GPU Supported Haptic Device Integrated Dental Simulation Environment

Transcription

1 GPU Supported Haptic Device Integrated Dental Simulation Environment Varlık Kılıç 1 Umut Koçak 2 E. İlhan Konukseven 3 Erkan Mumcuoğlu 4 Department of Mechanical Engineering Department of Health Informatics Department of Mechanical Engineering Department of Health Informatics ABSTRACT This study aims to construct a haptic device integrated virtual reality environment for simulating dental treatment operations. In this environment, it is aimed to combine GPU based graphical rendering and haptic rendering. By implementing graphical rendering on GPU, the quality and speed performance of the graphical rendering are enhanced and more CPU resource is dedicated to haptic rendering. However in order to compare the performances of the techniques, volume rendering and isosurface rendering techniques are implemented on both CPU and GPU. A data pre-processing method is introduced for reducing the computational load. In order to display multiple volumetric objects using the ray casting method, per pixel depth buffer modification is implemented. A haptic rendering method depends on density gradient vectors is also proposed for interacting with volumetric data. Keywords: haptic, GPU, ray-casting, dentistry education, virtual reality. 1 INTRODUCTION Recent developments in haptic device technology and intensive research on the field triggered an evolutionary approach to vocational education technologies. Especially, in the fields where hands on training is not applicable or ethical, e.g. medicine and dentistry, haptic applications promise experienced and high skilled trainees. In [1], a haptic device integrated virtual environment was constructed to design pre-surgical bone implants. A VRsimulation system for educating surgeons of the temporal bone milling processes was presented in [2, 3]. In the study [4], computationally efficient algorithms for the real time simulation of minimally invasive surgical (MIS) procedures were presented. A direct volume rendering technique, which supports low latency real time visual feedback in parallel with physical simulation on commodity graphics platforms, was developed in the study [5]. The papers [6, 7] describe a framework for training-oriented simulation of temporal bone surgery. Especially, in the field of dentistry, there exist several ongoing and completed projects. In the study [8], a virtual dental environment to realize stable and realistic cutting simulation using an impedance display haptic device and microcomputer was proposed. A force feedback dental surgical simulator was designed to be a regular part of the dental curriculum by providing a more uniform educational experience and superior performance feedback for the students than traditional training methods in another study [9]. A patented product [10] exists in the market which provides a haptic integrated virtual environment to train dentistry students on a single tooth. 1 varlik@metu.edu.tr 2 kocak@ii.metu.edu.tr 3 konuk@metu.edu.tr 4 mumcuoglu@ii.metu.edu.tr Although the studies mentioned above have very similar aims and the volumetric medical data used in these studies have quite similar structure, the techniques used for graphical and haptic rendering differ. However it is possible to classify the previously used graphical rendering techniques in two parts: surface-based rendering and volume rendering. In the surface-based rendering, the main goal is to draw polygons representing an iso-surface inside the volumetric data. On the other hand, volume rendering technique depends on the idea of blending the colors of whole voxels in the volume. There are several techniques of volume and surface-based rendering which can be implemented on either CPU or GPU (Graphical Processing Unit). The haptic rendering techniques used by the researchers of the previous studies mentioned above can also be classified into two categories: surface-based and volume based haptic rendering. The surface-based haptic rendering utilizes the stiffness and damping of the surfaces to determine reaction forces and feedback to the haptic device. On the other hand, volume based haptic rendering methods utilizes the material properties of the interacted voxels to determine forces. This study combines GPU and CPU based graphical rendering techniques and volume based haptic rendering to construct a haptic device integrated virtual reality environment for simulating dental treatment. In section 2, the data structures used to optimize the performance of the overall simulation environment are discussed. Section 3 explains the data modification technique which represents the milling operation of tooth. Volume based haptic rendering method used to evaluate and feedback the reaction forces between tooth and tool to the haptic device is presented in section 4. Section 5 is devoted to explain the CPU based iso-surface and volume rendering and GPU based iso-surface and volume rendering techniques by ray-casting method. Results and conclusions of the study are discussed in section 6 and 7. 