Patent Publication Number: US-9842424-B2

Title: Volume rendering using adaptive buckets

Description:
BACKGROUND 
     Field of the Invention 
     Embodiments presented herein generally relate to rendering images of three-dimensional (3D) volume and, more specifically to rendering 3D volumes using adaptive buckets. 
     Description of the Related Art 
     Graphic Processing Units (GPUs) are widely used for rendering volumes representing scenes. A volume contains elements that make up a three dimensional scene which may be rendered to produce an image for display such as a computer display, cinematic film, video, etc. GPU hardware executes rendering programs or subprograms, in parallel, which produces the output image(s) in substantially shorter time than a nonparallel computing system. 
     However, a GPU does not dynamically allocate memory. Dynamic memory allocation is a feature in modern programming languages that provides a mechanism to request a portion of available memory when it is required and to release memory when it is no longer required. Doing so allows programs to process data that has varying memory requirements more efficiently. 
     One drawback of a lack of dynamic memory allocation in GPUs is that in some instances the rendering of a volume may fail. For example, if an insufficient amount of memory has been allocated to the GPU, individual rendering processes may exceed their allocated memory and artifacts will result. In this case the rendering must be restarted with either more memory allocated to the GPU, a reduction in the number of pixels processed by the GPU, or both. This problem can be exacerbated if the failure occurs at the very end of the volume processing; requiring a complete re-rendering of the entire volume. 
     SUMMARY 
     One embodiment presented herein includes a method for rendering an image of a three-dimensional (3D) volume. This method may generally include dividing pixels of an image plane into a set of buckets to be rendered. Each bucket corresponds to a two-dimensional (2D) array of pixels. And each bucket includes rendering samples for pixels in the 2D array corresponding to the bucket. This method may also include determining, for each of one or more pixels of each 2D array, a sample count value specifying a maximum number of rendering samples to be included in the bucket corresponding to the 2D array and processing the set of buckets to generate an image of a 3D volume. Processing the set of buckets may generally include selecting a bucket from the set of buckets, generating a plurality of rendering samples used to determine a pixel value for each pixel in the 2D array corresponding to the selected bucket, and including, for each pixel, in the selected bucket, the generated plurality of rendering samples, up to the maximum number of rendering samples. The processing may further include, upon determining rendering samples generated for at least one pixel in the 2D array corresponding to the selected bucket exceeds the sample count value specifying the maximum number of rendering samples, the selected bucket is subdivided into at least two sub-buckets, which may be added to the set of buckets for processing. 
     Another embodiment includes a method for rendering at least a portion of an image of a three dimensional (3D) volume. This method may generally include, for each pixel in the portion of the image, generating one or more samples of the 3D volume used to determine pixel values for the pixel and storing, up to a per-pixel maximum, the samples generated for the pixel in a memory array. This method may further include upon determining a maximum count of samples generated for any of the pixels in the portion of the image exceeds the per-pixel maximum, repeatedly subdividing the portion of the image into at least two portions until the memory array can store the maximum count of samples for pixels in the subdivided portion of the image. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited aspects are attained and can be understood in detail, a more particular description of embodiments of the invention, briefly summarized above, may be had by reference to the appended drawings. 
       It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
         FIGS. 1A and 1B  illustrate an example of volume ray tracing through a scene during image rendering, according to one embodiment. 
         FIGS. 2A and 2B  illustrate a set of bucket memory arrays before and after an adaptive reallocation process, according to one embodiment. 
         FIG. 3  illustrates a method for rendering a 3D volume using a set of buckets, according to one embodiment. 
         FIG. 4  illustrates a method for rendering a bucket using an adaptive bucket size and fixed memory allocation, according to one embodiment. 
         FIG. 5  illustrates a method for subdividing the bucket when the number of samples exceeds the allocated memory, according to one embodiment. 
         FIGS. 6A and 6B  illustrate an example of buckets and sub-buckets during the adaptive subdivision process while rendering a 3D scene volume, according to one embodiment. 
         FIG. 7  illustrates an example computer system configured to carry out volume rendering and adaptive subdivision, according to one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments presented herein provide techniques for efficiently rendering scene volumes having scene dependent memory requirements. A typical scene volume often includes components such as illumination sources and objects. In some instances, to render the scene volume, a ray having an origin at a viewer&#39;s position is traced through a point on an image plane corresponding to a display pixel (also referred to herein as a “pixel”) and into the scene volume. As the ray is traced through the scene volume, samples related to the objects and illumination sources within the scene volume are computed for specific points along the ray. The collected samples are then used to generate intensity and/or color values for the corresponding display pixel. 
