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1、A High Quality Reflectance Model in Medical Image Visualization Yunpeng Zou School of BMIE, Northeastern University Shenyang, China y_p_ Jun Zhang Medical IT Division Neusoft Medical Systems Co., Ltd. Xiaoming Han Medical IT Division Neusoft Medical Systems Co., Ltd. Yan Kang School of BMIE Northeas
2、tern University Shenyang, Chian AbstractThe medical image visualization can help the doctor easy to diagnose, and the better quality can help doctor much more. The reflectance model is the key factor to make the quality better. Be enslaved to the computing power of CPU and GPU, some complicated refl
3、ectance models have not been used in medical visualization, the simple reflectance modelPhong model been used prevalently. With the growing computing power of GPU, this paper gives an improved reflectance model based on the Cook-Torrance reflectance model, which can render good quality in medical im
4、age visualization, and the velocity is 4 to 6 fps, that meet the real time rendering requirement. This reflectance model is a practical model for medical image visualization. Keywords-medical image visualization, reflactance model, Phong, Cook-Torrance, quanlity 1 INTRODUCTION Medical imaging modali
5、ties such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) produce high-quality 3D data, and with the visualization technology, doctor can diagnose in a direct way. comparing to the traditional 2D mode visualized image is more realistic, and easy to diagnose. Medical image visualizat
6、ion including so many methods, and the ray casting and texture mapping are two of the most prevalent method currently 4 5. No matter which method has been used, the model of how objects reflect light is the key factor for these methods to get a better result. Phong reflectance model, which is a line
7、ar combination of specular and diffuse reflection, is used mostly in medical image visualization field. The specular component was spread out around the specular direction by using a cosine function raised to a power. This paper present a reflectance model that is fit for medical image visualization
8、, and this reflectance model is based on the Cook-Torrance reflectance model. According feature of the medical imaging this model made some improvement. The Cook-Torrance reflectance model is based on geometrical optics and is applicable to a broad range of materials, surface conditions, and lightin
9、g situations. The basis of this model is a reflectance definition that relates the brightness of an object to the intensity and size of each light source that illuminates the object. Comparing to the Phong reflectance model, the Cook-Torrance model is more complex, but in resent years the computing
10、power of the GPU (graphic processing unit) increased rapidly, that means the complex reflectance model is possible been used in medical image visualization. 2 THE METHOD A. Basic Model Phong reflectance model which combines the specular reflectors with the diffuse (lambertian) reflectors, is the mos
11、t prevalent reflectance model in medical image visualization. Briefly the Phong reflectance model is: =+=MiinsiiliiaakkIfkII1)coscos( (1) Figure 1. The geometry of reflectance. The i means the number of the light source. The N represents the surface normal, L represents the 978-1-4244-4713-8/10/$25.
12、00 2010 IEEEvector in direction of light, and V represents the vector in direction of the viewer. Ia is the intensity of the incident ambient light, IaKa is the ambient reflectance. Il represents the intensity of the incident light. f is the Attenuation factor of the incident light. is the angle bet
13、ween the N and H. is the angle between L and H or V and H. The W(),which is the specular reflectivity of the surface, is the function of the angle of incidence and the wavelength of the incidence light. Practically, use the ks instead of the W(). n is the specular exponent, which is used to control
14、the degree of the specular component spreading out around the specular direction 6. It is easy to understand that the Phong reflectance model defines the intensity of the specular reflectance is the direct reflectance of the incidence light, and the n is used to describe the roughness of the surface
15、. The Phong reflectance model only uses the surface normal of the object, without any other property of the object. In practice The (NHi) is used to replace the (VRi), because the (VRi) is not easy to be calculated. Hi is the ideal surface normal of the specular light for reflecting the incident lig
16、ht to eyes of the viewer, and iH is the identity vector of the2VLi+. So the Phong reflectance model would be like this: =+=MinisidliiaaHNRLNRIfIRI1)()( (2) Torrance-Sparrow reflectance model builds the rough surface reflectance model based on the geometrical optics (ray theory). This model employs o
17、nly geometrical optics and applies when the surface roughness-to-wavelength ratio is greater than unity. The Torrance-sparrow reflectance model assumes that the surface consists of microfacets, Specular reflection from these facets plus a diffuse component due to multiple reflection and internal sca
18、ttering are assumed to be the basic mechanisms of reflection 7. Cook and Torrance give the specular component based on the Torrance-Sparrow reflectance model: )()(VNGLNDFRs= (3) D is the facet slope distribution function which represents the fraction of the facets that are oriented in the direction
19、H. G, the geometrical attenuation factor, accounts for the shadowing and masking of one facet by another. The Fresnel term F, which is a function of incidence angle and wavelength, describes how light is reflected from each smooth microfacet. Various facet sloop distribution functions have been cons
20、idered by Blinn 2 one of the formulation he described is the Gaussian model: 2)/(mceD= (4) The c is an arbitrary constant. Beckmann provided a comprehensive theory that encompasses all of these materials and is applicable to a wide range of surface conditions ranging from smooth to very rough 1. For
21、 rough surfaces, the Beckmann distribution function is )tan(2222cos1memD=. (5) The advantage of the Beckmann function is that it gives the absolute magnitude of the reflectance without introducing arbitrary constants; the disadvantage is that it requires more computation. In some angle of incidence,
