Patent Publication Number: US-8126279-B2

Title: Lifting-based view compensated compression and remote visualization of volume rendered images

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 61/003,619, filed on Nov. 19, 2007, the disclosure of which is incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present disclosure relates generally to the field of image visualization, and more specifically to methods and systems for compressing and remotely visualizing volume rendered images. 
     2. Discussion of Related Art 
     With tremendous advances in volume imaging modalities, remote visualization of volumetric images has gained importance in many applications such as medical imaging, nondestructive testing and computational fluid dynamics. 
     In one method of remote visualization, volumetric data is transmitted from a server to a client and one or more images are rendered on the client from the volumetric data for local display. However, image rendering can be a computationally intensive process, often requiring hardware acceleration to achieve a real time viewing experience. Thus, it is likely that the quality and frame rate would be limited in a client side rendering system. 
     In another method of remote visualization, the server performs all the rendering using dedicated hardware based on view-point requests from the client. This client-server model is shown in  FIG. 1 . The server  110  renders images from volumetric data  115  using dedicated hardware (e.g., a hardware accelerated rendering engine). The rendered images are compressed on the server  110 . The compressed rendered images are then transmitted from the server  110  to the client  120 . The client then decompresses the images for local display. For a given server-client bandwidth, an efficient compression scheme is vital for transmitting high quality rendered images. 
     Thus, there is a need for methods and systems that can more efficiently compress rendered images and remotely display those images. 
     SUMMARY OF THE INVENTION 
     An exemplary embodiment of the present invention provides a method for compressing 2D images. The method includes determining a depth map for each of a plurality of sequential 2D images of a 3D volumetric image, determining coordinate transformations between the 2D images based on the depth maps and a geometric relationship between the 3D volumetric image and each of the 2D images, performing a lifting-based view compensated wavelet transform on the 2D images using the coordinate transformations to generate a plurality of wavelet coefficients, and compressing the wavelet coefficients and depth maps to generate a compressed representation of the 2D images. Each depth map includes a plurality of depths that correspond to points in the corresponding 2D image. Each depth corresponds to a depth of a point in the 3D volumetric image that is representative of an intensity of the point in the 2D image. 
     An exemplary embodiment of the present invention includes a system for remotely visualizing an image. The system includes a network, a server workstation, a client workstation, and a client display. The server workstation includes a depth map generation unit, a mapping unit, and a compressing unit. The depth map generation unit determines a depth map for sequential 2D images of a 3D volumetric image. The mapping unit determines coordinate transformations between each of the 2D images based on the depth maps and a geometric relationship between the 3D volumetric image and each of the 2D images. The compressing unit performs a lifting-based view compensated wavelet transform on the 2D images using the coordinate transformations to generate a plurality of wavelet coefficients. The compressing unit compresses the wavelet coefficients and depth maps to generate a compressed representation of the 2D images. The client workstation receives the compressed representation of the 2D images across the network and restores the 2D images from the compressed representation. The client display displays the restored 2D images. 
     An exemplary embodiment of the present invention includes a method for compressing 2D images of a 3D volumetric image. The method includes rendering the 2D images from the 3D volumetric data using ray casting, determining a depth for each point of each 2D image based on a weighted sum of sample point depths in the 3D volumetric image, determining coordinate mappings between each 2D image based on the depths and a geometric relationship between the 3D volumetric image and each of the 2D images, performing a lifting-based view compensated wavelet transform on the 2D images using the coordinate mappings to generate a plurality of wavelet coefficients, and compressing the wavelet coefficients and depths to generate a compressed representation of the 2D images. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments of the invention can be understood in more detail from the following descriptions taken in conjunction with the accompanying drawings in which: 
         FIG. 1  illustrates a conventional model for performing remote visualization of volumetric data; 
         FIG. 2  illustrates a method of compressing rendered images of volumetric data according to an exemplary embodiment of the present invention; 
         FIG. 3  illustrates a method of using ray casting to render images from volumetric data; 
         FIG. 4  illustrates a geometric relationship between a rendered image and a volume; 
         FIG. 5  illustrates a high-level block diagram of a system for remotely visualizing volumetric images, according to an exemplary embodiment of the present invention; 
         FIG. 6  illustrates a system for remotely visualizing volumetric images, according to another exemplary embodiment of the present invention; and 
