CN101923729A - Reconstruction method of three-dimensional shape of lunar surface based on single gray level image - Google Patents

Reconstruction method of three-dimensional shape of lunar surface based on single gray level image Download PDF

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CN101923729A
CN101923729A CN 201010262508 CN201010262508A CN101923729A CN 101923729 A CN101923729 A CN 101923729A CN 201010262508 CN201010262508 CN 201010262508 CN 201010262508 A CN201010262508 A CN 201010262508A CN 101923729 A CN101923729 A CN 101923729A
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CN101923729B (en
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李建胜
徐青
陈杰
郝向阳
蓝朝桢
周杨
孙伟
邢帅
西勤
何钰
卢战伟
王同合
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PLA Information Engineering University
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Abstract

The invention relates to a reconstruction method of a three-dimensional shape of a lunar surface based on a single gray level image, belonging to the technical field of computer simulation. The method comprises the following steps: firstly, extracting the gray level value information of each pixel point in the single gray level image of the lunar surface, and finding out the pixel point with the maximum gray level value; dividing the maximum gray level value by the gray level value of each pixel point in the image to acquire the cosine of the inclination angle of each pixel point; carrying out an approximate spherical hypothesis on the lunar surface to acquire the cosine of the deflection angle of each pixel point; computing the inclination angle and the deflection angle of each pixel point, then computing the surface normal vector of each pixel point, and converting the surface normal vector into the height coordinate value of each pixel point; carrying out filtering treatment; and reconstructing the three-dimensional shape of the lunar surface by utilizing the OpenGL technology according to each acquired surface normal vector and each acquired height coordinate value. The method of the invention can reduce the requirements for implementation of three-dimensional surface restoration, improve the speed and the efficiency of restoration and simplify the steps of restoration; and by using the method for carrying out treatment, the three-dimensional shape of the lunar surface can be more accurately reconstructed.

Description

Menology reconstruction method of three-dimensional shape based on individual gray level image
Technical field
The present invention relates to menology reconstruction method of three-dimensional shape, belong to the computer simulation technique field based on individual gray level image.
Background technology
By menology 3D shape that the lunar map picture of taking is analyzed and researched is one of fundamental research of moon exploration.In the various countries' lunar exploration engineering that comprises China's " Chang'e I " and in the works, the research of menology dimensional topography is in critical positions all the time.Remain a kind of important menology dimensional topography analytical approach at present by image reconstruction menology 3D shape.Six kinds of contained measurements of the LRO of the U.S.'s in October, 2008 emission have two kinds in order to measure moon landform in equipping, and one of them takes the lunar map picture exactly.As far back as nineteen fifty-one, just find that menology has the characteristic of approximate lambert's body (Lambertian) reflection model before the human moonfall.The domestic nearest moon 3D shape restoration methods that has proposed based on binocular stereo vision, but there are two width of cloth image registration problems in the binocular stereo vision method.The single width gray level image light and shade that the seventies in 20th century, Horn proposed is recovered 3D shape, and (Shape-from-Shading, SFS) method obtains many scholars' attention.The principle of SFS algorithm is to calculate the intensity of reflected light of respective point on the three-dimensional object surface according to each point gray-scale value on the image, and by the analysis of physics and geometrical optics as can be known, the geometric configuration of catoptrical intensity and body surface character and body surface has relation.In order to eliminate the pathosis of problem, typical SFS algorithm has minimization algorithm, finite element algorithm, neural network algorithm and viscosity to separate theory etc., yet the ubiquitous problem of algorithm has following two at present: the one, and the reflection model of selecting does not meet the reflection characteristic of body surface; The 2nd, constraint condition of introducing and solution procedure are too complicated, and it is slow to find the solution speed, and efficient is low.
Summary of the invention
The purpose of this invention is to provide a kind of menology reconstruction method of three-dimensional shape, find the solution slow, the inefficient problem of speed to solve existing reconstructing method based on individual gray level image.
