Fast volumetric rendering of NURBS-based surfaces Andreas Maier Chair of Pattern Recognition (Computer Science 5) Friedrich-Alexander-University Erlangen-Nuremberg Monday, 07 September 2015

Motivation  High spatial resolution scanning of the knee is currently only possible in a laying position  Knee pain often only occurs when the knee is under pressure (i.e. the knee bears weight)  Only imaging in weight-bearing position allows insights on the structural alterations that cause the knee pain => Use a C-arm system to scan in a horizontal trajectory

Motivation  X-ray acquisitions require the use of ionizing radiation  Exposure of X-rays to any human subjects should be minimized  Design and implementation of novel trajectories require a “testing environment”  The “test environment” should be as realistic as possible

Outline Simulation of X-ray images using X-Cat Open CL acceleration based on HHardware tessellation AAppend buffer-based triangle drawing PPixel-based absorption modeling Results Summary and Outlook

Simulation of X-ray images with X-cat  X-Cat is a 3D model of the human body based on the visual human  Supports the simulation of motion:  Breathing  Heart beat  Based on 3D/3D Spline surfaces:  Each surface is 2D that changes over time: (u, v, t)  Each tuple (u, v, t) corresponds to a 3D point (x, y, z)

Simulation of X-ray images with X-cat (2)  Simulation of an x-ray image:  Render 3D volume at time t  Write volume to disk (~500 MB)  Load volume for projection  Project to 2D  Save image to disk  133 to 495 projections required per simulated scan  X-Cat internally employs ray casting and iterative computation of ray spline intersections

Outline Simulation of X-ray images using X-Cat Open CL acceleration based on HHardware tessellation AAppend buffer-based triangle drawing PPixel-based absorption modeling Results Summary and Outlook

Open CL acceleration 3D Points Tessellate spline 2D Points + z Project points List of intersections Draw to “append buffer” Line segments Order intersections along z Resolve overlays Absorption value Evaluate absorption model (mono- or polychromatic)

Hardware Tessellation  Ray / Spline intersection are computationally inefficient  Sampling of points and triangles is fast (Tessellation)  Tessellation in hardware is even faster  Hardware tessellation causes a slight loss in accuracy (here: ~ 28 micron) => Results in a 2D grid of 3D Points

Append buffer-based drawing  Projection of 3D points yields 2D points plus their z coordinate  Use 2D neighborhood relation of the set of points to generate and draw triangles (use any triangle rasterizing algorithm)  Draw points into an “append buffer” like structure  Idea: Save all drawn values

z buffer-based drawing Screen bufferz buffer x y If (z < z buffer(x, y)){ screen buffer(x, y) = color; z buffer(x, y) = z; } x y

2 Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer

3 Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer

4 3 Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer 21 00

54 3 Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer

Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer 21 00

Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer 21 00

Append buffer-based drawing (2) append buffer pixel buffer append buffer pointer 21 00

Append buffer-based drawing (3)  By saving more than one entry per pixel we can store:  ID of the painted object  Depth value  Pointer to the next element in the list  Access to append buffer and pixel counter need to be atomic  Especially access to the global append buffer pointer is expensive  Reading from the append buffer is highly not coalesced

Pixel-based absorption modeling  Read the list from the append buffer  Sort the intersections along z  Remove impossible cases (e.g. three intersections in a row of the same object)  Compute length of line segments along z  Evaluate absorption model

Outline Simulation of X-ray images using X-Cat Open CL acceleration based on HHardware tessellation AAppend buffer-based triangle drawing PPixel-based absorption modeling Results Summary and Outlook

Results – Tesselation (10 6 points) 1DTime [ms]Accuracy [mm] CPU (Java)625- Open CL E-7 Open CL Texture DTime [ms]Accuracy [mm] CPU (Java)2582- Open CL E-7 Open CL Texture DTime [ms]Accuracy [mm] CPU (Java) Open CL E-5 Open CL Texture

Results – Projection X-Cat Heart (23 Splines) 30 x 30 Time [ms] 50 x 50 Time [ms] 100 x 100 Time [ms] Global append buffer Local append buffer Z-Buffer Monochromatic absorption

Outline Simulation of X-ray images using X-Cat Open CL acceleration based on HHardware tessellation AAppend buffer-based triangle drawing PPixel-based absorption modeling Results Summary and Outlook

Summary and Outlook Simulation of X-ray images is required to save dose X-Cat can be accelerated using  Hardware tessellation  Append buffer-based triangle drawing  Pixel-based absorption modeling Computation of one projection can be done in 200 ms Current state of the software still requires some debugging Next: Sample motion fields and volumes

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