         FIG. 7  illustrates a lifting-based view compensated wavelet transform according to an exemplary embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     In general, exemplary methods and systems for compressing and remotely visualizing volume rendered images will now be discussed in further detail with reference to  FIGS. 1-7 . 
     It is to be understood that the systems and methods described herein may be implemented in various forms of hardware, software, firmware, special purpose processors, or a combination thereof. In particular, at least a portion of the present invention is preferably implemented as an application comprising program instructions that are tangibly embodied on one or more program storage devices (e.g., hard disk, magnetic floppy disk, RAM, ROM, CD ROM, etc.) and executable by any device or machine comprising suitable architecture, such as a general purpose digital computer having a processor, memory, and input/output interfaces. It is to be further understood that, because some of the constituent system components and process steps depicted in the accompanying figures are preferably implemented in software, the connections between system modules (or the logic flow of method steps) may differ depending upon the manner in which the present invention is programmed. Given the teachings herein, one of ordinary skill in the related art will be able to contemplate these and similar implementations of the present invention. 
       FIG. 2  illustrates a method of compressing rendered images of volumetric data, according to an exemplary embodiment of the present invention. Referring to  FIG. 2 , the method includes the steps of: determining a depth map for each of a plurality of sequential 2D images of a 3D volumetric image (S 201 ), determining coordinate transformations between each of the 2D images based on the depth maps and a geometric relationship between the 3D volumetric image and each of the 2D images (S 202 ), performing a lifting-based view compensated wavelet transform on the 2D images using the coordinate transformations to generate a plurality of wavelet coefficients (S 203 ), and compressing the wavelet coefficients and depth maps to generate a compressed representation of the 2D images (S 204 ). 
     The determination of the depth map and the coordinate transformations will be discussed with reference to  FIG. 3  and  FIG. 4 .  FIG. 3  illustrates a method of using ray casting to render a 2D image (e.g., a frame) from volumetric data.  FIG. 4  illustrates a geometric relationship between the rendered image and the volume. 
     Referring to  FIG. 3 , a ray from each pixel in the image I 2  is passed through the volume. The intensities at sample points on the ray are used for computing the pixel value of a point (x, y) from which the ray emerges. The distance into the volume of the sample point on the ray that best describes the pixel value (e.g., an intensity) of the point (x, y) is referred to as the depth of point (x, y). The depth for each point in the image I 2  may be calculated using a sum of weighted depths of sample points along a corresponding ray cast from the ray casting. The collection of the depths for each point of the image I 2  is referred to as a depth map. 
     Since every sample point on the ray emanating from point (x, y) can have some contribution to the pixel value, a centroid depth value C 2 (x 2 , y 2 ) is computed. Referring to  FIG. 4 , the ray is considered to be along the Z 2  axis. The sample point i distance z 2   i  is weighted by the fractional contribution of the sample point to the pixel value. The equation for determining the red component C 2   r (x 2 , y 2 ) of the centroid depth C 2 (x 2 , y 2 ) may be represented by equation 1 as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
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     The parameters x 2 , y 2 , and z 2  respectively represent the x, y, and z components of the image I 2  at a viewpoint P 2 . A viewpoint is a view of the volume from a particular perspective that yields a 2D image, such as image I 2 . The viewpoint P 2  is parameterized by a distance d 2 , azimuth θ 2  and elevation φ 2  with respect to the X w , Y x , Z x  axes of the world coordinate system of the volume. The line OP 2  subtends angles θ 2  and φ 2  with planes Y w Z w  and X w Z w , respectively. A view coordinate system v 2 ≡X 2 Y 2 Z 2  is formed with view-point P 2  as the origin and line P 2 O as the negative Z 2  axis. The image I 2  of dimension L×L is formed on the plane X 2 Y 2 , where L is the diagonal length of the volumetric data. The dimension L should be set to ensure a sufficient number of pixels in the image to cover the volume at any view-point. 
     The number of sample points on the ray is denoted as N(x 2 , y 2 ). The parameter I 2   r (x 2 ,y 2 ) represents the red component of the image I 2 . The parameter I 2   r (x 2 ,y 2 ) may be represented by the following equation 2: 
                           ⁢           I   2   r     ⁡     (       x   2     ,     y   2       )       =       ∑     i   =   1       N     (       x   2     ,     y   2       )         ⁢       r   ^     ⁡     (       x   ⁢           ⁢   2     ,     y   ⁢           ⁢   2     ,     z   2   i       )           ⁢     
     ⁢           ⁢   where   ⁢     
     ⁢         r   ^     ⁡     (       x   2     ,     y   2     ,     z   2   i       )       =         r   ⁡     (       x   2     ,     y   2     ,     z   2   i       )       *     α   ⁡     (       x   ⁢           ⁢   2     ,     y   ⁢           ⁢   2     ,     z   2   i       )       *     ⁢     ∐     j   =   1       i   -   1       ⁢       (     1   -     α   ⁡     (       x   ⁢           ⁢   2     ,     y   ⁢           ⁢   2     ,     z   2   j       )         )     .                   (   2   )               
The parameter α represents the opacity (e.g., degree of transparency) of a sample point i. A normalized opacity value between 0 and 1 may be used, where 1 represents fully opaque and 0 represents fully transparent.
 