For achieving the above object, the menology reconstruction method of three-dimensional shape step based on individual gray level image of the present invention is as follows:
(1) extracts each gray values of pixel points information in individual menology gray level image, find out the wherein pixel of maximum gradation value;
(2) each gray values of pixel points and maximum gradation value in the image are divided by, obtain the cosine at each pixel inclination angle; According to the menology reflection characteristic, menology is done the almost spherical hypothesis, try to achieve the cosine of each pixel drift angle;
(3) according to the inclination angle cosine value of each pixel, the surface normal vector that the drift angle cosine value is tried to achieve each pixel;
(4) the surface normal vector of each pixel that will try to achieve is converted to the height coordinate value of each pixel;
(5) utilize medium filtering that each the height coordinate value that calculates is carried out Filtering Processing;
(6) according to the surface normal vector and the height coordinate value that obtain, utilize OpenGL technology reconstruct menology 3D shape.
Further, maximum gradation value is in the described step (1) , the pairing pixel of this maximum gradation value is designated as
Further, pixel in described step (2) image
Figure 284923DEST_PATH_IMAGE003
Gray-scale value
Figure 144295DEST_PATH_IMAGE004
With maximum gradation value
Figure 815448DEST_PATH_IMAGE001
Be divided by, obtain pixel
Figure 723361DEST_PATH_IMAGE005
The inclination angle
Figure 297824DEST_PATH_IMAGE006
Cosine
Figure 265780DEST_PATH_IMAGE007
According to the menology reflection characteristic, menology is done the almost spherical hypothesis, try to achieve pixel
Figure 424229DEST_PATH_IMAGE005
The drift angle
Figure 198150DEST_PATH_IMAGE008
Cosine
Figure 391234DEST_PATH_IMAGE009
, wherein
Figure 93873DEST_PATH_IMAGE010
,
Figure 474039DEST_PATH_IMAGE011
Be x for the gradation of image value, the calculus of differences of y axle obtains.
Further, described step (3) is according to pixel
Figure 989334DEST_PATH_IMAGE003
Inclination angle cosine value, the surface normal vector that the drift angle cosine value is tried to achieve this pixel,
Figure 36924DEST_PATH_IMAGE012
, wherein
Figure 409000DEST_PATH_IMAGE013
Mould for vector.
Further, described step (4) is with the pixel that obtains
Figure 777926DEST_PATH_IMAGE003
The surface normal vector be converted to the height coordinate value, formula is
Figure 831333DEST_PATH_IMAGE014
Further, the medium filtering in the described step (5) is to establish the height sequence of sets
Figure 733430DEST_PATH_IMAGE015
, with length be
Figure 276407DEST_PATH_IMAGE016
Moving window it is carried out medium filtering, obtain the window correspondence
Figure 834427DEST_PATH_IMAGE016
Number
Figure 52044DEST_PATH_IMAGE017
, wherein,
Figure 74227DEST_PATH_IMAGE018
Be the value of window center point,
Figure 725788DEST_PATH_IMAGE019
With this
Figure 567842DEST_PATH_IMAGE020
Number is pressed the size ordering of numerical value, and getting its sequence number is several conducts of middle
Figure 589150DEST_PATH_IMAGE018
Filtering output, establish
Figure 403522DEST_PATH_IMAGE021
Be filtering output, then
Figure 288301DEST_PATH_IMAGE022
Further, also add illumination model after the reconstruct menology 3D shape in the described step (6).
Further, described illumination model is the Hapke illumination model, for
Figure 617652DEST_PATH_IMAGE023
, wherein
Figure 816552DEST_PATH_IMAGE024
, ,
Figure 541111DEST_PATH_IMAGE026
,
Figure 859222DEST_PATH_IMAGE027
, ,
Figure 447515DEST_PATH_IMAGE029
Further, obtain influencing radiation value according to illumination model ,
Figure 978040DEST_PATH_IMAGE031
Further, the menology 3D shape stack texture to reconstruct shows.
