing part changes according to the brightness at four angles, image place and to detect its optimum envelope circle zone automatically.Original image by a given assumed condition, is derived the transformation equation of original image to spherical co-ordinate to the spherical coordinate transformation part, and uses this equation spot projection that optimum envelope circle zone is interior to the spherical interior surface of correspondence.Adjacent image feature point extraction and compatible portion at first use the feature point extraction algorithm that spherical interior surface is carried out feature point extraction, these unique points are tentatively mated again, and use the spherical interior surface characteristic then, calculate Optimum Matching unique point pair set.Set up spatial model, at first suppose the All Around The World space is at first projected on the sphere, point when looking each original image and be camera lens and axially being in the three dimensions diverse location on this sphere is by the projection of camera lens refraction back on ccd, each is opened original image and comprises effective visual angle, rotation, wave, pitching, camera lens nonlinear distortion zoom factor and radially shine upon six-freedom degree, it is a complete in theory model, its effective visual angle of wherein identical camera lens, zoom factor with radially shine upon identical, the thinking of determining this model parameter is based on Optimum Matching unique point pair set, foundation draws optimum hybrid parameter about the optimization equation of all unknown parameters.Generate the panoramic picture part, at first the optimum envelope of every original image is justified region projection to same sphere, adopt edge joint position image smoothing transitional technology again, intersection is sewed and mend, generate the spherical model panorama.To be described in detail respectively above-mentioned five parts below.
The image pre-service
The image of external fish eye lens and sigma lens shooting is respectively soft-shelled turtle eye pattern picture (CircularFisheye Image) and drum shaft images (Drum Fisheye Image) (in conjunction with Fig. 4).Wherein, all in circular curve, circular curve is the border circle 401 of this drum shaft images and soft-shelled turtle eye pattern picture to the imaging region of image, and circular curve is called optimum envelope circle zone with inner region.As seen from the figure, the border circle is a black with the color of exterior domain, and brightness is near 0, and the brightness of image value of border circle inner region is generally all much larger than 0.Wherein, change the most violent with near the colour brightness value the circle of border.Set by the comparatively violent point of brightness value variation in the detected image utilizes the principle of least square that it is carried out the circular curve match, can the border circle of fish eye images be positioned, thereby realizes the automatic search that the fish eye images border is round.Among the present invention, for identical camera lens gained picture, its optimum envelope circle is set identical radius, this is because when panning picture, because the focal length of camera is locked, the maximum gauge of imaging surface is by inherent characteristics such as the fov decision of camera lens, therefore, same camera lens gained picture, its optimum envelope circle should have identical diameter in theory.
Original image is to spherical coordinate transformation
Arrive spherical interior surface transformation of coordinates equation for the optimum envelope circle zone of deriving original image, at first, fish-eye equidistant model is analyzed, Fig. 5 is desirable equidistant model synoptic diagram.Light l
1By fish eye lens center 504, project to A point on the plane 501, ccd place after the refraction, l
2Project to B point on the plane 501, ccd place.Obviously A point and B point are respectively light l in the whole space
1With light l
2With the intersection point on plane, ccd place 501, then on the imaging surface 502 every bit corresponding to each the bar incident ray in the real world.With optical center 504 is that the centre of sphere is done a Spherical Surface S and these all ray intersections get spherical interior surface 506, can think that imaging surface 502 reflects the projection of back on plane, ccd place 501 for all luminous points on the spherical interior surface 506 through camera lens.Wherein, the projection of sphere centre P on plane, ccd place 501 is the center 505 of imaging surface 502.If this sphere meets the following conditions:
I) spherical interior surface 506 and the maximal value D of the Plane intersects gained length of curve of the centre of sphere (optical center) 504 excessively
MaxEqual the radius of circle R of imaging surface 502
CTwice.
By sphere formula D as can be known
Max=R
Sφ
Max(1)
Here R
SBe the radius of a ball of spherical interior surface 506, φ
MaxBe maximum subtended angle, in order to narrate conveniently note φ
MaxBe maximum visual angle, it corresponding to spherical interior surface 506 on the maximal value of any two incident ray angles.