     The green and blue components C 2   g (x 2 ,y 2 ) and C 2   b (x 2 ,y 2 ) may be computed in a manner similar to those discussed above with respect to equation 1 to compute the final centroid depth C 2 (x 2 , y 2 ). Thus, a depth map, including depth values for each non-zero pixel in image I 2  is generated. For pixels with I 2   r (x 2 ,y 2 )=0, the value of C 2   r (x 2 ,y 2 ) is taken to be the depth value at a pixel that is closest to point (x 2 ,y 2 ) in the row x 2 . If any of the depths are still zero, the above approach is repeated on column y 2 . The above approach for generating depth maps can be repeated for each of the sequential 2D images referenced in  FIG. 2  so that a depth map may be determined for each of the sequential 2D images (see S 201  of  FIG. 2 ). 
     Referring to  FIG. 4 , assume another image I 1  (not shown) has been rendered at viewpoint P 1  with parameters d 1 , azimuth θ 1  and elevation φ 2  with respect to the X w , Y x , Z x  axes of the volume of the world coordinate system. The depth map generated for image I 2  and the geometric relationship between I 2  and the volumetric data can be used to predict the pixels values of image I 2  (from image I 1 ). Based on coordinate system transformations, it can be shown that a point, represented as (x 2 , y 2 , z 2 ), in view coordinate system v 2 , can be transformed to the world coordinate representation (x w , y w , z w ) through the matrix multiplication defined by equation 3 as follows: 
                       (           x   w               y   w               z   w             1         )     =       M   2     →     w   *     (           x   2               y   2               z   2             1         )           ⁢     
     ⁢   where   ⁢     
     ⁢       M     2   →   w       =       (           cos   ⁡     (     θ   2     )               -     sin   ⁡     (     θ   2     )         *     sin   ⁡     (     ϕ   2     )                 sin   ⁡     (     θ   2     )       *     cos   ⁡     (     ϕ   2     )               d   *     sin   ⁡     (     θ   2     )       *     cos   ⁡     (     ϕ   2     )                 0         cos   ⁡     (     ϕ   2     )             sin   ⁡     (     ϕ   2     )             d   *     sin   ⁡     (     ϕ   2     )                   -     sin   ⁡     (     θ   2     )                 -     cos   ⁡     (     θ   2     )         *     sin   ⁡     (     ϕ   2     )                 cos   ⁡     (     θ   2     )       *     cos   ⁡     (     ϕ   2     )               d   *     cos   ⁡     (     θ   2     )       *     cos   ⁡     (     ϕ   2     )                 0       0       0       1         )     ⁢           .               (   3   )               
Similarly, the world coordinate system can be transformed to view coordinate system v 1  using M w→1 . Thus, transformations from coordinate system v 2  to v 1  can be accomplished using M 2→1  where M 2→1 =M w→1 *M 2→w .
 
     For the red component of the pixel (x 2 , y 2 ) in image I 2 , the coordinate system v 2  location corresponding to the centroid depth value is (x 2 ,y 2 ,C 2   r (x 2 ,y 2 )) (x 2 ,y 2 ). This representation, can be transformed to view coordinate system v 1  to locate the red component of pixel (x 1   r ,y 1   r ) in image I 1  using equation 4 as follows: 
                       (           x   1   r               y   1   r           )     =         2   →   1       *     (           x   ⁢           ⁢   2               y   ⁢           ⁢   2                 C   2   r     ⁡     (       x   2     ,     y   2       )               1         )         ,           (   4   )               
where    2→1  is a 2×4 matrix containing the first 2 rows of M 2→1 . The same can be repeated for the green and blue components of the pixel (x 2 , y 2 ) to determine the green and blue components of pixel (x 1 , y 1 ). Thus, using depth map C 2 , a geometric mapping (e.g., a transformation) from image I 2  to image I 1  may be obtained. This geometric transformation is denoted μ 2→1 .
 