     In one embodiment, the pixels corresponding to an image plane are divided into smaller regions of pixels referred to as “buckets.” The number of pixels in each bucket may be determined based on the total amount of memory available to the GPU and the estimated maximum number of samples needed to evaluate each pixel in the bucket. For example, one hundred megabytes of memory may be available to a GPU. It may be estimated that each pixel will require a maximum of 64 samples. As a result, it may be determined that each bucket should be a size equal to 256×256 pixels. 
     In one aspect, each bucket is rendered in order to generate a final rendering of a scene volume. To render an individual bucket, samples are computed at specific points along a ray during ray tracing of each pixel in the bucket. A sample may include any suitable information, including the location or depth of the sample, material properties at the sample location, illumination at the location, or other information. For example, the samples for a particular pixel may include density values for the pixel at several different sample locations. The density values may be used to determine the pixel intensity for a pixel. In one aspect, samples may be generated for a pixel until either the maximum predicted number of samples is reached, or the ray exits the volume. 
     In one embodiment, should the number of samples exceed the estimated maximum number of samples needed to evaluate each pixel, any additional samples are not saved as continuing to save the additional samples runs the risk of overwriting the memory allocated to neighboring pixels. However, the total number of samples required to render the pixel, inclusive of any additional samples, (also referred to as the “sample count”) is recorded. Thereafter, the sample count for each of the pixels in the bucket is checked against the estimated maximum number of samples (also referred to as the “maximum sample count”). If none of the sample counts exceeds the estimated maximum sample count, the pixels in the bucket are determined to have been rendered successfully, and the rendering for a subsequent bucket is performed. However, if a sample count for any pixel exceeds the estimated maximum sample count, the bucket is subdivided into a pair of sub-buckets and the sub-buckets are then re-rendered. 
     In one embodiment, a bucket is divided in half along a selected axis, either the X axis or the Y axis, of the pixels corresponding to the bucket. Should the bucket require further subdivision, the selection of the axis is alternated for each subdivision to prevent narrow “strips”. In re-rendering a sub-bucket, the amount of memory used for the re-rendering may be equal to the original amount of memory allocated to entirety of the corresponding bucket. The sample count for each pixel in the sub-bucket is checked during the re-rendering and if any sample count exceeds the estimated maximum sample count for the sub-bucket, the sub-bucket is subdivided once again and re-rendered. The process of subdividing a bucket continues until all of the pixels in the original bucket are rendered. If other buckets have unsaved samples, such buckets are subdivided and rendered in a comparable manner. Dividing a bucket in half effectively doubles both the memory available for rendering the resulting sub-buckets and the maximum number of samples which can be collected for each pixel in the sub-bucket. 
     The approach described herein is more efficient because it allows for faster rendering of large areas of a scene where the expected number of samples is sufficient to render each pixel in a bucket. Only buckets covering complex geometry or lighting are subdivided. Further, re-rendering a subdivided bucket avoids re-rendering the entire image using new estimates of the necessary memory, over allocating memory, or using smaller, less efficient buckets. Once a bucket has been successfully rendered, the subdivision scheme used during the rendering of the bucket can be saved. The subdivision schemes for the buckets in an image can be reused during an interactive process of rendering and re-rendering the image during the image development process. 
       FIGS. 1A and 1B  illustrate an example of volume ray tracing through a scene during image rendering, according to one embodiment. As shown in  FIG. 1A , scene  100  includes viewer position  102 , image plane  104 , light source  106 , view ray  108 , scene volume  110  and scene object  114 . Viewer position  102  defines a spatial location in scene  100  of a viewer&#39;s eyes or camera used to view an image of a 3D volume. Image plane  104 , represents the image output display. Image plane  104  is positioned between viewer position  100  and scene volume  110 . Image plane  104  is divided into picture elements (pixels). Light source  106  represents illumination data for the scene  100  as well as a source of the illumination data for the sample computations. Examples of light source  106  include point light sources, spotlights, directional lights, area light sources, images, volumetric lights, etc. View ray  108  originates at view position  102 , passes through a pixel position in image plane  104  and through scene volume  110 . Scene object  114  is present in scene volume  110  such that scene object  114  is divided into discrete volume elements, or voxels, along with scene volume  110 . View ray  108  is shown passing through scene object  114 . 