By condition i) as can be known: R
Sφ
Max=2R
C(2)
Know by fish eye lens head model principle again: for any incident ray l, if it equate with the angle theta of camera lens axial 503, so it with the intersection point A on plane, ccd place 501 to the equating of the center 505 of imaging surface 502 apart from QA, and
QA=cθ (3)
Wherein, c is a constant.Formula (3) shows that imaging surface 502 is disc, and along radially being linear.
Can draw following important conclusion 1 thus: for any 1 Q on the spherical interior surface 506, its projection A on the flake picture equals Q point and the minimal path of P point on sphere to the length d at the center 505 of imaging surface 502
In addition, by formula (1), (2), (3) and explanation thereof as can be known,
c=2R
C/φ
max=R
S (4)
It is the center with 504 of optical centers that the above-mentioned Spherical Surface S of this explanation is one, and c is the sphere of radius.
Based on conclusion 1, can release conclusion 2:
The radius of a ball be arbitrfary point on the spherical interior surface 506 of c (
, θ) to the imaging surface 502 some polar coordinates (ρ, α) corresponding relation between is as follows:
Formula (5) is further analyzed as can be known, and when c be during arbitrarily greater than 0 constant, formula (5) has been set up the spherical interior surface and the round regional mapping relations of optimum envelope of any radius size.
Utilization formula (5) can be mapped to whole optimum envelope circle zone on the sphere that radius is c, also the regional area or the discrete point set in optimum envelope circle zone can be mapped on the sphere that radius is c, simultaneously, also can use the reverse-power of (5) formula is the sphere of c with radius, or the discrete point set on sphere regional area or the sphere is mapped to two dimensional surface.
Adjacent image feature point extraction and coupling
Comparative maturity has a Harris angle detection algorithm etc. in the conventional images feature point extraction algorithm, use them can extract unique point in the image preferably, go out adjacent matching characteristic point pair set M based on the proper vector of unique point or the correlativity rough matching between the unique point then, it has characterized the set based on the most similar point of certain tolerance of feature among two width of cloth figure.Know axially coplane basically of the pairing camera lens of adjacent spherical interior surface by 3 conditions of shooting of the presently claimed invention, promptly the axial 503 place straight lines of the camera lens among Fig. 5 and intersect at same point on same plane.
Reach a conclusion 3 thus: if a certain unique point is to M=((X
1, Y
1), (X
2, Y
2)) be the same point in the space, then its corresponding spherical coordinates (
, θ) in,
Substantially equal, promptly have: X
1≈ X
2, the difference of θ value with they the corresponding center angle between vowing be directly proportional i.e.: Y
1-Y
2≈ k (yaw1-yaw2)+b.
Utilization conclusion 3 can draw Optimum Matching unique point pair set R in theory from M, the unique point that they have characterized adjacent image is identical point in real space.Consider that it waves for each width of cloth image, pitching the unknown, different images its wave, the pitching difference, and the present invention is not strict to the requirement of waving, the difference of waving corresponding between promptly per two width of cloth figure may be inequality.But because the point that two width of cloth figure overlap in the zone has the identical alternate position spike opposite sex, therefore can consider from M, to select at random a unique point right, alternate position spike between calculating at 2, again all unique points are compared carry out otherness based on this alternate position spike, it is right to write down all unique points that satisfy condition, and must gather R '.After repeatedly selecting at random, the R ' that the unique point number is maximum is Optimum Matching unique point pair set R.
The specific implementation step is as follows:
(a) alternate position spike of calculated characteristics point pair set M
For arbitrary characteristics point to M
i=((X
1i, Y
1i), (X
2i, X
2i)), 1≤i≤I, I gather the unique point of M to sum, and its alternate position spike is: Δ
i=(Δ X
i, Δ Y
i)=(X
1i-X
2i, Y
1i-Y
2i);
(b) putting loop variable i initial value is 0, and its maximum cycle value is N, and N is greater than 0, less than the right sum of unique point, and setpoint distance threshold values e, it is used for judging whether the otherness of two unique points is consistent, sets Optimum Matching unique point pair set R=Φ;
(c) it is right to choose the j unique point arbitrarily from M, calculates and corresponding Δ of M and Δ
jApart from d, pairing unique point pair set is R ' during note d<e, i.e. R '={ M
k|| | Δ
k-Δ
j||<e, 1≤k≤I};
(d) if the unique point of R ' to sum greater than the unique point of R to sum, then put R=R ';
(e) put i=i+1, if i>N then withdraws from circulation, this moment, R was the Optimum Matching unique point pair set of being asked, otherwise, return step (c).