     The above transformation generation procedure can be repeated for each of the sequential 2D images referenced in  FIG. 2  so that coordinate transformations between each of the 2D images are determined (See S 202  of  FIG. 2 ). 
     Once the coordinate transformations have been determined, as discussed above with reference to  FIG. 2 , a lifting-based view compensated wavelet (LVCWT) transform is performed on the 2D images using the determined coordinate transformations to generate a plurality of wavelet coefficients (S 203 ) and the wavelet coefficients and depth maps are compressed to generate a compressed representation of the 2D images (S 204 ). 
       FIG. 5  is a high-level block diagram of a system of remotely visualizing images, according to an exemplary embodiment of the present invention. The system  500  includes a network  520 , a server workstation  510 , a client workstation  530 , and a client display  535 . 
     The server workstation  510  includes a depth map generation unit  512 , a mapping unit  514 , and a compressing unit  516 . The depth map generation unit  512  determines the depth maps for sequential 2D images of a 3D volumetric image. 
     The mapping unit  514  determines the coordinate transformations between each of the 2D images based on the depth maps and a geometric relationship between the 3D volumetric image and each of the 2D images. 
     The compressing unit  516  performs the lifting-based view compensated wavelet transform on the 2D images using the coordinate transformations to generate a plurality of wavelet coefficients. The compressing unit  516  compresses the wavelet coefficients and depth maps to generate a compressed representation of the 2D images. 
     The client workstation  530  receives the compressed representation of the 2D images across the network and restores the 2D images from the compressed representation. The client display  535  displays the restored 2D images. 
     While not illustrated in  FIG. 5 , the client workstation  530  may further include a client input device (e.g., a mouse, keyboard, etc.) that enables a user to select desired viewpoints. The client workstation  530  may then send the selected viewpoints across the network to the server workstation  510  so that the server workstation  510  can render the 2D images based on the received viewpoints. 
     The performance of the LVCWT transform and the compression of the wavelet coefficients will be described with reference to  FIG. 6 and 7 .  FIG. 6  illustrates a more detailed system for remotely visualizing volumetric images, according to an exemplary embodiment of the present invention. Referring to  FIG. 6 , the system  600  includes a ray casting unit  605 , a depth map generation unit  610 , a compressor  615 , a de-compressor  640 , and a display.  FIG. 7  illustrates a LVCWT transform, according to an exemplary embodiment of the present invention. 
     The ray casting unit  605 , depth map generation unit  610 , and compressor  615  may be disposed within a server workstation. The de-compressor  640  may be disposed within a client workstation connected to the server via a network. The ray casting unit  605  may render the 2D images from volumetric data using the ray casting described above. The ray casting may be performed by a hardware rendering engine included within the ray casting unit  605  of the server. The depth map generation unit  610  may generate depth maps for each of the rendered 2D images as described above. 
     The compressor  615  includes a lifting-based view compensated wavelet transforming unit  620 , a first jpeg2000 decoder  625 , a first jpeg2000 encoder  630 , and a second jpeg2000 encoder  635 . The de-compressor  640  includes a lifting-based view compensated inverse wavelet transforming unit  645 , a first JPEG2000 decoder  650 , and a second JPEG2000 decoder  655 . While not shown in  FIG. 6 , the client workstation may further include a graphical processing unit (GPU) to perform the inverse wavelet transform. 
     The lifting-based view compensated wavelet transforming unit  620  performs a lifting-based view compensated wavelet transform on the rendered images. A lifting-based view compensated wavelet transform is a modified form of a lifting-based wavelet transform. 
     Referring to the lifting-based wavelet transform, assume that images I 0 , I 1 , . . . , I 2k , I 2k+1 , . . . , denote the sequence of rendered images corresponding to view-points P 0 , P 1 , . . . , P 2k , P 2k+1 , . . . , respectively. The rendered images are all of size L×L. The 5/3 wavelet transform across the sequence of rendered images is first considered. In a first lifting step (e.g., a prediction step), the pixel value of point (x, y) in an odd-indexed image is predicted from the pixel value of point (x, y) in the neighboring even-indexed images. The prediction residual (e.g., high pass coefficients) is given by equation 5a as follows:
 
 S   2k+1 ( x,y )=I 2k+1 ( x,y )−½[I 2k ( x,y )+I 2k+2 ( x,y )].   (5a)
 
In a second lifting step (e.g., an update step), the low pass coefficients are obtained using equation 5b as follows:
 
 S   2k ( x,y )=I 2k ( x,y )+¼[ S   2k−1 ( x,y )+ S   2k+1 ( x,y )].   (5b)
 
The high pass coefficients are then scaled by a half.
 