       FIG. 1B  illustrates a sampling process which occurs during ray tracing through scene volume  110 . Once view ray  108  is defined, the rendering process traces view ray  108  through scene volume  110 . During volume rendering samples may be computed for each pixel at defined points along view ray  108 . Each sample specifies an opacity associated with the pixel at a given depth. Depending on the underlying features of the render process, representative sample  116  may be computed at the intersection of view ray  108  with the boundary of a voxel (highlighted by the gray circles), at the voxel center, or based on a stochastic model. If a sampling point is located between voxels a value of the sample may be interpolated from the surrounding voxels, e.g. trilinear interpolation. To render a 3D volume, a phase function or scattering distribution function may be used. For example, well known phase functions include isotropic scattering, a Henyey-Greenstein function or Mie scattering. As another example, a bidirectional reflectance distribution function (BRDF), or variation thereof, may be used. In addition, any kind of information of the illumination in the scene can be used during the sampling process. The diagram of illumination ray  112  shows one method for collecting illumination data for a sample  116 . Sample  116  is the origin for illumination ray  112  with light source  106  providing the direction for illumination ray  112 . Illumination ray  112  is sampled in the same manner as view ray  108  between sample  116  and light  106 . The samples are used to determine a contribution of intervening scene volume  110  and scene object  114  voxels on the illumination of sample  116 . 
     Adaptive Bucket Subdivision 
       FIGS. 2A and 2B  illustrate a set of bucket memory arrays before and after an adaptive reallocation process, according to one embodiment.  FIG. 2A  includes pixel sample buffers  202 ,  204 , and  206 . The sample memory locations in the memory array allocated to each pixel bucket are labeled “Sample 1”, “Sample 2”, etc. accordingly. Array locations that contain sample data are shaded.  FIG. 2A  illustrates a situation where the estimated number of samples for the pixels in the bucket was sufficient. The number of pixels in each bucket is based on the total amount of memory available in the GPUs system and an estimate of the number of samples needed to evaluate each pixel in the bucket. In  FIG. 2A , the available memory in the GPUs system supported a bucket size of 256×256 pixels with an estimate of the maximum number of samples for each pixel in the bucket as 64 samples. Note, for simplicity, pixels are described below as being associated with a single camera ray. However, embodiments may be implemented where several rays are fired per pixel as well as where a single ray might contribute to several output pixels. The term pixel sample buffer is used to broadly refer to volume rendering samples collected using any of these variations. 
     In  FIG. 2A , pixel sample buffer  202  represents the first pixel in the bucket and stores 4 samples. Pixel sample buffer  206  is associated with the last pixel in the bucket, or pixel number 65,536, and pixel sample buffer  206  stores 63 samples. Pixel sample buffer  204  contains 64 samples, which does not exceed the predicted maximum number of samples required for a ray. 
     In one embodiment, a rendering component compares the sample count values to the estimated maximum sample count to determine if any sample count values exceeded the estimated maximum sample count. In the example of  FIG. 2A , none of the examples exceeds the predicted 64-sample maximum, so no further sub-dividing is required. The rendering process completes for this bucket and moves to the next bucket. Additionally, the final subdivision scheme for a particular bucket (i.e., a scheme of any bucket subdivisions that can be reused to render that same bucket, e.g., using different lighting parameters or object properties) is saved for interactive development of images. 
       FIG. 2B  shows the memory allocated to a bucket based on a bucket size of 256×256 pixels and memory for 64 samples for each pixel. In  FIG. 2B , pixel sample buffer  208  corresponds to the first pixel in the bucket, pixel sample buffer  210  corresponds to a pixel sample buffer between pixel sample buffer  208  and pixel sample buffer  212  corresponds to the last pixel in the bucket. As in  FIG. 2A , sample memory locations are indicated by the inset boxes and labeled “Sample 1”, “Sample 2”, etc. accordingly. Similarly, each pixel sample buffer is associated with an independent view ray and the samples for a particular view ray are saved in the associated pixel sample buffer memory locations. Memory locations that contain the sample data are shown as shaded boxes. Both pixel sample buffer  208  and pixel sample buffer  212  are shown with 63 samples which fit in the available memory. However, the view ray associated with pixel sample buffer  210  required 127 sample points during the ray tracing. In one embodiment, the rendering process stores up to the predicted number of samples for tracing a ray (up to 64 in our example). At the same time, the rendering process continues to render such a ray to determine how many samples are needed, without saving samples beyond the predicted maximum number. Only 64 samples are actually saved because storing additional samples would overwrite memory allocated to a different pixel in the bucket. The additional samples are represented by the dashed outline boxes. In this example, the sample count for pixel sample buffer  210  records 127 samples. This value is used in the adaptive subdivision process. 
     On returning from the rendering process, the rendering process determines whether any sample count for a pixel in the bucket exceeded the maximum. As shown in  FIG. 2B , the maximum sample count returned is 127. Because this exceeds the maximum, (i.e., 64), the rendering component divides this bucket in half along a selected dimension. In one embodiment, the selected dimension alternates between an X (horizontal) and Y (vertical) subdivision to avoid thin or “slivered” sub-buckets. Of course, other schemes for diving a bucket into two (or more) sub-buckets may be used as well. For example, one well-known subdivision scheme in 2D is a split in four quadrants. The decision on how to split (2-ways, 4-ways, N-ways and where), can be made if more information of the required sample counts within a bucket is collected. If, for instance, samples counts are returned for every pixel, instead of the maximum of all pixels in a bucket. 