The present invention is for emulation menology 3D shape, based on traditional SFS method, adopted the lambert's body illumination reflection model that meets the menology reflection characteristic, menology is done spherical hypothesis, then image is done the approximate differential computing and obtain height function, again the result is done medium filtering, the correctness that assurance is found the solution, thus realized utilizing the single width gray level image to recover the menology 3D shape.Adopt method of the present invention can reduce the requirement that three-dimensional surface recover to be implemented, improve speed and the efficient recovered, simplify the step of recovering, after handling through this method, the 3D shape of reconstruct menology more accurately.
Further, add the Hapke illumination model, because the Hapke model mainly is at the moon reflection case that is caused by single source, according to the geometrical property of light in the menology reflection, with the reflection coefficient of menology to light, calculate the radiation intensity that arrives the observation place by the light of menology reflection, better actual conditions of pressing close to menology.
Description of drawings
Fig. 1 is a process flow diagram of the present invention;
Fig. 2 is the moonscape emulation gray-scale map of embodiment;
Fig. 3 is to the cloud data display effect behind Fig. 1 reconstruct three-dimensional surface among the embodiment;
Fig. 4 is the displayed map of embodiment after to Fig. 1 reconstruct three-dimensional surface;
Fig. 5 is embodiment to Fig. 1 reconstruct 3D shape and adds the design sketch of Hapke illumination;
Fig. 6 be embodiment to Fig. 1 reconstruct 3D shape after the design sketch of stack Hapke illumination and texture;
Fig. 7 is the menology image that NASA takes;
Fig. 8 be embodiment to Fig. 7 reconstruct shape after the design sketch of stack texture and illumination.
Embodiment
The SFS algorithm is an intensity of reflected light of calculating respective point on the three-dimensional object surface according to each point gray-scale value on the image, and by the analysis of physics and geometrical optics as can be known, the geometric configuration of catoptrical intensity and body surface character and body surface has relation.
If will show the menology shape, the half-tone information in the image need be converted to the amount relevant with moon geological information.According to lambert's body reflection law, the diffuse reflection light intensity that desirable diffuse reflection body surface reflects is directly proportional with the cosine of the angle between incident light and the body surface normal vector, that is:
Figure 518743DEST_PATH_IMAGE032
,
In the formula,
Figure 460416DEST_PATH_IMAGE033
Be the intensity that diffuses of body surface,
Figure 123479DEST_PATH_IMAGE034
Be the intensity of light source,
Figure 586821DEST_PATH_IMAGE035
Be the body surface reflection coefficient,
Figure 993531DEST_PATH_IMAGE036
Be the angle between incident light and the surface normal.
If the unit normal vector of body surface at illuminated some place is
Figure 288247DEST_PATH_IMAGE037
, reflection spot to the vector of unit length of pointolite is
Figure 59893DEST_PATH_IMAGE038
, the vector form that can be expressed as then: ,
When pointolite is far from illuminated surface, Change very for a short time, thereby it can be seen as a constant.The light that this moment, pointolite sent is directional light, by vector Definite fully.Under gradient space, suppose
Figure 864766DEST_PATH_IMAGE041
Be light source incident vector,
Figure 365018DEST_PATH_IMAGE042
Method vector for the body surface each point.For natural light, the incident vector is a definite value, and for the body surface normal vector, according to higher mathematics knowledge, provides functional form , that is:
Figure 821986DEST_PATH_IMAGE044
Hence one can see that Be the object surfaces gradient.On mathematics, the dot product of two vectors equals the product of their moulds and included angle cosine, that is:
Figure 985300DEST_PATH_IMAGE046
The dot product of two vectors can also be expressed as:
Figure 209608DEST_PATH_IMAGE047
,
Can get thus:
Figure 599001DEST_PATH_IMAGE048
,
Can set up with any point on the gray level image by following formula
Figure 181554DEST_PATH_IMAGE049
The intensity that diffuses at place is:
Figure 594081DEST_PATH_IMAGE050
?，
The intensity that diffuses of body surface
Figure 684397DEST_PATH_IMAGE033
Being reflected on the image is exactly this dot image brightness.By following formula as can be known, when
Figure 928297DEST_PATH_IMAGE051
Value is 1, when promptly light source direction is identical with surperficial direction of normal,
Figure 383549DEST_PATH_IMAGE052
Be maximal value.Finding the solution the SFS problem is exactly according to following formula, utilizes the brightness of known image and light source direction to determine the body surface gradient
Figure 80109DEST_PATH_IMAGE053
, and by With
Figure 511670DEST_PATH_IMAGE054
Relation can further obtain the object surfaces height
Figure 200140DEST_PATH_IMAGE055
According to above-mentioned formula, each point has two surface graded components to be asked in the scene, and every had only a known gray scale, so it is the inverse process of a morbid state.
