Resilient image compression and decompression
An image processing method includes selecting an image in fixed storage of a computer and loading the selected image into memory of the computer. The method further includes representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values. Thereafter, the initial two-dimensional array of pixel values may be transformed into a hierarchy of progressively axially decremented two-dimensional arrays of signs and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs. Finally, each of the two-dimensional arrays of signs and each pair of one-dimensional values may be stored in the fixed storage as a compressed form of the selected image.
1. An image processing method comprising:
selecting an image in fixed storage of a computer;
loading the selected image into memory of the computer;
representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values;
transforming the initial two-dimensional array of pixel values into a hierarchy of progressively axially decremented two-dimensional arrays of signs each of positive or negative, and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs by submitting the initial two-dimensional array to a recursive encoding operation that receives as input, a grid of specified dimension and that produces as output, on condition that the grid has a specified dimension of 1×1, a serialized form of the grid, but on condition that the grid has a specified dimension larger than 1×1, a concatenation of two encoded grids of a dimensionality half that of the specified dimension, and a bit stream representative of a sign array accounting for element-wise signs of positive or negative for an absolute value of a sum of the grid and an up-sampled form of a negated form of a decoded form of an output produced by the encoding operation receiving as input a down-sampled form of the grid, the concatenation after all recursive calls to the encoding operation have unwound, defining the hierarchy; and,
storing in the fixed storage each of the two-dimensional arrays of signs and each pair of one-dimensional values as a compressed form of the selected image.
2. The method of claim 1 , wherein the pixel values include at least one color intensity value.
3. The method of claim 2 , wherein each color intensity value is a combination of three eight-bit intensity values of a color space.
4. The method of claim 1 , further comprising:
loading the hierarchy into the memory of the computer; and,
generating a reconstructed two-dimensional array of pixel values from the hierarchy of progressively axially decremented two-dimensional arrays of signs and the pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of sign.
5. The method of claim 1 , further comprising:
loading the hierarchy into the memory of the computer; and,
generating a reconstructed two-dimensional array of pixel values from the hierarchy of progressively axially decremented two-dimensional arrays of signs and the pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of sign by submitting the hierarchy defined by the concatenation to a recursive decoding operation that receives as input, a data stream indicating a dimension, and that produces as output, on condition that the indicated dimension is 1×1, a de-serialized form of the data stream, but on condition that the indicated dimension is greater than 1×1, a grid of pixel values resulting from a summation of (1) an up-sampled form of a first output grid produced by the decoding operation receiving as input a first portion of the de-concatenated concatenation that is of a dimension half that of the indicated dimension, with (2) a product of a deserialized second sign array portion of the de-concatenated concatenation and an up-sampled form of a third output grid produced by the decoding operation receiving as input a third portion of the de-concatenated concatenation that is of a dimension half that of the indicated dimension, the summation after all recursive calls to the decoding operation have unwound, defining the reconstructed two-dimensional array of pixel values.
6. An image processing data processing system comprising:
a host computer with memory and at least one central processing unit (CPU);
fixed storage storing an image; and,
an image processing module comprising computer program instructions executing in the memory of the computer and adapted to perform:
selecting an image in the fixed storage;
loading the selected image into the memory;
representing the loaded image in the memory by the CPU as an initial two-dimensional array of pixel values;
transforming by the CPU the initial two-dimensional array of pixel values into a hierarchy of progressively axially decremented two-dimensional arrays of signs each of positive or negative, and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs by submitting the initial two-dimensional array to a recursive encoding operation that receives as input, a grid of specified dimension and that produces as output, on condition that the grid has a specified dimension of 1×1, a serialized form of the grid, but on condition that the grid has a specified dimension larger than 1×1, a concatenation of two encoded grids of a dimensionality half that of the specified dimension, and a bit stream representative of a sign array accounting for element-wise signs of positive or negative for an absolute value of a sum of the grid and an up-sampled form of a negated form of a decoded form of an output produced by the encoding operation receiving as input a down-sampled form of the grid, the concatenation after all recursive calls to the encoding operation have unwound, defining the hierarchy; and,
storing by the CPU in the fixed storage each of the two-dimensional arrays of signs and each pair of one-dimensional values as a compressed form of the selected image.