The present invention uses above-mentioned adjacent image feature point extraction and matching algorithm, directly soft-shelled turtle eye or the corresponding spherical interior surface of drum shaft images is carried out feature point extraction and mates, and can find the Optimum Matching unique point of adjacent image right very exactly.
Spherical interior surface position joining relation each other can be learnt or can be discerned by human eye by photographic sequence among the present invention, and this mutual relationship is by write-in program in advance or can input when the coupling.
Above-mentioned adjacent image feature point extraction and matching algorithm include, but are not limited to the part to the pairing spherical interior surface of adjacent image, perhaps change the gained spherical interior surface from the local optimum envelope regional utilization formula of circle (5) and carry out feature point extraction and coupling.
Set up the complete space model, determine model parameter
By the above as can be known, under the equidistant model prerequisite of ideal, spherical interior surface 506 is to be the centre of sphere with optical center 504 among Fig. 5, and radius is the part of the Spherical Surface S of c.Any original image, with formula (5) its optimum envelope is justified region projection to S, this shows that the camera lens axial 503 of all original image correspondences all is transferred to the same position of spherical interior surface 506 in this conversion process, and this conversion has guaranteed that all spherical interior surfaces are on same sphere.Know by photographing request, that takes is constantly different, the center of camera lens is in same point, therefore as long as photographic images is sorted according to taking constantly, with a certain the pairing spherical interior surface of image as benchmark, identical operations positioned when the pairing spherical interior surface of residual image was taken according to original image, and promptly available these spherical interior surfaces are combined into whole space.Unknown quantitys all in this position fixing process is carried out parametrization, then formed the parameter space of whole model.Fig. 3 has shown 3 kinds of rotation parameters of every flake picture, effectively the inherent characteristic of camera lens is not only depended at the visual angle, more depend on the selection of optimum envelope circle, among the present invention, effectively the visual angle is with respect to optimum envelope radius of circle, the angle of two pairing incident raies of end points of certain bar diameter is effective visual angle in the optimum envelope circle, so it also needs by parametrization.In addition, because real lens does not satisfy desirable equidistant model, there is non-linear twisted phenomena, can be similar to this nonlinear relationship: r=α * sin (β θ) with following formula, wherein r is the distance that point-of-interest arrives the regional center of circle of optimum envelope circle, θ be camera lens axially with from the optical center point to this point-of-interest actual scenery the angle of institute's corresponding point line, α is a zoom factor, thereby realize the mapping one by one of putting on actual scene and soft-shelled turtle eye or the drum shaft images plane, β is mapping parameters radially.Consider the physical characteristics of camera lens, promptly identical camera lens, therefore during shooting, its focal length is locked, is definite value, and they are consistent to the ray refraction characteristic, then sets identical fov, α and β value for identical camera lens.Therefore, the parameter of model parameter SPACE V adds up to an integer in 3 * (N+1) to 5 * N.The principal feature of the complete space model that the present invention sets up is N the corresponding spherical interior surface of sample image, it overlaps area part by scaling (fov variation), rotation is waved, the position consistency after five kinds of variations of pitching, nonlinearities change (adjusting α and β) in the space.
Because what Optimum Matching unique point pair set R characterized is to be identical point in luv space after they pass through above-mentioned five kinds of variations respectively, its distance error quadratic sum E should equal 0 in theory.Based on this principle, definite process of model parameter is adjusted unknown parameter exactly, makes the process of E convergence 0, promptly
The adjustment model V parameter makes Optimum Matching unique point pair set
Range difference reaches minimum with E after the conversion of process V parameter.R wherein
iBe that i opens soft-shelled turtle eye or drum shaft images and the Optimum Matching unique point of an adjacent image is right thereafter, F
IkBe the k unique point of last secondary figure, B
IkBe the unique point of the back secondary figure of correspondence, N is total number of soft-shelled turtle eye or drum shaft images, K
iBe R
iElement number.Definite process of this model parameter promptly
Optimization problem, it comes down to a non-linear least square problem.Wherein, f
i(, V) and g
i(, V) be the variation function that acts on the adjacent back width of cloth figure of i figure respectively with it.