2 DATA REPRESENTATION The data structure used to represent the tooth and the tool is critical to achieve a real time haptic and graphical rendering. To optimize the performance of the simulation environment the following data structures are used. Tooth Data: The tooth data is stored in a 3D voxel array. Each voxel holds a scalar density value and a gradient vector that keeps the direction and magnitude of the density gradient. This structure allows constant time access to the density and gradient information of the voxels collided or occupied by the tool. Tool Data: A mathematical function that defines the volume inside or outside of the tool may be used to determine if a tooth voxel is occupied or not as the tool center manipulated inside the workspace. This representation limits the use of tools that has irregular geometry. Moreover it

2 necessitates the use of a bounding box around the tool center and traversal of all voxels inside this box whether the voxels satisfy the mathematical function or not and as a result the running speed is reduced. The data structure used to represent tooth data may also be used for the tool. Even if this enables use of irregularly shaped tools, the traversal of all voxels in the 3D voxel array is still necessary to detect any tool-tooth collusion. Also, for the slender tool geometries, there exists a large number of empty voxels in the 3D voxel array which will cause redundant memory usage. Therefore, a one dimensional integer array is preferred to store the tool data. Since the tool center is controlled and updated through the haptic device, the position vectors of tool voxels with respect to the tool center are indexed and stored. This structure not only allows the use of irregularly shaped tools but also provides a rapid and efficient traversal of tool voxels to detect any tool-tooth interaction. Moreover, the memory is allocated only for the voxels which are occupied by the tool; excess memory usage is avoided completely. Optimizing the data structure for the tooth and the tool is necessary but not sufficient to achieve real time rendering. Some supporting data structures explained below is used to maximize the rendering speed. Modified Voxels List: During traversal of tool voxels to detect any tool-tooth collusion the density and the density gradient vector of the collided tooth voxels are updated. However, the marching cubes algorithm [11], used to render the iso-surfaces on CPU, needs to be called after all of the modifications in density and gradient data are completed. Also it is not efficient to call marching cubes algorithm for the whole data in terms of running speed. Thus any voxel that faces a modification in density or gradient data is added to this modified voxel list and marching cubes algorithm is recalled only for these voxels. The list is deleted after the marching cubes algorithm has succeeded. This data structure is not employed for the other rendering techniques used in this study. Surface Display List: This data structure holds triangle list corresponding to each voxel if iso-surface rendering technique on CPU is used for graphical rendering. This structure is a one dimensional hash table that holds the display lists of triangles corresponding to the voxels that the iso-surface is passing through. The triangles of the iso-surface passing through a voxel are compiled in a display list and this display list is added to the Surface Display List with an index generated using 3D voxel coordinates. This structure provides compact memory usage by avoiding no iso-surface passing voxels and enables fast access to the triangle lists for updating the surface during data modification. This data structure is not employed for the techniques other than iso-surface rendering. Density Texture: this data structure is used to convert 3D tooth data to 1D array and to bind it as a 3D texture for volume rendering on CPU. The format of the data is RGBA, in which red, green blue and alpha channels are same as the density of the corresponding voxel. Gradient Texture: this data structure is also used to convert 3D gradient data to 1D array and to bind it as a 3D texture for volume rendering on CPU. Moreover it is used in haptic force evaluation since this data is not affected in the data modification step unlike the gradient vector component of tooth data. However it is updated at the end of the data modification step. The format of the data is RGBA, in which red, green, blue channels correspond to the x, y, z components of the gradient respectively and Alpha channel is the magnitude of the gradient vector of the corresponding voxel. Density SubTexture: this is a 1D array which is used to locally update 3D texture corresponding tooth density for volume rendering on CPU. The format of