     In  FIG. 2B , the X dimension is selected and each of the two sub-bucket sizes is now 128×256 pixels. Pixel sample buffer  214  and pixel sample buffer  216  represent two buffers in the sub-bucket after the memory has been allocated to each sub-bucket. Before being subdivided the allocated memory could contain a maximum of 64 samples per pixel. After the adaptive subdivision process, pixel sample buffers  214  and  216  show the maximum per pixel memory capacity is now 128 samples or double (2×64) the capacity of the original level bucket. The number of required samples (127) the pixel associated with pixel sample buffer  210  encountered will fit into the reallocated memory associated with pixel sample buffer  214 . 
     When the rendering process for the sub-bucket returns, the rendering component compares the sample counts for the sub-bucket pixels to the new maximum number of samples value. If none of the sample counts exceed the new maximum number of samples in the sub-bucket, the rendering process finishes with the current sub-bucket and moves to the next sub-bucket where the rendering process is repeated. Should a sub-bucket rendering process return with a sample count greater than the estimated maximum number of samples in the sub-bucket, then the adaptive subdivision is repeated. The adaptive sub-division process continues until all the pixels in the original bucket render successfully. The rendering process then moves to the next top level bucket and the entire process is repeated until all the top level buckets have been successfully rendered. The final subdivision scheme for a particular bucket (i.e., a scheme of any bucket subdivisions that can be reused to render that same bucket, e.g., using different lighting parameters or object properties) is saved for interactive development of images. 
       FIG. 3  illustrates a method for rendering a 3D volume using a set of buckets, according to one embodiment Although the method steps are described relative to  FIGS. 1-2, and 4-7 , persons skilled in the art will understand that any system configured to perform the method steps, in any order, falls within the scope of the present invention. 
     As shown, method  300  begins at step  305 , where the rendering component determines the size of a bucket for rendering a 3D volume. In one embodiment, e.g., the bucket size is determined relative to an amount of memory available to the rendering pipeline and a predicted or estimated maximum number of samples needed to evaluate any given pixel. Doing so results in an M×N bucket corresponding to an M×N array of pixels. While not required, M and N may each be a power of 2, e.g., a bucket of 256×128 pixels or 256×256 pixels. For each pixel, the bucket generally corresponds to a portion of memory used to store rendering samples. At step  310 , the rendering component allocates enough memory for the determined bucket size and assigns indices into the resulting memory buffer (i.e., the bucket) for each pixel. That is, the rendering component sets indices to the range of memory used to store samples for each pixel. Again, the amount of memory allocated to each bucket provides enough memory to collect samples used to render each pixel up to the predicted maximum number of samples. If a pixel requires more samples, such additional samples are generated (to allow for the number of samples actually required to be determined), but samples in excess of the maximum are not stored in the bucket. Instead, the bucket with a pixel requiring additional samples is divided into two sub-buckets, allocated memory, and re-rendered. 
     At step  315 , an image of the 3D volume to be rendered is divided into buckets of size M×N as determined at step  305 . At  320 , the rendering component renders each bucket until the image is generated, as described in additional detail below.  FIG. 4  illustrates a method for rendering a bucket using an adaptive bucket size and fixed memory allocation, according to one embodiment. Although the method steps are described relative to elements of  FIGS. 1-3, and 5-7 , persons skilled in the art will understand that any system configured to perform the method steps, in any order, falls within the scope of the present invention. 
     As shown, the method  400  begins at step  402 , where the rendering component selects a bucket to render. The next bucket could be the first top level bucket or the next sub-bucket following a subdivision. At step  404 , pixel data for the bucket is distributed on the GPU processors for parallel ray tracing process. At step  406 , a view ray is computed for a pixel in the bucket selected at step  402 . The origin for view ray generally corresponds to a position of a view camera. At step  408 , sampling begins, e.g., where view ray enters scene volume. Note, however, the advancement of the view need not begin at the intersection with the next voxel, it can be earlier or later, depending on which marching algorithm is used. For example, in one embodiment, a data adaptive marching algorithm is used. Doing so allows the step size to change while marching depending on the complexity of the scene. 
     At each step, the sampling process increments the sample count as shown in step  410  and collects sample values used to render the pixel. At step  412 , the sample count is compared to the maximum number of samples per ray. If the sample count is greater than the maximum sample number, the process does not store the sample values in memory but branches around the storage step and continues processing. If the sample count value is less than or equal to the estimated maximum sample number, at step  414  the sample values are stored in the array. At step  416 , the ray tracing stops. If view ray exits the scene volume, then the ray trace for that view ray is complete and the sample count value is returned to the rendering component. If the view ray did not exit the scene volume, the ray trace is not complete and control returns to step  408 . 
