Resampling and picture resizing operations for multi-resolution video coding and decoding

A method of performing upsampling of base layer image data with a computing device that implements an image or video encoder or decoder, wherein the computing device includes a processor and memory, the method comprising, for a position in an upsampled array:

• with the computing device, computing a position in the base layer image data, wherein y indicates a vertical value for the position in the base layer image data, wherein derivation of y includes computation that is mathematically equivalent in result to (j*C+D)>>S, and wherein:
• j indicates a vertical value for the position in the upsampled array;
• C approximates 2S+F multiplied by an inverse of a vertical scale factor;
• D is an offset;
• S is a shift value;
• and
• F is based on a number of bits in a fractional component of y.

A system comprising a processor, memory and computer-readable storage that stores computer-executable instructions for causing the system to perform a method of upsampling, wherein the method comprises, for a position in an upsampled array:

• computing a position in base layer image data, wherein y indicates a vertical value for the position in the base layer image data, wherein derivation of y includes computation that is mathematically equivalent in result to (j*C+D)>>S, and wherein:
• j indicates a vertical value for the position in the upsampled array;
• C approximates 2S+F multiplied by an inverse of a vertical scale factor;
• D is an offset;
• S is a shift value;
• and
• F is based on a number of bits in a fractional component of y.

A system comprising a processor, memory, a wireless communication connection, a display, and computer-readable storage that stores computer-executable instructions for causing the system to perform a method comprising:

• receiving encoded data in a bitstream over the wireless communication connection;
• decoding the encoded data to reconstruct video pictures, including:
• decoding base layer image data;
• upsampling the base layer image data, including for a position in an upsampled array:
• computing a vertical value y for a position in the base layer image data, wherein derivation of y includes computation that is mathematically equivalent in result to (j*C+D)>>S, and wherein j indicates a vertical value for the position in the upsampled array, C approximates 2S+F multiplied by an inverse of a vertical scale factor, D is an offset, S is a shift value, and F is based on a number of bits in a fractional component of y;
• computing a horizontal value x for the position in the base layer image data, wherein derivation of x includes computation that is mathematically equivalent in result to (i*C′+D′)>>S′, and wherein i indicates a horizontal value for the position in the upsampled array, C′ approximates 2S′+F′ multiplied by an inverse of a horizontal scale factor, D′ is an offset that can be the same or different as D, S′ is a shift value that can be the same or different as S, and F′ is based on a number of bits in a fractional component of x;
• selecting a vertical filter based on F least significant bits of y and selecting vertical integer positions to be filtered based on remaining bits of y, wherein vertical interpolation of the base layer image data uses the vertical filter at the vertical integer positions;
• and
• selecting a horizontal filter based on F′ least significant bits of x and selecting horizontal integer positions to be filtered based on remaining bits of x, wherein horizontal interpolation of results of the vertical interpolation uses the horizontal filter at the horizontal integer positions;
• and
• decoding an enhancement layer;
• and
• outputting the reconstructed video pictures on the display.