the data is the same as Density Texture s. Gradient SubTexture: this is a 1D array which is used to locally update 3D texture corresponding tooth density gradient for volume rendering on CPU. The format of the data is the same as Gradient Texture s. GPU Texture: this data structure is 1D array and it is used to transfer the density and density gradient components of the voxels as a 3D texture to the fragment programs, iso-surface and volume rendering on GPU, running on graphics hardware. The format of the data is RGBA, in which red, green, blue channels correspond to the x, y, z components of the gradient vector respectively and alpha channel is the density of the corresponding voxel. GPU SubTexture: this is a 1D array which is used to locally update 3D texture corresponding tooth density and density gradient components of voxels for volume rendering on GPU. The format of the data is the same as GPU Texture s. readtoolpositionrotation for each ToolData voxel if collided with a non-empty ToothData voxel set ToothData voxel density to 0 correct neighboring ToothData voxels gradients if iso-surface rendering on CPU add voxel and neighbors to ModifiedVoxelsList else update modification area bounding box limits read density gradient vector from GradientTexture add to tool modification force read density gradient vector from GradientTexture add to tool contact force if iso-surface rendering on CPU for each ModifiedVoxelList voxels update GradientTexture if a display list exists in SurfaceDisplayList delete the display list call MarchingCubes if a triangle list ocuured compile and add to the SurfaceDisplayList delete ModifiedVoxelList else if volume rendering on CPU for each voxel in modification area update GradientTexture update DensityTexture update GradientSubtexture and bind to 3D texture update DensitySubtexture and bind to 3D texture else if graphical rendering on GPU for each voxel in modification area update GradientTexture update GPUTexture update GPUSubTexture and bind to 3D texture total tool force = scale1 * tool contact force total tool force += scale2 * tool modification force render total tool force to haptic device Figure 1: Pseudo code for data modification loop 3 DATA MODIFICATION Data modification method is also a critical issue which affects the speed performance and display quality of the simulation directly. In order to achieve a realistic simulation environment, it is not possible to define a unique modification method which is optimum for all graphical rendering techniques. Instead the data modification method is conditioned to use data structures of the graphical rendering technique in use. The main idea of the presented pseudo code in Figure 1 for data modification is updating the Tooth Data, evaluating

3 force feedback and conducting the necessary updates in the corresponding data structures of the graphical rendering technique in use. During data modification, it is aimed to reduce the tooth voxel density which is collided by tool voxels to zero. However as the tool traverse inside the tooth data, the density of a tooth voxel is set to zero when tool voxel center crosses the tooth voxel border. This fact results in sudden density changes which is not realistic. To smooth density decrease, the ratio of tooth tool voxel collision is evaluated by trilinear interpolation using tool voxel center position and center of 8 neighboring tooth voxels, and the density decrease, modification ratio, of the tooth voxel is calculated by scaling the tooth voxel density by this ratio. 4 HAPTIC RENDERING In order to provide a realistic force feedback, two kinds of forces are implemented. First one is the contact force and represents the surface to surface interaction. And the second one is the modification force that represents the resistance of the material to modification. The well-known spring model is not suitable to evaluate the contact forces since the data is kept as 3D density information. The location of the surface (thus the elastic deformation of the surface due to tool interaction) cannot be evaluated. However at the tooth surfaces the density gradient has relatively greater values due to sudden density changes. Moreover this is valid for the voxels in the neighborhood of the surface, since the density gradient of the voxels are calculated by using a 5x5x5 volumetric kernel. This situation is presented for 1D case in Figure 2. In the Figure 2a, the tool is approaching to a nonempty voxel and it faces with an increasing magnitude of density gradient vector. The direction of the density gradient vector that the tool faces is normal to tooth face and is towards inside the tooth. This study utilizes this fact to model material stiffness and the vectored sum of gradient vectors at the tooth voxels(empty or not empty) occupied by the tool voxels is used to evaluate the contact force by multiplying a negative scale factor. Although a 5x5x5 volumetric kernel is