22、 part of the incident or reflect light may been masked by the V-groove cavity, which is depicted in Fig 2. LHV Figure 2. Geometry of V-groove cavity also simultaneous masking and shadowing Because the attenuation of the intensity of the reflect light, which is caused by the structure of the V-groove
23、 cavity, so G can be defined as 2; )()(2,)()(2, 1min(VHLNHNLHVNHNG= (6) Cook and Torrance have adopted a practical compromise to obtain the spectral and angular variation of F. They measured normal reflectance for a polished surface to fit the Fresnel equation. They assume the = 0, then calculate th
24、e F though measuring the incident light with different wavelength, and get the relationship between the wavelength of the incident light and the index of refraction. With the index of refraction can calculate the F in any angle of incidence 3. B. Our Method In medical image visualization the object
25、with different CT value can get the different color and the opacity value though adjusting the transfer functions. The surface of the object can be seen in different colors, because the object absorbs the light with different color and reflects the light with the same color comparing itself. So peop
26、le can see the color of the object, but in Phone or Cook-Torrance reflectance model there is no connection between the object and the incident light. There formula based on the geometrical optics, but medical image visualization not just demands the structure been rendered but also asks for more col
27、orful and more realistic image. So in this paper when we calculate the diffuse light, we use the color of the object which is gotten from the transfer functions instead of the color of the incident light. And we use the white light as the specular light because the specular light in real world all l
28、ooks like white color. In this model the formula would be like =+=MiisMiwiidoiaaLNRIfLNRCfIRI11)()( (7) The Co represents the color of the object, and Iw represents the white color light. There is also some deficiency if the color of the object is not bright and the result will be darkness, So shoul
29、d make the Rd a little bit great, also when the result is over brightness the Rd should be less. That means this formula does not abbey the law of conservation of energy, which is used just for better result. Medical image visualization only includes some object such as skin, bone, etc, that means i
30、f we know the refractive index we can easily get the F. Fresnel formula is )(tan)(tan)(sin)(sin212222+=F (8) represents the angle of incidence and )arccos(HL=. represents the angle of refraction and )sinarcsin(n=. r represents the refractive index. 3 RESULT In this paper we use the computer with ATI
31、 Graphic card 4830, and the rendering language is CG and OpengGL, the volume rendering method is texture mapping. The information of two series data used in this paper and the rendering condition are displayed in table 1. The rendering results are given from Fig 3 to Fig 8. TABLE I. INFORMATION OF T
32、HE DATA AND RESULT Part Size Num of slices View port size Framerate foot 512*512*250 766 500*500 6.41 head 512*512*310 787 500*500 4.26 Figure 3. Nylon socks with r: 1.53 and m:0.4. Figure 4. Skin with r: 1.4 and m: 0.25. Figure 5. Skull with r: 1.5 and m: 0.3. Figure 6. Shining but rough surface wi
33、th r: 5.0 and m: 0.3. Figure 7. Smooth but dingy surface with r: 1.5 and m: 0.1. Figure 8. Shining and smooth surface with r: 5.0 and m: 0.3. 4 DISCUSSIONS AND CONCLUTIONS By changing the r and m, the wanted high quality result could be gotten. The r is greater, the result is brighter, and the r is
34、less, the result is darker the r control more or less lights been reflected, that can be seen in Fig. 5 and Fig. 6. The m is greater, he result is smoother, and the m is less, the result is rougher the m control surface is smooth or rough, that can be seen in Fig. 7 and Fig. 8. As can be seen from t
35、he Table.1, the number of slice is greater than number of the voxels in any dimension of the data, which guarantee no voxel of the data will be missed in process of sampling. When all the information of the data has been represented, the framrate is 4 to 6 fps, which means this reflectance model cou
36、ld be used in real-time interactive rendering. This model based on the Cook-Torrance reflectance model, and for the feature of the medical imaging some improvement has been made. This model use the color of the object instead of the incident light when calculating the diffuse light, and use the whit
37、e light as the incident light when calculating the specular light. Using the color of the object makes the result more colorful so the tissues could be distinguished by color and shadow. Using the white light not just fits for the nature phenomena the specular light looks like in white color, but al
38、so avoids employing the wavelength only involving the refraction index in this model, which makes this pattern less complex but very practical. Generally this model, which can provide a realistic and real-time rendering result, is useful and practical in medical image visualization. 5 ACKNOWLEDGMENT
39、 The authors would like to express their great thanks to the financial supports of National Nature Science Foundation (grant No.60771067). 6 REFERENCES 1 Beckmann, Petr and spizzichino, Andre, “The Scattering of Electromagnetic Waves from Rough Surface,” MacMillan, pp. 1-33, 70-98, 1963. 2 Blinn, F.
40、 James, “Computer Display of Curved Surface,” PhD dissertation, University of Utah, Salt Lake City, 1978. 3 R. L. Cook, and K. E. Torrance, “A Reflectance Model for Computer Graphics,” Computer Graphics, vol. 15, no. 3, 1981. 4 Klaus Engel, Markus Hadwiger, Joe M Kniss, Christof Rezk-salama and Dani
41、el Weiskopt, Real-time Volume Graphic. USA: A.K.Peters, 2006. 5 T. McReynolds, D. Blythe, B. Grantham, and S. Nelson, “Advanced graphic programming techniques using OpenGL,” In SIGGRAPH 2000 course notes, 2000. 6 B. T. Phong, “Illumination for Computer-Generated Image,” PhD dissertation, University of Utah, Salt Lake City, 1973. 7 K. E. Torrance, and E. M. Sparrow, “Theory for Off-specular Reflection From Roughened Surfaces,” Journal of the Optical Society of America, vol. 57, pp.1105-1114, September 1967.