The above-mentioned non-linear least square problem of utilization Levenberg-Marquardt algorithm optimization among the present invention.What the iteration parameter initial value was chosen is analyzed as follows: known that by shooting condition under the assistance of the special-purpose The Cloud Terrace of panorama, every pairing rotation of image, pitching are all less, their initial value all can be set at 0 or approach a decimal of 0.In addition, can suppose that a certain width of cloth figure wherein is a reference map, the initial value that waves of its correspondence is 0.By Y in the conclusion 3 noted earlier
1-Y
2≈ k (yaw1-yaw2)+b, the difference of waving between the adjacent image can be by unique point to calculating, and therefore, the setting step of waving initial value is as follows:
(1), calculates the difference of yaw between per two adjacent figure by Optimum Matching unique point pair set R
Wherein: j=1, Λ, N, Y
JiBe i unique point of j width of cloth figure corresponding to reference map, when j<N, Y
J+1, iFor i unique point of corresponding j+1 width of cloth figure, when j=N, Y
J+1, iI unique point for corresponding reference map.
(2) the k width of cloth figure yaw initial value behind the reference map is
In iterative process, the present invention considers the error that the feature point extraction matching algorithm exists on feature point extraction and coupling, cause to exist unique point right among the Optimum Matching unique point pair set R, by on its its corresponding theory real change function f (, V) and g (, V) after the effect, there is bigger error in the position in the space.Therefore, the present invention checks all matching characteristic points to the margin of error after changing by introduce a threshold values σ in iterative process, and characteristic of correspondence point is to deleting from R during greater than σ with the margin of error, and the continuation iterative process is up to optimum.By this method matching characteristic point that filter error is bigger preferably.
Generate panoramic picture
In case model parameter is determined, just conversion can be carried out in the optimum envelope circle zone of every soft-shelled turtle eye or drum shaft images, and it is projected to the relevant position of same sphere, carries out colour mixture to overlapping the zone then, generates panoramic picture.The step that the single image conversion is projected to sphere is:
(1) for soft-shelled turtle eye or drum shaft images arbitrarily, based on the corresponding rotation in the model parameter, wave, three its rotation matrixs of calculation of parameter of pitching M;
(2) with the inverse matrix premultiplication Spherical Surface S of rotation matrix M, be about to the pairing position, segment projecting plane that Spherical Surface S rotates to this soft-shelled turtle eye or drum shaft images;
(3) above-mentioned Spherical Surface S is rotated around the x axle again
(4) size of the z coordinate figure of this Spherical Surface S and cos (fov/2) relatively keeps the sphere of z>cos (fov/2), and this sphere is the expansion sphere in the optimum envelope circle zone of this soft-shelled turtle eye or drum shaft images.
All original images are repeated above step, their projections are positioned on the sphere, carry out colour mixture, make its brightness and color transition steadily can obtain panoramic picture for the zone that overlaps.
More than generate the panoramic picture process, comprise above all or part step is repeated in the optimum envelope circle zone of every width of cloth soft-shelled turtle eye or drum shaft images, with the stretch-out view of the round zone of the optimum envelope that obtains every width of cloth soft-shelled turtle eye or drum shaft images on same ball plane, and carry out amalgamation.