used to evaluate gradient vectors at tooth voxels, neighboring tooth voxels may have distinct gradient vectors due to the discrete data. This fact may cause sudden changes in the tool contact force especially when a tool voxel cross tooth voxel border. To avoid this artifact, the tooth data gradient vector at the tool voxel center is evaluated by trilinear interpolation using the gradient vectors of 8 neighboring tooth voxel of tool center position. Similarly, the modification force is evaluated by summing the gradient vectors of the tooth voxels modified by the tool voxel, Figure 2b. However during this summation the gradient vectors are scaled with the modification ratio discussed in section 3. Then the total modification force is scaled by a negative scale factor, which represents the resistance of the material to modification. However the scale factors used to evaluate contact force and modification force are distinct but both negative. (a) (b) Figure 2: 1D representation of density, density gradient around the traveling tool 5 GRAPHIC RENDERING Mainly two distinct graphical rendering approaches are implemented to render the volumetric tooth data to compare speed performance. First approach is the ray casting [12, 13] on GPU and includes iso-surface and volume rendering techniques by ray casting. As a second approach, marching cubes [11] based iso-surface and volume rendering techniques are implemented on CPU. 5.1 Ray Casting on GPU Ray casting [12, 13] method depends on the idea of sending rays from optic center of the camera through each pixel on the image plane. When the stopping condition is satisfied the ray is stopped. The color of the pixel is decided according to the data gathered on the ray s path during traversal. This approach may be utilized to display both surface and volumetric data and it provides better visualization than the classical approaches in existence of shiny surfaces. However, because of the fact that the standard graphics hardware does not have support for rendering the volumetric data directly, the raytracing method is one of the most commonly used techniques to display volumetric data. In this study, to increase the realism of the scene, two distinct fragment programs are developed. These two fragment programs implements the ray casting method to display the volumetric data which is stored in the GPU Texture structure. The first fragment program draws iso-surfaces and the second one displays the whole volumetric data by blending.

4 5.1.1 IsoSurface by Ray Casting on GPU The main idea of this fragment program developed is to draw a bounding box covering the 3D texture in the display loop. The colors and depth values of each pixel on the surfaces of this bounding box are set by casting a ray from the corresponding pixel into the 3D texture in the direction from camera to the pixel. The ray casting operation is stopped when the density value stored in the alpha channel of the GPU Texture just crosses the specified iso-value, and the color of the pixel is set to a specified value by an opacity value of 1. Then pixel based Phong lighting model is applied to determine the diffuse and specular components of the light according to the gradient information gathered from the RGB channel of the GPU Texture. Lastly the depth value of the pixel is corrected according to the z - value of the final ray position which is evaluated using the following equation; 1/ z 1/ F d = 1 (1) 1/ N 1/ F Where, d is the depth value between 0(closest) and 1(farthest) and is written to the depth buffer, z is the final position of the ray, F is the far plane distance and N is the near plane distance. Figure 3: Screenshot of two intersecting volumetric tooth objects rendered by iso-surface ray-casting on GPU. In the case of no iso-value crossing, the color of the pixel is set to black with an alpha value of 0 and the depth is set to the maximum depth value 1. This provides the ability of displaying several intersecting or non-intersecting volumetric objects in the same scene, by applying the ray casting operation independently and allows keeping the volumetric data of the objects in distinct 3D textures (Figure 3) Blending by Ray Casting on GPU Similar to the preceding fragment program, the aim of this one is displaying volumetric data by ray-casting operation. However, instead of drawing iso-surfaces, this fragment program calculates the color of the pixels by blending a specified color value scaled by the density values of GPU Texture as the ray travels in the volume. The depth value of the pixel is corrected according to the z value of the ray when it first faces a non-zero density value by using equation (1). The diffuse color component is added to the final blended color value according to the gradient vector at the position where the depth is set. Lastly the ray-casting operation is stopped when the blended alpha value saturates. 