The process flow diagram of the menology reconstruction method of three-dimensional shape based on individual gray level image of the present invention as shown in Figure 1, specific embodiment is an example with Fig. 2 moonscape emulation gray level image, table 1 is part pixel gray-scale value tabulation in the image of Fig. 2.
Figure 383997DEST_PATH_IMAGE056
1, establishes moon view data point
Figure 972290DEST_PATH_IMAGE058
Gray-scale value be
Figure 333126DEST_PATH_IMAGE004
, at first obtain the point of gray-scale value maximum in the view data
Figure 941962DEST_PATH_IMAGE002
, its gray-scale value
Figure 912192DEST_PATH_IMAGE001
2, will
Figure 922874DEST_PATH_IMAGE059
The gray-scale value of point With
Figure 111595DEST_PATH_IMAGE001
Do division, its result is as the inclination angle cosine of this pixel
Figure 823200DEST_PATH_IMAGE007
。As shown in table 2 below is the inclination angle cosine value data list that table 1 image slices vegetarian refreshments gray-scale value calculates.
Figure 252169DEST_PATH_IMAGE061
Figure 453343DEST_PATH_IMAGE062
According to the menology reflection characteristic, can do almost spherical hypothesis, the then drift angle of pixel to menology
Figure 36771DEST_PATH_IMAGE008
Cosine can calculate by following formula, , wherein
Figure 396394DEST_PATH_IMAGE010
,
Figure 706153DEST_PATH_IMAGE011
The representative image gray-scale value is x, and the calculus of differences of y axle is promptly differentiated to x, y.Inclination angle cosine value data list as shown in table 3 below, that table 1 image slices of serving as reasons vegetarian refreshments gray-scale value calculates.
3, obtain just can calculating the surface normal vector at this some place after the inclination angle and drift angle of pixel,
Figure 456383DEST_PATH_IMAGE064
,
Figure 296163DEST_PATH_IMAGE013
Be the mould of vector, can be set at 1.
4, can draw the three-dimensional appearance of menology according to the surface normal vector, be to the cloud data display effect figure behind Fig. 1 reconstruct three-dimensional surface as shown in Figure 3; Fig. 4 is to the displayed map behind Fig. 1 reconstruct three-dimensional surface.The surface normal vector can only be described the features of shape of menology, can not obtain the relative height value of surface point, so, need carry out of the conversion of surface normal vector to the height coordinate value,
Figure 839139DEST_PATH_IMAGE065
Height value data list as shown in table 4 below, that table 1 image slices of serving as reasons vegetarian refreshments gray-scale value recovers.
Figure 459477DEST_PATH_IMAGE066
5, obtain altitude information after owing to there is the influence of picture noise, if especially imaging surface exists under the situation of spike sudden change, the height value that calculates has than mistake, so also need utilize medium filtering to carry out the processing of following filtering:
If sequence of sets
Figure 50995DEST_PATH_IMAGE015
, with length be
Figure 309063DEST_PATH_IMAGE016
Moving window it is carried out medium filtering, obtain the window correspondence
Figure 226204DEST_PATH_IMAGE016
Number
Figure 68258DEST_PATH_IMAGE067
, wherein, Be the value of window center point, With this
Figure 224935DEST_PATH_IMAGE016
Number is pressed the size ordering of numerical value, and getting its sequence number is several conducts of middle
Figure 67469DEST_PATH_IMAGE068
Filtering output, establish Be filtering output, then As shown in table 5 below, for table 1 picture point is recovered and filtered height value data list.