       FIG. 5  illustrates a method for subdividing the bucket when the number of samples exceeds the allocated memory, according to one embodiment. Although the method steps are described relative to  FIGS. 1-4, and 6-7 , persons skilled in the art will understand that any system configured to perform the method steps, in any order, falls within the scope of the present invention. 
     As shown, method  500  begins at step  502 , when the rendering component receives the return values from rendering pixels for one of the initial M×N buckets. At step  504 , the rendering component determines a maximum sample count for the rendered bucket. That is, after obtaining 3D rendering samples for each pixel in the bucket, the rendering component determines the greatest sample count needed for any pixel in that bucket. If the maximum sample count exceeds the estimated maximum sample count (step  506 ), then at least one pixel did not have enough memory to store the rendering samples needed for that pixel. In such a case, a loop begins where the bucket is repeatedly subdivided until bucket sizes having capacity to store the samples needed for each pixel are reached (or alternatively, reaching a minimum bucket size). 
     At step  508 , the bucket with at least one sample count exceeding the maximum is divided into two sub-buckets. As noted, bucket subdivision can be alternated between a horizontal and vertical subdivision. At step  510 , the sample counts for the two subdivided buckets are evaluated. Dividing the bucket into two sub-buckets effectively doubles the number of samples that can be stored for each pixel (given memory allocated to a bucket being held constant). At step  510 , the greatest sample count obtained for any pixel in each of the two sub-divided buckets is compared to an adjusted maximum sample count, e.g., 2× the previous maximum sample count. If the samples can be recorded in the two sub-buckets, then the subdividing stops and the method proceeds to step  512 . 
     Otherwise, if one (or both) of the subdivided buckets still has a pixel with a recorded sample count that exceeds the adjusted maximum, then such bucket(s) may be subdivided again (repeating steps  506 ,  508 , and  510 ). Before doing so, at step  514 , the rendering component may test whether a minimum bucket size has been reached (e.g., 16×16 pixels). Until reaching this limit, the rendering component repeats steps  506 ,  508  and  510  until reaching a bucket size that can accommodate the largest needed sample count. 
     Once the subdivision process is complete, at step  512 , memory is allocated to the subdivided buckets. Note, in one embodiment, this may occur by simply adjusting an indexing scheme into the one large memory buffer to account for the subdivisions. Additionally, the subdivided buckets may be appended to a list of not yet completed buckets to be rendered. 
     At step  514  the bucket and sub-bucket parameters are saved and the ray tracing process continues. This rendering component then selects a next bucket to process until all of the image is fully rendered. 
       FIGS. 6A and 6B  illustrate an example of buckets and sub-buckets during the adaptive subdivision process while rendering a 3D scene volume, according to one embodiment. As shown  FIG. 6A  includes image plane  104 , scene object  114 , buckets  602 ,  604 ,  606 ,  608 , and bucket grid  610 . Image plane  104  contains pixels assigned intensity values as a result of rendering. The rendering process is accelerated by using GPUs and by processing image plane pixels in buckets. Bucket grid  610  overlaid on image plane  104  is shown by the dotted lines. Each box in bucket grid  610  represents a 256 by 256 pixel bucket. The overall dimensions of image plane  104  in this example are 1920 by 804 pixels. In this example, scene object  114  is shown centered relative to image plane  104  and would therefore be rendered in the center of the output display. Buckets  602 ,  604 ,  606 , and  608  illustrate buckets covering portions of scene object  114  and that could have more samples than the estimated maximum number of samples. Therefore buckets  602 ,  604 ,  606 , and  608  represent candidate buckets for adaptive subdivision and memory reallocation during bucket rendering on the GPUs. 
     Referring to  FIG. 6B , adaptive bucket subdivision results are shown for buckets  602 ,  604 ,  606 , and  608 . In addition to the elements in  FIG. 6A ,  FIG. 6B  includes sub-buckets  604 A, sub-bucket  604 B, sub-bucket  608 A, sub-bucket  608 B, and sub-bucket  608 C. Bucket  604  was subdivided because the number of samples needed for bucket  604  exceeded the estimated maximum number of samples. After one bucket subdivision, the allocated memory was sufficient to contain the number of samples required to render the pixels in sub-bucket  604 A and sub-bucket  604 B. Also, the subdivision of bucket  604  into sub-bucket  604 A and sub-bucket  604 B was along the X dimension as shown by the vertical line dividing bucket  604 . For reference,  FIG. 2B  (discussed earlier) depicts the memory allocation, generally, for the bucket subdivision of bucket  604 . 