5.2 CPU-based approaches In order to compare the results of the rendering techniques implemented using fragment programs on GPU, a surface based and a volume rendering technique are implemented on CPU. The iso-surface based rendering technique is achieved by the well-known marching cubes [11] algorithm with some modifications to update only the modified zone. The volume rendering technique is based on rendering the volumetric data by using 3D texture, multi-texturing, blending and slicing Iso-Surface The well-known marching cubes algorithm [11] is used to determine the iso-surface corresponding to the current tooth surface. However to speed up the rendering, this algorithm is modified to run only for the voxels in the Modified Voxels List. The determined triangles by the marching cubes algorithm, corresponding to the iso-surfacing through a voxel, are compiled in a display list and added to the Surface Display List hash table with an index generated using the 3D coordinates of the tooth voxel. The normal vectors of the vertices of the triangles are evaluated by trilinear interpolation using the gradient component of the Tooth Data and vertex coordinates of the generated triangles. In the display loop, the display lists in the Surface Display List are rendered Volume rendering In order to render the scene graphically by using volume rendering technique, 3D textures; Density Texture and Gradient Texture are used. View-aligned slices [14], normal vectors of which are kept constant towards the camera as the camera view changes, are drawn by taking color values from the corresponding coordinates of rotated 3D textures. In order to achieve a realistic lighting, lighting should be calculated for each pixel in the slices drawn, which will prevent the rendering to be real-time. Therefore multitexturing [15] property of OpenGL is used. At first Gradient Texture is mapped to the polygon by calculating the dot product of the Gradient Texture s value and polygon s color value. Then this value is multiplied with the density value of the corresponding voxel from Density Texture. To achieve a realistic 3D view of the tooth, the blending is applied while the slices are drawn back to front. However to speed up the rendering, Density SubTexture and Gradient SubTexture which only include the density and gradient information of the local deformation zone are used to update global 3D textures. Moreover, the number of slices is reduced [16] in case of a camera or object rotation to keep the rendering rate near the real time limit. 6 IMPLEMENTATION AND RESULTS This haptic device integrated dental surgery simulation environment is developed and tested on a Pentium IV 3.2 GHz PC with 2 GB RAM, NVIDIA GeForce 6600 GT graphics hardware and Windows XP operating system. The haptic device used in the system is Sensable Phantom Omni which has 3 DOF force feedback capability.

5 Figure 4: A screenshot during dental operation Two different tooth data [17] with different resolutions are used to simulate dental operations in the developed virtual environment. First one is composed of 256x256x161 voxels and the second one has 128x128x80 voxels and obtained by down sampling the first. In order to increase the speed performance, a data pre-processing step is added to eliminate the empty regions of the data by finding the tightest bounding box during data loading. Table 1, 2 shows the performances of the different methods in a view port with a size of 512x512 pixels in frame per second (fps). The values on the left of the slash show the speed without modification, the right ones shows the speed during modification. Table 1: Frame rates of various graphical rendering techniques for different tool and data size, without pre-processing of data Data Size 128x128x80 256x256x161 Tool Size 10x10x10 16x16x16 10x10x10 16x16x16 CPU Iso 133/ /77 35/29 35/22 CPU Vol 6/6 6/5 2/2 2/1 GPU Iso 13/13 13/13 6/6 6/6 GPU Vol 4/4 4/4 1/1 1/1 that the number of slices drawn is doubled and the act of rotating a larger texture. This shows that for larger data sizes, the usage of GPU based methods will be advantageous. Moreover, according to the graphical results presented in Figure 5, one can state that GPU based ray casting approaches give better image quality due per pixel color and lighting calculation. When compared with the results presented in the previous studies [12, 13], it is obvious that an improvement in speed is achieved if the used hardware and data size are taken into account. The presented graphical outcomes, in Figure 5, show that almost the same rendering quality is obtained. Moreover the speed of GPU based methods is not affected during modification. This yields more stable and robust haptic force feedback. The haptic rendering strategy results in realistic force feedback for representing the surface stiffness during tooltooth contact and for rendering the modification force. However, the change in tool position between two subsequent frames may