Table 5 table 1 picture point is recovered and filtered height value
6, pass through said method, utilize the OpenGL technology menology dimensional topography of emulation can be shown, but for effect is close to the real terrain of menology, also need to add illumination model, be to Fig. 1 reconstruct 3D shape as shown in Figure 5 and add the design sketch of Hapke illumination.Method has adopted the Hapke illumination model.The Hapke model mainly is at the moon reflection case that is caused by single source, according to the geometrical property of light in the menology reflection, with the reflection coefficient of menology, calculate the radiation intensity that arrives the observation place by the light of menology reflection, better actual conditions of pressing close to menology to light.The Hapke model can be expressed as:
Figure 807575DEST_PATH_IMAGE071
，
Wherein
Figure 606904DEST_PATH_IMAGE072
The albedo of expression celestial body surface atural object correspondence,
Figure 694071DEST_PATH_IMAGE073
The condition that the expression viewpoint direction overlaps with light source direction,
Figure 123915DEST_PATH_IMAGE074
Representation unit angle scattering equation,
Figure 427857DEST_PATH_IMAGE075
The bidirectional reflectance coefficient of expression scattered beam in infinitely-great medium. With
Figure 408769DEST_PATH_IMAGE077
Can represent by the product of celestial body surface gradient vector respectively, promptly
Figure 806252DEST_PATH_IMAGE078
?，
Figure 98955DEST_PATH_IMAGE079
?，
Wherein
Figure 177770DEST_PATH_IMAGE080
The unit vector of expression light source direction,
Figure 738064DEST_PATH_IMAGE081
The unit vector of expression viewpoint direction.
Because when the reflection angle of light and incident angle were approaching, the direction vector of light source and the direction vector of viewpoint were very approaching, singularity can appear in the Hapke model at this moment, and bigger error can appear in result calculated.Therefore, adopt a kind of improved model:
, wherein
Figure 522667DEST_PATH_IMAGE083
Be the normal vector of light source direction, Be light source direction vector and
Figure 819973DEST_PATH_IMAGE085
Be the vector of viewpoint direction, ,
Figure 826554DEST_PATH_IMAGE025
,
Figure 247171DEST_PATH_IMAGE026
,
Figure 782058DEST_PATH_IMAGE027
,
Figure 957824DEST_PATH_IMAGE028
, , The albedo of expression celestial body surface atural object correspondence.
6.1, improved model simplified the expression formula of Hapke model, make it singularity can not occur, and kept the fundamental property of Hapke model.
6.2, the image radiation value that obtains at last
Figure 794958DEST_PATH_IMAGE030
Can be expressed as:
Figure 79309DEST_PATH_IMAGE031
7, under this illumination model, scene stack texture is shown that effect is better true to nature.The stack texture is to utilize texture technology among the OpenGL, the general step that texture is drawn is: definition texture mapping, control texture, explanation texture mapping mode and definition texture coordinate, it realizes that function is glTexImage2D (), is the design sketch to stack Hapke illumination and texture after Fig. 1 reconstruct 3D shape as shown in Figure 6.
Shown in Figure 7 is the menology image that NASA takes; Fig. 8 be reconstructing method according to the present invention to Fig. 7 reconstruct shape after the design sketch of stack texture and illumination.

Claims (10)

1. menology reconstruction method of three-dimensional shape based on individual gray level image is characterized in that this method step is as follows:
(1) extracts each gray values of pixel points information in individual menology gray level image, find out the wherein pixel of maximum gradation value;
(2) each gray values of pixel points and maximum gradation value in the image are divided by, obtain the cosine at each pixel inclination angle; According to the menology reflection characteristic, menology is done the almost spherical hypothesis, try to achieve the cosine of each pixel drift angle;
(3) according to the inclination angle cosine value of each pixel, the surface normal vector that the drift angle cosine value is tried to achieve each pixel;
(4) the surface normal vector of each pixel that will try to achieve is converted to the height coordinate value of each pixel;
(5) utilize medium filtering that each the height coordinate value that calculates is carried out Filtering Processing;
(6) according to the surface normal vector and the height coordinate value that obtain, utilize OpenGL technology reconstruct menology 3D shape.
