CN101923729B - 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 PDFInfo
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- CN101923729B CN101923729B CN2010102625080A CN201010262508A CN101923729B CN 101923729 B CN101923729 B CN 101923729B CN 2010102625080 A CN2010102625080 A CN 2010102625080A CN 201010262508 A CN201010262508 A CN 201010262508A CN 101923729 B CN101923729 B CN 101923729B
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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
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
Through 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 through 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 according to the intensity of reflected light of respective point on the each point gray-scale value Calculation of Three Dimensional body surface on the image, can be known that by the analysis of physics and geometrical optics 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 realizing above-mentioned purpose, the menology reconstruction method of three-dimensional shape step based on individual gray level image of the present invention is following:
(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;
The surface normal vector of each pixel that (4) will try to achieve converts the height coordinate value of each pixel into;
(5) utilize medium filtering that each the height coordinate value that calculates is carried out Filtering Processing;
(6), utilize OpenGL technology reconstruct menology 3D shape according to the surface normal vector and the height coordinate value that obtain.
Further; Maximum gradation value is
in the said step (1), and the pairing pixel of this maximum gradation value is designated as
.
Further; The gray-scale value
of pixel in said step (2) image
is divided by with maximum gradation value
, obtains the cosine
at pixel
inclination angle
; According to the menology reflection characteristic; Menology is done the almost spherical hypothesis; Try to achieve the cosine
of pixel
drift angle
; Wherein
,
are x for the gradation of image value, and the calculus of differences of y axle obtains.
Further; Said step (3) is according to the inclination angle cosine value of pixel
, the surface normal vector that the drift angle cosine value is tried to achieve this pixel;
, wherein
is the mould of vector.
Further; Said step (4) converts the surface normal vector of the pixel that obtains
into the height coordinate value, and formula is
.
Further; Medium filtering in the said step (5) is to establish height sequence of sets
; Use the moving window of length that it is carried out medium filtering for
; Obtain corresponding
number
of window; Wherein,
is the value of window center point,
; This
number is pressed the size ordering of numerical value; Getting its sequence number is the filtering output of number as
of middle; If
is filtering output, then
.
Further, also add illumination model after the reconstruct menology 3D shape in the said step (6).
Further, said illumination model is the Hapke illumination model, for
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 the moon reflection case that causes to by single source, according to the geometrical property of light, with the reflection coefficient of menology to light in the menology reflection; 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 according to the intensity of reflected light of respective point on the each point gray-scale value Calculation of Three Dimensional body surface on the image, can be known that by the analysis of physics and geometrical optics the geometric configuration of catoptrical intensity and body surface character and body surface has relation.
If will show the menology shape, need the half-tone information in the image 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 out is directly proportional with the cosine of the angle between incident light and the body surface normal vector; That is:
In the formula;
is the intensity that diffuses of body surface;
is the intensity of light source;
is the body surface reflection coefficient, and
is the angle between incident light and the surface normal.
If the unit normal vector of body surface at illuminated some place is
; Pip is
to the unit vector of spot light; Then can be expressed as following vector form:
When pointolite is far from illuminated surface;
changes very little, thereby can see it as constant.The light that this moment, pointolite sent is directional light, and is definite fully by vector
.Under gradient space; Suppose
and be light source incident vector,
is the method vector of 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; Provide functional form
, that is:
.
Hence one can see that, and
is the object surfaces gradient.On mathematics; The dot product of two vectors equals the product of their moulds and included angle cosine, that is:
.
Can set up the intensity of locating with any point on the gray level image
that diffuses through following formula is:
It is exactly this dot image brightness that the intensity that diffuses of body surface
is reflected on the image.Can know through following formula; When
value is 1; Be light source direction when identical with surperficial direction of normal,
is maximal value.Finding the solution the SFS problem is exactly according to following formula; Utilize the brightness and the light source direction of known image to confirm body surface gradient
, and the relation with
can further be obtained object surfaces height
by
.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 is as shown in Figure 1, and specific embodiment is an example with Fig. 2 moonscape emulation gray level image, and table 1 is part pixel gray-scale value tabulation in the image of Fig. 2.