     The bucket subdivisions made to bucket  608  illustrate a situation which requires a second bucket subdivision. Bucket  608  is first subdivided as the number of samples required to render bucket  608  pixels exceeded the estimated maximum number of samples. The first subdivision is shown by the vertical line dividing bucket  608  in two, and the arrangement of the resulting sub-buckets would have been similar to sub-buckets  604 A and  604 B. However, one of the initial sub-buckets required further subdivision because the allocated memory was insufficient to contain the required number of samples. The second bucket subdivision is shown by the horizontal line dividing the sub-bucket and creating sub-bucket  608 A and sub-bucket  608 C. Sub-bucket  608 B, one of the two original sub-buckets of bucket  608 , did not require further subdivision. The memory allocated to sub-bucket  608 B was sufficient to contain the required number of samples to render the pixels in sub-bucket  608 B. 
     The result of both original sub-buckets requiring further subdivision is shown by bucket  606  in  FIG. 6B . Bucket subdivision is repeated for each sub-bucket, alternating the direction from the containing bucket, or sub-bucket, until the allocated memory is sufficient to contain the required number of samples. The bucket subdivision parameters are saved after a bucket is successfully rendered. The bucket subdivision parameters can be reused during image development to rapidly re-render an image of a 3D volume. For example, the subdivision parameters saved for bucket  602  would contain the information to re-render bucket  602  using the bucket subdivision scheme that includes the second bucket subdivision for one sub-bucket. The bucket subdivision parameters saved for bucket  606  that contain the information to re-render bucket  606  but using the subdivision parameters, which specify the second subdivisions for both sub-buckets. 
       FIG. 7  illustrates an example computer system configured to carry out volume rendering and adaptive subdivision, according to one embodiment. System  700  may be a personal computer, video game console, personal digital assistant, rendering engine, or any other device suitable for practicing one or more embodiments of the present invention. 
     As shown, system  700  includes a central processing unit (CPU)  702  and a system memory  704  communicating via a bus path that may include a memory bridge  705 . CPU  702  includes one or more processing cores, and, in operation, CPU  702  is the master processor of system  700 , controlling and coordinating operations of other system components. System memory  704  stores software applications and data for use by CPU  702 . CPU  702  runs software applications and optionally an operating system. Memory bridge  705 , which may be, e.g., a Northbridge chip, is connected via a bus or other communication path (e.g., a HyperTransport link) to an I/O (input/output) bridge  707 . I/O bridge  707 , which may be, e.g., a Southbridge chip, receives user input from one or more user input devices  708  (e.g., keyboard, mouse, joystick, digitizer tablets, touch pads, touch screens, still or video cameras, motion sensors, and/or microphones) and forwards the input to CPU  702  via memory bridge  705 . 
     Graphics processing units (GPU)  722  are coupled to memory bridge  705  via a bus or other communication path (e.g., a PCI Express, Accelerated Graphics Port, or HyperTransport link); in one embodiment GPU  722  includes at least one graphics processing unit (GPU) and graphics memory (not shown) supporting a display processing function. Graphics memory includes a display memory (e.g., image buffer  730  discussed below) used for storing pixel data for each pixel of an output image. Graphics memory can be integrated in the same device as the GPUs, connected as a separate device with the GPUs, and/or implemented within system memory  704 . 
     As shown GPU  722 , includes rendering component  724 , bucket memory  726 , sample count  728 , scene volume memory  730 , and image buffer  732 . Rendering component  724 , in operation, controls and coordinates rendering operations on GPU  722 . Rendering component  724  manages adaptive bucket subdivision procedures, allocation and assignment of bucket memory  726 , initializing sample count  728 , and evaluating the values returned by sample count  728 . GPU  722  also contains scene volume memory  730 . Scene volume memory  730  is accessible by volume ray tracing processes and contains scene volume  114 , scene object  110 , light  106 , and other relevant scene data, as described above. Scene volume memory  730  can be integrated in the same device as bucket memory  726 , connected as a separate device with GPU  722 , and/or implemented within system memory  704 . Image buffer  732  is used for storing pixel data for each pixel of an output image that is generated by the volume ray tracing processes controlled by the rendering component  724 . 
     GPU  722  periodically deliver pixels to display devices  710  (e.g., a screen or conventional CRT, plasma, organic light-emitting diode (OLED), surface-conduction electron-emitter display (SED), or liquid crystal display (LCD) based monitor or television). Additionally, GPU 2   722  may output pixels to film recorders adapted to reproduce computer generated images on photographic film. GPU  722  can provide display devices  710  with an analog or digital signal. 
     A system disk  714  is also connected to I/O bridge  707  and may be configured to store content and applications and data for use by CPU  702  and GPU  722 . System disk  714  provides non-volatile storage for applications and data and may include fixed or removable hard disk drives, flash memory devices, and CD-ROM, DVD-ROM, Blu-ray, HD-DVD, or other magnetic, optical, or solid state storage devices. 