2. menology reconstruction method of three-dimensional shape according to claim 1 is characterized in that: maximum gradation value is in the described step (1)
Figure 2010102625080100001DEST_PATH_IMAGE001
, the pairing pixel of this maximum gradation value is designated as
Figure 257461DEST_PATH_IMAGE002
3. menology reconstruction method of three-dimensional shape according to claim 2 is characterized in that: pixel in described step (2) image
Figure 2010102625080100001DEST_PATH_IMAGE003
Gray-scale value
Figure 347777DEST_PATH_IMAGE004
With maximum gradation value
Figure 591676DEST_PATH_IMAGE001
Be divided by, obtain pixel
Figure 2010102625080100001DEST_PATH_IMAGE005
The inclination angle Cosine
Figure 2010102625080100001DEST_PATH_IMAGE007
According to the menology reflection characteristic, menology is done the almost spherical hypothesis, try to achieve pixel
Figure 307271DEST_PATH_IMAGE008
The drift angle
Figure 935698DEST_PATH_IMAGE009
Cosine
Figure 299683DEST_PATH_IMAGE010
, wherein
Figure 660257DEST_PATH_IMAGE011
,
Figure 611158DEST_PATH_IMAGE012
Be x for the gradation of image value, the calculus of differences of y axle obtains.
4. menology reconstruction method of three-dimensional shape according to claim 3 is characterized in that: described step (3) is according to pixel
Figure 43277DEST_PATH_IMAGE003
Inclination angle cosine value, the surface normal vector that the drift angle cosine value is tried to achieve this pixel,
Figure 933872DEST_PATH_IMAGE013
, wherein
Figure 793244DEST_PATH_IMAGE014
Mould for vector.
5. menology reconstruction method of three-dimensional shape according to claim 4 is characterized in that: described step (4) is with the pixel that obtains
Figure 402080DEST_PATH_IMAGE003
The surface normal vector be converted to the height coordinate value, formula is
Figure 2010102625080100001DEST_PATH_IMAGE015
。
6. menology reconstruction method of three-dimensional shape according to claim 5 is characterized in that: the medium filtering in the described step (5) is to establish the height sequence of sets , with length be
Figure 2010102625080100001DEST_PATH_IMAGE017
Moving window it is carried out medium filtering, obtain the window correspondence
Figure 274669DEST_PATH_IMAGE017
Number
Figure 242625DEST_PATH_IMAGE018
, wherein,
Figure 2010102625080100001DEST_PATH_IMAGE019
Be the value of window center point,
Figure 401074DEST_PATH_IMAGE020
With this
Figure 174995DEST_PATH_IMAGE017
Number is pressed the size ordering of numerical value, and getting its sequence number is several conducts of middle Filtering output, establish
Figure 2010102625080100001DEST_PATH_IMAGE021
Be filtering output, then
Figure 793420DEST_PATH_IMAGE022
。
7. menology reconstruction method of three-dimensional shape according to claim 6 is characterized in that: also add illumination model after the reconstruct menology 3D shape in the described step (6).
8. menology reconstruction method of three-dimensional shape according to claim 7 is characterized in that: described illumination model is the Hapke illumination model, for
Figure 2010102625080100001DEST_PATH_IMAGE023
, wherein
Figure 439165DEST_PATH_IMAGE024
,
Figure 2010102625080100001DEST_PATH_IMAGE025
,
Figure 751197DEST_PATH_IMAGE026
,
Figure 2010102625080100001DEST_PATH_IMAGE027
,
Figure 300253DEST_PATH_IMAGE028
,
Figure 2010102625080100001DEST_PATH_IMAGE029
9. menology reconstruction method of three-dimensional shape according to claim 8 is characterized in that: obtain influencing radiation value according to illumination model
Figure 734645DEST_PATH_IMAGE030
,
10. menology reconstruction method of three-dimensional shape according to claim 9 is characterized in that: the menology 3D shape stack texture to reconstruct shows.
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