1, the gray-scale value of establishing moon view data point
is
; At first obtain the maximum point
of gray-scale value in the view data, its gray-scale value
.
2, the gray-scale value
of point is done division with
with
, and its result is as the inclination angle cosine of this pixel
。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.
According to the menology reflection characteristic; Can do the almost spherical hypothesis to menology; Then the drift angle of pixel
cosine can obtain through computes;
; Wherein
,
representative image gray-scale value are x; 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,
4, can draw the three-dimensional appearance of menology according to the surface normal vector, as shown in Figure 3 is to the cloud data display effect figure behind Fig. 1 reconstruct three-dimensional surface; 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.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.
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
; Use the moving window of length that it is carried out medium filtering for
; Obtain corresponding
number
of window; Wherein,
is the value of window center point,
.This
number is pressed the size ordering of numerical value; Getting its sequence number is the filtering output of number as
of middle; If
is 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 can the menology dimensional topography of emulation be shown; But for effect is close to the real terrain of menology, also need add illumination model, as shown in Figure 5ly be to Fig. 1 reconstruct 3D shape and add the design sketch of Hapke illumination.Method has adopted the Hapke illumination model.The Hapke model mainly is the moon reflection case that causes to 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:
Wherein
representes the corresponding albedo of celestial body surface atural object; The condition that
expression viewpoint direction overlaps with light source direction;
representation unit angle scattering equation, the bidirectional reflectance coefficient of
expression scattered beam in infinitely-great medium.
and
can be represented by the product of celestial body surface gradient vector respectively, promptly
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
is the normal vector of light source direction;
is that the vector of light source direction is the vector of viewpoint direction with
;
;
;
;
;
;
, the corresponding albedo of
expression celestial body surface atural object.
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.
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 (), and as shown in Figure 6 is design sketch to stack Hapke illumination and texture after Fig. 1 reconstruct 3D shape.
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 following:
(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;
The surface normal vector of each pixel that (4) will try to achieve converts the height coordinate value of each pixel into;
(5) utilize medium filtering that each the height coordinate value that calculates is carried out Filtering Processing;
(6), utilize OpenGL technology reconstruct menology 3D shape according to the surface normal vector and the height coordinate value that obtain.
3. menology reconstruction method of three-dimensional shape according to claim 2; It is characterized in that: the gray-scale value
of pixel in said step (2) image
is divided by with maximum gradation value
, obtains the cosine
at pixel
inclination angle
; According to the menology reflection characteristic; Menology is done the almost spherical hypothesis; Try to achieve the cosine
of pixel
drift angle
; Wherein
,
are x for the gradation of image value, and the calculus of differences of y axle obtains.
4. menology reconstruction method of three-dimensional shape according to claim 3; It is characterized in that: said step (3) is according to the inclination angle cosine value of pixel
, the surface normal vector that the drift angle cosine value is tried to achieve this pixel;
, wherein
is the mould of vector.
6. menology reconstruction method of three-dimensional shape according to claim 5; It is characterized in that: the medium filtering in the said step (5) is to establish height sequence of sets
; Use the moving window of length that it is carried out medium filtering for
; Obtain corresponding
number
of window; Wherein,
is the value of window center point,
; This
number is pressed the size ordering of numerical value; Getting its sequence number is the filtering output of number as
of middle; If
is filtering output, then
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 said step (6).
8. menology reconstruction method of three-dimensional shape according to claim 7 is characterized in that: said illumination model is the Hapke illumination model, for
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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US10489970B2 (en) * | 2015-11-06 | 2019-11-26 | Microsoft Technology Licensing, Llc | 2D image processing for extrusion into 3D objects |
CN105869206B (en) * | 2016-04-12 | 2018-09-18 | 广州华欣电子科技有限公司 | three-dimensional rebuilding method and device |
CN108961391B (en) * | 2018-06-12 | 2022-12-13 | 温州大学激光与光电智能制造研究院 | Surface reconstruction method based on curvature filtering |
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