7. The system of claim 6 , wherein the pixel values include at least one color intensity value.
8. The system of claim 7 , wherein each color intensity value is a combination of three eight-bit intensity values of a color space.
9. The system of claim 6 , further comprising:
loading the hierarchy into the memory; and,
generating by the CPU in the memory a reconstructed two-dimensional array of pixel values from the hierarchy of progressively axially decremented two-dimensional arrays of signs and the pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of sign.
10. The system of claim 6 , further comprising:
loading the hierarchy into the memory; and,
generating by the CPU in the memory a reconstructed two-dimensional array of pixel values from the hierarchy of progressively axially decremented two-dimensional arrays of signs and the pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of sign by submitting the hierarchy defined by the concatenation to a recursive decoding operation that receives as input, a data stream indicating a dimension, and that produces as output, on condition that the indicated dimension is 1×1, a de-serialized form of the data stream, but on condition that the indicated dimension is greater than 1×1, a grid of pixel values resulting from a summation of (1) an up-sampled form of a first output grid produced by the decoding operation receiving as input a first grid portion of the de-concatenated concatenation that is of a dimension half that of the indicated dimension, with (2) a product of a deserialized second sign array portion of the de-concatenated concatenation and an up-sampled form of a third output grid produced by the decoding operation receiving as input a third portion of the de-concatenated concatenation that is of a dimension half that of the indicated dimension, the summation after all recursive calls to the decoding operation have unwound, defining the reconstructed two-dimensional array of pixel values.
11. A computer program product for image processing, the computer program product including a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a device to cause the device to perform a method including:
selecting an image in fixed storage of a computer;
loading the selected image into memory of the computer;
representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values;
transforming the initial two-dimensional array of pixel values into a hierarchy of progressively axially decremented two-dimensional arrays of signs each of positive or negative, and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs by submitting the initial two-dimensional array to a recursive encoding operation that receives as input, a grid of specified dimension and that produces as output, on condition that the grid has a specified dimension of 1×1, a serialized form of the grid, but on condition that the grid has a specified dimension larger than 1×1, a concatenation of two encoded grids of a dimensionality half that of the specified dimension, and a bit stream representative of a sign array accounting for element-wise signs of positive or negative for an absolute value of a sum of the grid and an up-sampled form of a negated form of a decoded form of an output produced by the encoding operation receiving as input a down-sampled form of the grid, the concatenation after all recursive calls to the encoding operation have unwound, defining the hierarchy; and,
storing in the fixed storage each of the two-dimensional arrays of signs and each pair of one-dimensional values as a compressed form of the selected image.
12. The computer program product of claim 11 , wherein the pixel values include at least one color intensity value.
13. The method of claim 12 , wherein each color intensity value is a combination of three eight-bit intensity values of a color space.
14. The computer program product of claim 12 , further comprising:
loading the hierarchy into the memory of the computer; and,
generating a reconstructed two-dimensional array of pixel values from the hierarchy of progressively axially decremented two-dimensional arrays of signs and the pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of sign.
15. The computer program product of claim 11 , further comprising:
loading the hierarchy into the memory of the computer; and,
generating a reconstructed two-dimensional array of pixel values from the hierarchy of progressively axially decremented two-dimensional arrays of signs and the pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of sign by submitting the hierarchy defined by the concatenation to a recursive decoding operation that receives as input, a data stream indicating a dimension, and that produces as output, on condition that the indicated dimension is 1×1, a de-serialized form of the data stream, but on condition that the indicated dimension is greater than 1×1, a grid of pixel values resulting from a summation of (1) an up-sampled form of a first output grid produced by the decoding operation receiving as input a first portion of the de-concatenated concatenation that is of a dimension half that of the indicated dimension, with (2) a product of a deserialized second sign array portion of the de-concatenated concatenation and an up-sampled form of a third output grid produced by the decoding operation receiving as input a third portion of the de-concatenated concatenation that is of a dimension half that of the indicated dimension, the summation after all recursive calls to the decoding operation have unwound, defining the reconstructed two-dimensional array of pixel values.