become large if the frame rate over tool speed ratio is low. In such a case, the force felt by the user exhibits an unrealistic, unstable and discontinuous behavior. Particularly, the tool can be positioned inside the tooth data without any resistive force by giving a sudden displacement to tool, if the gradient vectors of the tooth data around tool voxels for the two subsequent frames are zero. Or the discontinuity in resistance force due to rapid tool movements creates unstable vibrations. This problem obviously arises from low sampling rate of the tool position. It is observed that it is possible to reach higher tool speed without feeling unstable feedback force when the frame rate is high. This shows that for larger data sizes GPU based methods are advantageous since higher frame rates can be achieved Table 2: Frame rates of various graphical rendering techniques for different tool and data size, with pre-processing of data Data Size 128x128x80 256x256x161 Tool Size 10x10x10 16x16x16 10x10x10 16x16x16 CPU Iso 133/ /77 35/29 35/22 CPU Vol 21/21 21/21 8/5 8/4 GPU Iso 40/39 40/39 21/21 21/21 GPU Vol 10/10 10/9 5/5 5/5 The comparison of the results presented in Table 1 and 2 implies that the data pre-processing, which eliminates empty voxels of the data during data loading, creates a considerable improvement in the frame rates of all methods other than CPU Iso. The main reason is that the active size of the 3D texture used is directly reduced by the data preprocessing step and the size of 3D texture used in these methods determines the frame rates. The results presented in table 2 shows that the fastest algorithm is the CPU Iso which is actually marching cubes method. However, using two times larger data size reduces the speed of the marching cubes approximately 4 times, while the speeds of the GPU based methods are halved. The main reason for this outcome is that the ray casting method is affected by the change of size in only one dimension. However the resulting number of triangles in the marching cubes method is squared depending on surface area. Similarly in volume rendering on CPU, the speed is reduced more than 2 times, because of the fact a) b) c) d) Figure 5: Various Screenshots of the Haptic Device Integrated Dental Simulation Environment using a) iso-surface rendering on GPU, b) volume rendering on GPU, c) marching cubes on CPU and d) volume rendering on CPU.

6 7 CONCLUSION In this paper, it is tried to construct a haptic device integrated dental simulation environment. In order to achieve more realistic graphical representations of the simulation environment and to allocate more computational resources to haptic rendering, graphical rendering techniques are implemented on GPU. In the fragment programs developed per-pixel depth buffer modification is added to the standard ray casting methods. This allows displaying more than one intersecting or non-intersecting volumetric objects in the same scene without creating occlusions. With the addition of data pre-processing step, better speed performances are achieved. Also higher frame rates are obtained for GPU based ray tracing methods, if compared with the results presented in the previous studies [12, 13]. The comparison of the performance results of the CPU and GPU based rendering techniques implies that GPU based methods are less affected from the size of data. Moreover the data modification does not inhibit their performance. Considering these outcomes, one can state that the GPU based techniques is more suitable to be used with haptic rendering for large data sizes. Although a realistic haptic force feedback is achieved for tool-tooth contact and tooth modification forces at higher frame rate over tool speed ratios, the proposed haptic rendering strategy is not appropriate for evaluating the modification forces, because of the fact that the modification force is calculated after the modification. In fact the modification should be determined using the applied force as in real case. Thus modification strategy needs improvement. For further improvements in graphical and haptic rendering parallel processing strategy may be implemented to separate haptic and graphical rendering. Modification force evaluation for haptic rendering may be re-discussed considering the principles of metal cutting. To further speed up the simulation environment, the graphical rendering strategy may be changed not to clear depth and color bits in case of no camera and object transformation and updating only the pixels corresponding to a smaller volumetric region around the modification area. ACKNOWLEDGEMENTS This study is financially supported by The Scientific and Technological Research Council of Turkey (TUBITAK) (104S607 (SBAG-3072)) and conducted in - Computer Aided Design and Computer Aided Manufacturing Center (METU-CADCAM). REFERENCES [1] Scharver, C. Evenhouse, R. Johnson, A. 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