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

A method of upsampling for multi-resolution video coding or decoding using a computing device that implements a video encoder or decoder, the computing device including a processing unit and memory, the method comprising:

• with the computing device that implements the video encoder or decoder, performing upsampling of a video picture according to a horizontal upsampling scale factor and a vertical upsampling scale factor, wherein the upsampling comprises computation of an interpolated sample value at horizontal position i and vertical position j in an upsampled array, and wherein the computation comprises:
• computing a derived horizontal sub-sample position x in a manner that is mathematically equivalent in result to the formula x=(i*C+D)>>S, wherein C is derived by approximating a value equivalent to 2S+F multiplied by an inverse of the horizontal upsampling scale factor, and wherein F, C, D, and S are integer values;
• computing a derived vertical sub-sample position y in a manner that is mathematically equivalent in result to the formula y=(j*C+D)>>S, wherein C is derived by approximating a value equivalent to 2S+F multiplied by an inverse of the vertical upsampling scale factor;
• and
• interpolating a sample value at the derived sub-sample position x, y.

A method of upsampling for multi-resolution video coding or decoding using a computing device that implements a video encoder or decoder, the computing device including a processing unit and memory, the method comprising:

• with the computing device that implements the video encoder or decoder, performing upsampling of a video picture according to an upsampling scale factor, wherein the upsampling comprises computation of an interpolated sample value at horizontal position i and vertical position j in an upsampled array, and wherein the computation comprises:
• computing a derived horizontal sub-sample position x in a manner mathematically equivalent in result to the formula x=((2J*i+Q)*C+D)>>S, wherein C is derived by approximating a value equivalent to 2S+F multiplied by an inverse of the upsampling scale factor, and wherein F, C, D, S, J and Q are integers;
• computing a derived vertical sub-sample position y in a manner that is mathematically equivalent in result to the formula y=((2J*j+Q)*C+D)>>S;
• and
• interpolating a sample value at the derived sub-sample position x, y.