Automatically the Intelligentized method that generates high-definition full views based on soft-shelled turtle eye or drum shaft images of the present invention, it realizes process flow diagram as shown in Figure 6, in order to set forth implementation method of the present invention and main points better, describe as follows below in conjunction with a specific embodiment:
With 4 sheets of drum shaft images amalgamations is example.At first utilization is taken equipment and is obtained drum shaft images, fix tripod before the shooting earlier, load onto The Cloud Terrace (preferably using special-purpose pan and tilt head), regulate the The Cloud Terrace plane, the digital camera that the sigma camera lens is housed is fixed on the The Cloud Terrace to horizontal level in order to guarantee to take precision.During shooting, note not mobile tripod.After having clapped the image of a direction, with the The Cloud Terrace rotating certain angle, make another direction of axially facing of camera lens, take next, will notice that the angle of rotating must be less than the horizontal fov of camera lens this moment, to satisfy certain coincidence zone is arranged between the adjacent image, repeat aforesaid way and take and make the summation of all images comprise level 360 degree spatial informations to get final product.For example horizontal fov is the sigma camera lens of 120 degree, takes 4 sheets of drum shaft images and can satisfy above-mentioned condition.The characteristics of drum shaft images see among Fig. 1 that (b) schemes among (b) figure and Fig. 4, and its picture size is 3072*2048.Its feature is that imaging region is the center of circle with the ccd plate center, is the circle of diameter and the common factor of ccd egative film with the longest edge, thereby makes imaging region look like cydariform.In above-mentioned 4 width of cloth drum shaft images loading routines, the optimum envelope circle of utilization image pre-treatment step 601 searching images.Original image by on optimum envelope circle region projection to a spherical interior surface of formula (5) with above-mentioned 4 width of cloth drum shaft images, wherein, is got c=2R to spherical co-ordinate switch process 602 in the present embodiment
C/ π.Obviously, the centre of sphere of four spherical interior surfaces of above-mentioned conversion gained is identical in three dimensions to spherical interior surface center gained direction vector.The pairing camera lens of its original image axially then at same surface level, has certain included angle each other, is setting up the complete space model, is determining in the model parameter step 604, will consider this angle difference value when the variable of choosing iterative algorithm waves initial value.Have two kinds of methods can obtain above-mentioned difference value, method one is, the angle of The Cloud Terrace rotation during records photographing, and general The Cloud Terrace all has this function, with above-mentioned record value loading routine, when perhaps taking, rotates identical angle, then Δ yaw during amalgamation
j=2 π/N, N are the total number of sample image.Method two is to obtain by adjacent image feature point extraction and the unique point in the coupling step 603.Adjacent image feature point extraction and adjacent image feature point extraction use the feature point extraction algorithm to extract the unique point of above-mentioned spherical interior surface with coupling step 603, and the positional information and the proper vector of these unique points go on record.Based on the unique point that proper vector can tentatively be mated adjacent spherical interior surface, its matching characteristic point is to having shown that just proper vector is nearest with Euclidean distance tolerance in the adjacent spherical interior surface.Inherent characteristic when therefore also needing with the positional information of unique point and shooting to above-mentioned matching characteristic point to selecting.In the present embodiment, setpoint distance threshold values e=5 can obtain Optimum Matching unique point pair set R relatively accurately.In addition, consider and set up the complete space model, determine in the model parameter step 604 to calculate and wave initial value and will use R, and set up the complete space model, determine to set up in the model parameter step 604 this intermediate steps of complete space model and can not influence R.Therefore directly in adjacent image feature point extraction and coupling step 603, calculate the difference of waving
Wherein, k=π/fov
0, fov
0Be the initial value of fov, in a single day the b=pi/2 setting up the complete space model, determining to have determined reference map in the model parameter step 604, waves initial value and can determine.Set up the complete space model, determine that model parameter step 604 takes into account all possible variable, the line parameterization of going forward side by side, structure complete space model.In the present embodiment, all four images all are to obtain with same camera lens, therefore, the pairing effective visual angle of each spherical interior surface (fov) and nonlinear distortion relation is identical, and total number of model parameter V is 3 * (N+1) individual, in addition, first width of cloth figure that present embodiment is selected when taking is a reference map, thereby calculate the initial value that waves of four width of cloth images, and pitching, the rotation initial value of setting them all be 0, be used to delete threshold values σ=0.05 of possible errors unique point in the selected iterative algorithm.Generally speaking, above-mentioned iterative process iteration can obtain satisfied result about 10 times.Generating panoramic picture step 605 at first changes all above-mentioned spherical interior surfaces based on above-mentioned model and parameter thereof and projects on the same sphere, perhaps the optimum envelope of all soft-shelled turtle eyes or drum shaft images is justified region projection to same sphere, and they are carried out colour mixture generation final image.