Mutual information based registration of 3D-image volumes on GPU using novel accelerated methods of histogram computation

A digital data processing method of determining mutual information of two images by executing software using a central processing unit (CPU), comprising

• computing a histogram representing a probability that pixel values in a first image coincide with pixel values in a transformation of a second image by a two-pass approach that includes:
• A. a first pass that includes utilizing the graphics processing unit (GPU) that is coupled to the CPU to draw a polygon covering a two-channel first render target comprising pixels each of which has (i) a first channel representing an image intensity of a corresponding pixel from the first image and (ii) a second channel representing an image intensity of a corresponding pixel from the transformation of the second image,
• B. the first pass further including (i) storing in a texture on the GPU locations of the samples in the first image and the transformation of the second image, (ii) storing the first image and the transformation of the second image in respective textures on the GPU, (iii) utilizing the GPU to draw the polygon by the steps of identifying, for each pixel in the two-channel first render target, the location of a corresponding sample point in each of the first and second images, and writing to that pixel in the two-channel first render target intensities of those sample points,
• C. a second pass that includes utilizing the GPU to render a second render target at vertices corresponding to values in pixels of the two-channel first render target,
• D. the second pass further including (i) interpreting the two-channel first render target as a buffer of vertices, (ii) setting up the second render target with N×N pixels and initializing them with zeros, where N represents a maximum binning value for the histogram, and (iii) rendering, for each sample point over which the probability and histogram are to be computed, rendering a single vertex in the second render target using coordinates from the buffer of vertices, and
• E. returning the second render target as representing the histogram.

A digital data processing method of determining mutual information of two images by executing software using a central processing unit (CPU), comprising

• computing a histogram representing a probability that pixel values in a first image coincide with pixel values in a transformation of a second image by a two-pass approach that includes:
• A. a first pass that includes utilizing the graphics processing unit (GPU) that is coupled to the CPU to draw a polygon covering a two-channel first render target comprising pixels each of which has (i) a first channel representing an image intensity of a corresponding pixel from the first image and (ii) a second channel representing an image intensity of a corresponding pixel from the transformation of the second image,
• B. the first pass further including (i) storing the first image and the transformation of the second image in respective textures on the GPU. (ii) utilizing the GPU to draw the polygon by the steps of computing with any of a pixel shader and a vertex shader of the GPU a location of a sample point in each of the first image and the transformation of the second image corresponding to each pixel in the two-channel first render target, and writing to that pixel in the two-channel first render target intensities of those sample points,
• C. a second pass that includes utilizing the GPU to render a second render target at vertices corresponding to values in pixels of the two-channel first render target,
• D. the second pass further including (i) interpreting the two-channel first render target as a buffer of vertices, (ii) setting up the second render target with N×N pixels and initializing them with zeros, where N represents a maximum binning value for the histogram, and (iii) rendering, for each sample point over which the probability and histogram are to be computed, rendering a single vertex in the second render target using coordinates from the buffer of vertices,
• E. returning the second render target as representing the histogram.

In a digital data processing method of determining the mutual information of two images by executing software on a central processing unit (CPU), comprising

• computing a histogram representing a probability that pixel values in a first image coincide with pixel values in a transformation of a second image by a two-pass approach that includes:
• A. a first pass that includes utilizing the graphics processing unit (GPU) that is coupled to the CPU to draw a polygon covering a one-channel render first target,
• B. the first pass further including (i) storing in a texture on the GPU locations of the samples in the first image and the transformation of the second image, (ii) storing the first image and the transformation of the second image in respective textures on the GPU;
• (iii) utilizing the GPU to draw the polygon by the steps of identifying, for each pixel in the one-channel first render target, the location of a corresponding sample point in each of the first and second images, and writing to that pixel a value expressed as
• A(x)*N+B(T(x))
• where
• A(x) denotes a pixel value at sample location x in the first image,
• B(T(x)) denotes a pixel value at sample location x in the transformation of the second image,
• N is a maximum binning value for the histogram,
• C. a second pass that includes utilizing the GPU to render a further, one-dimensional second render target representing a histogram of the one-channel first render target,
• D. interpreting the one-dimensional second render target as a two-dimensional histogram expressed as follows
• p
• A
• ,
• B
• ∘
• T
• ⁡
• (
• a
• ,
• b
• )
• =
• p
• A
• ,
• B
• ∘
• T
• 1
• ⁢
• D
• ⁡
• (
• a
• *
• N
• +
• b
• )
• .