     A switch  716  provides connections between I/O bridge  707  and other components such as a network adapter  718  and various add-in cards  720  and  721 . Network adapter  718  allows system  700  to communicate with other systems via an electronic communications network, and may include wired or wireless communication over local area networks and wide area networks such as the Internet. 
     Other components (not shown), including universal serial bus (USB) or other port connections, film recording devices, and the like, may also be connected to I/O bridge  707 . For example, an audio processor may be used to generate analog or digital audio output from instructions and/or data provided by CPU  702 , system memory  704 , or system disk  714 . Communication paths interconnecting the various components in  FIG. 7  may be implemented using any suitable protocols, such as PCI (Peripheral Component Interconnect), PCI Express (PCI-E), AGP (Accelerated Graphics Port), HyperTransport, or any other bus or point-to-point communication protocol(s), and connections between different devices may use different protocols, as is known in the art. 
     In one embodiment, GPU  722  incorporates circuitry optimized for graphics and video processing, including, for example, video output circuitry, and constitutes a graphics processing unit (GPU). In another embodiment, GPUs  722  incorporates circuitry optimized for general purpose processing. In yet another embodiment, GPU  722  may be integrated with one or more other system elements, such as the memory bridge  705 , CPU  702 , and I/O bridge  707  to form a system on chip (SoC). In still further embodiments, GPU  722  is omitted and software executed by CPU  702  performs the functions of GPU  722 . 
     Pixel data can be provided to GPU  722  directly from CPU  702 . In some embodiments of the present invention, instructions and/or data representing a scene are provided to a render farm or a set of server computers, each similar to system  700 , via network adapter  718  or system disk  714 . The render farm generates one or more rendered images of the scene using the provided instructions and/or data. These rendered images may be stored on computer-readable media in a digital format and optionally returned to system  700  for display. Similarly, stereo image pairs processed by GPU  722  may be output to other systems for display, stored in system disk  714 , or stored on computer-readable media in a digital format. 
     Alternatively, CPU  702  provides GPU  722  with data and/or instructions defining the desired output images, from which GPU  722  generates the pixel data of one or more output images, including characterizing and/or adjusting the offset between stereo image pairs, in the case of stereoscopic images. The data and/or instructions defining the desired output images can be stored in system memory  704  or graphics memory within GPU 2   722 . For example, CPU  702  could execute a client media player application (not shown) that receives a media stream from a content provider, and transmits the media stream to the GPU  722  for viewing on the display device  710 . In an embodiment, GPU  722  includes 3D rendering capabilities for generating pixel data for output images from instructions and data defining the geometry, lighting shading, texturing, motion, and/or camera parameters for a scene. GPU  722  can further include one or more programmable execution units capable of executing shader programs, tone mapping programs, and the like. 
     CPU  702 , render farm, and/or GPU  722  can employ any surface or volume rendering technique known in the art to create one or more rendered images from the provided data and instructions, including rasterization, scanline rendering REYES or micropolygon rendering, ray casting, ray tracing, image-based rendering techniques, and/or combinations of these and any other rendering or image processing techniques known in the art. 
     It will be appreciated that the system shown herein is illustrative and that variations and modifications are possible. The connection topology, including the number and arrangement of bridges, may be modified as desired. For instance, in some embodiments, system memory  704  is connected to CPU  702  directly rather than through a bridge, and other devices communicate with system memory  704  via memory bridge  705  and CPU  702 . In other alternative topologies GPU  722  is connected to I/O bridge  707  or directly to CPU  702 , rather than to memory bridge  705 . In still other embodiments, I/O bridge  707  and memory bridge  705  might be integrated into a single chip. The particular components shown herein are optional; for instance, any number of add-in cards or peripheral devices might be supported. In some embodiments, switch  716  is eliminated, and network adapter  718  and add-in cards  720 ,  721  connect directly to I/O bridge  707 . 
     In one embodiment, a scene volume and lighting sources are created. After the scene volume dimensions are established, the scene volume is divided into volume elements (voxels). A view position and view direction are defined and an image plane, situated along the view direction between the view position and the scene volume, is established based on parameters that include the pixel resolution of the display. The pixels in an image plane are initially grouped into M×N arrays—referred to above as buckets. The initial grouping of the image plane pixels into buckets generates the top level buckets. An estimate of the number of samples needed to render each pixel in the bucket, along with the bucket size, is used to determine an amount of memory to allocate to render the buckets. For example, assume a value of 256 for M with the number of samples set to 64. The total GPU memory assigned to a bucket is computed based on the bucket size, M, and the estimated number of samples. The rendering component then allocates GPU memory to store samples for pixels in the buckets. 