     The lifting-based wavelet transform is preferred over other transforms because it remains invertible, even when non-invertible operations are performed inside the lifting steps. The lifting-based view compensated wavelet transform (LVCWT) is generated by incorporating the previously determined coordinate transformations into the lifting steps. 
     A geometric transformation (e.g., mapping) from image I i  to image I j  is denoted as μ i→j . In a first lifting step of LVCWT, the pixel value of a point (x, y) in I 2k+1  is predicted from pixels μ 2k+1→2k (x,y) and μ 2k+1→2k+2 (x,y) in image I 2k  and image I 2k+2  respectively. The prediction residual is then given by equation 6a as follows:
 
 S   2k+1 ( x,y )=I 2k+1 ( x,y )−½[I 2k (μ 2k+1→2k ( x,y ))+I 2k+2 (μ 2k+1→2k+2 ( x,y ))].   (6a)
 
Since μ 2k+1→2k (x,y) and μ 2k+1→2k+2 (x,y) may be non-integers, interpolation may be used to compute the pixel value. For example, the pixel value may be computed using various interpolation methods such as linear interpolation, cubic-convolution, B-spline interpolation, etc. In the second lifting step, the pixel value of the point (x, y) in I 2k  is updated with pixels μ 2k→2k−1 (x,y) and μ 2k→2k+1 (x,y) in S 2k−1  and S 2k+1  respectively. The resulting low pass coefficients are given by equation 6b as follows:
 
 S   2k ( x,y )=I 2k ( x,y )+¼[ S   2k−1 (μ 2k→2k−1 ( x,y ))+S 2k+1 (μ 2k→2k+1 ( x,y ))].   (6b)
 
The high pass coefficients are then scaled by half.
 
     The high and low pass coefficients may be interpreted as high and low pass coefficient frames. For example, high pass coefficient frames are generated using a coordinate transformation from a first viewpoint to a prior viewpoint and a coordinate transformation from the first viewpoint to a future viewpoint. Low pass coefficient frames are generated using a coordinate transformation from a second viewpoint to a prior viewpoint and a coordinate transformation from the second viewpoint to a future viewpoint. 
     Each coordinate transformation may include a first and a second coordinate transformation. The first coordinate transformation maps points from an origin viewpoint of the 3D volume to a viewpoint of a first one of the images. The second coordinate transformation maps points from a viewpoint of a second one of the images to the origin viewpoint. The first and second coordinate transformations may be represented respectively as first and second matrixes, where the coordinate transformation may be determined by performing a matrix multiplication on the first and second matrixes. As described above, each matrix includes parameters of distance d, azimuth angle θ, and elevation angle φ with respect to a view-point from which the 3D volume is viewed. 
     In the inverse LVCWT, high pass coefficients are first scaled by 2. The lifting steps are then applied in reverse order with signs of the prediction and update values reversed. While an exemplary embodiment of the present invention has been described using the 5/3 wavelet transform, the above approach may be applied to any transform that can be factorized into lifting steps. 
     Referring back to  FIG. 6 , the first jpeg2000 encoder unit  630  compresses the depth maps as side information. Each depth map may be coded independently. The encoder may only use a fraction f of the target bit rate to generate the side information. The second jpeg2000 encoder  635  of the compressor  615  compresses the upper and lower coefficients generated by the wavelet transforming unit  620 . The compressed coefficients and depth maps are sent (e.g., across a network) to the de-compressor  640 . The first JPEG2000 decoder  650  of the de-compressor  640  decodes/decompresses the compressed depth maps. The second JPEG2000 decoder  655  of the de-compressor  640  decodes/decompresses the compressed coefficients. The lifting-based inverse view compensated wavelet transforming unit  645  performs a lifting-based inverse view compensated wavelet transform on the de-compressed/decoded coefficients and depth maps to restore the originally rendered 2D images. The restored images can then be visualized on the display  660 . 
     While  FIG. 6  illustrates the use of JPEG2000 encoders and decoders, the present invention is not limited thereto. For example, the depth maps and coefficients may be compressed/decompressed using any compression/de-compression technique as contemplated by one of ordinary skill in the art. Although not illustrated in  FIG. 6 , the depth maps of the depth map generation unit may be sent directly to the wavelet transforming unit  620 . While embodiments of the present invention have been discussed with respect to ray casting, images may be rendered using other approaches, such as light field rendering or rendering based on graphical processing units (GPUs). 
     It is to be understood that the particular exemplary embodiments disclosed above are illustrative only, as the invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. It is therefore evident that the particular exemplary embodiments disclosed herein may be altered or modified and all such variations are considered within the scope and spirit of the invention.