     The GPU process each bucket by obtaining rendering samples for each pixel in each given bucket. To do so, pixel view rays may be traced from the view position, through the pixel, and on through the scene volume. Rendering samples are obtained along the view ray. After the all pixel samples needed for a each pixel are computed, the rendering component determines a maximum number of samples needed for any pixel in that bucket. If no pixel ray sample count exceeds this maximum, the rendering component advances to the next bucket and repeats the pixel ray processing. 
     If, however, the rendering component determines that at least one pixel required more samples than allocated, the bucket containing that pixel subdivided. In one embodiment, the bucket is divided in half along a vertical or horizontal dimension in an alternating manner. For example, if the top level bucket is 256×256 pixels, and the division is in the X dimension, the resulting sub-bucket dimensions are each 128×256 pixels. The sample counts for the subdivided buckets are then evaluated. Because the bucket now stores samples for one-half of the original number of pixels, the number of samples per pixel is effectively doubled (at least using a scheme that divides each bucket in two equally). If the sample count still exceeds this greater sample count, the bucket is divided again. This process generally repeats until reaching a bucket size with an adequate number of samples or reaching a minimum bucket size. Any subdivided buckets are then added to a list of buckets remaining to be rendered. This rendering process is used to process each of the initial M×N buckets. The final determination of the subdivisions is stored for reuse during interactive image development. Rendering the entire image stops when all the top level buckets have been successfully rendered. 
     In the preceding, reference is made to embodiments of the invention. However, it should be understood that the invention is not limited to specific described embodiments. Instead, any combination of the following features and elements, whether related to different embodiments or not, is contemplated to implement and practice the invention. Furthermore, although embodiments of the invention may achieve advantages over other possible solutions and/or over the prior art, whether or not a particular advantage is achieved by a given embodiment is not limiting of the invention. Thus, the following aspects, features, embodiments and advantages are merely illustrative and are not considered elements or limitations of the appended claims except where explicitly recited in a claim(s). Likewise, reference to “the invention” shall not be construed as a generalization of any inventive subject matter disclosed herein and shall not be considered to be an element or limitation of the appended claims except where explicitly recited in a claim(s). 
     As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     Embodiments of the invention may be provided to end users through a cloud computing infrastructure. Cloud computing generally refers to the provision of scalable computing resources as a service over a network. More formally, cloud computing may be defined as a computing capability that provides an abstraction between the computing resource and its underlying technical architecture (e.g., servers, storage, networks), enabling convenient, on-demand network access to a shared pool of configurable computing resources that can be rapidly provisioned and released with minimal management effort or service provider interaction. Thus, cloud computing allows a user to access virtual computing resources (e.g., storage, data, applications, “software as a service” (SaaS), and even complete virtualized computing systems) in “the cloud,” without regard for the underlying physical systems (or locations of those systems) used to provide the computing resources. 
     Typically, cloud computing resources are provided to a user on a pay-per-use basis, where users are charged only for the computing resources actually used (e.g. an amount of storage space consumed by a user or a number of virtualized systems instantiated by the user). A user can access any of the resources that reside in the cloud at any time, and from anywhere across the Internet. In context of the present invention, a user may access applications (e.g., volume renderers) or related data available in the cloud. For example, volume rendering using adaptive buckets could execute on a computing system in the cloud and render images by adaptively subdividing pixel regions. In such a case, the volume rendering using adaptive bucket could render images by adaptively subdividing pixel regions and store the processed pixels as well as the subdivision scheme for the image at a storage location in the cloud. Doing so allows a user to access this information from any computing system attached to a network connected to the cloud (e.g., the Internet). 
     Advantageously, subdividing buckets when the memory allocated for pixel samples is insufficient, is more efficient, as well as providing a solution to the problem presented by current GPUs that do not allow dynamic memory allocation during the rendering process. The absence of dynamic memory allocation can create situations in which the number of pixels that can be rendered at any one time and with enough memory to assure the collection of the maximum number of deep samples in the scene must be determined through trial and error or large amounts of memory must be allocated very inefficiently. In either case the number of unproductive rendering iterations increases and even more so during interactive image development. Adaptive bucket subdivision allows image rendering to proceed using estimated values for bucket size and the number of samples expected for each bucket pixel. When the estimates are wrong, the portion of the scene generating the problem can be “isolated” and resources “focused” on the problem area by reducing the bucket size and concomitantly increasing the available memory to the sub-bucket. Larger areas that do not exceed the estimates will be processed faster by taking full advantage of the parallel nature of volume ray tracing. Adaptive bucket subdivision obviates the need for re-rendering large areas of the image or possibly the entire image in situations where the required number of samples exceeds the estimated maximum number of samples. The subdivision scheme for an image may be saved for reuse in rendering the image during interactive development of the image or saved to better determine estimates of the maximum sample numbers for buckets. 
     While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.