Fast integer and directional transforms for data encoding
Methods, apparatuses and systems directed to frequency domain transforms, including fast integer transforms and directional integer transforms. Further disclosed is a video codec that utilizes a novel class of fast integer and directional transforms.
1. A method, comprising
accessing a set of N input values stored in a memory; and
computing a set of N Discrete Cosine Transform (DCT) coefficients, including a DC coefficient, from the N input values by applying an ordered set of operations, the ordered set of operations comprising lifted butterfly operations;
wherein the lifted butterfly operations results in, for any given input value pair comprising a first input value and a second input value, an output value pair comprising the average of the first and second input values and half the difference between the first and second input value, and
wherein during the computing, a DC basis function is maintained to be flat by applying a set of the lifted butterfly operations initially on the N inputs values and then recursively on low pass outputs of a previous stage, and by arranging the ordered set of operations such that the DC coefficient of the DCT coefficients is substantially equal to the average value of the N inputs values.
2. The method of claim 1 wherein the ordered set of operations further comprise a shifted add operation.
3. The method of claim 1 wherein the ordered set of operations further comprise a shifted subtract operation.
4. The method of claim 1 wherein the ordered set of operations is configured based on application of a genetic optimization algorithm.
5. A method comprising
accessing a two-dimensional block of video frame information stored in a memory;
applying, in a first transform pass, a set of 1-dimensional transforms to the pixel values of the two-dimensional block along a first diagonal direction to compute a resulting set of DCT coefficients;
grouping the set of DCT coefficients resulting from the first transform pass into two or more diagonal partitions that are separated along diagonal directions of the block;
applying, in a second transform pass and relative to each diagonal partition, 1-dimensional transforms to respective sets of same order coefficients in the set of DCT coefficients resulting from the first transform pass and grouped in the two or more diagonal partitions; and
applying a 1-dimensional transform having a length corresponding to the number of diagonal partitions to the DC coefficients of the two or more diagonal partitions to compute a single DC coefficient.
6. The method of claim 5 wherein applying the 1-dimensional transforms comprises:
accessing a set of N input values of the block stored in the memory; and
computing a set of N Discrete Cosine Transform (DCT) coefficients, including a DC coefficient, from the N input values by applying an ordered set of operations, the ordered set of operations comprising lifted butterfly operations;
wherein the lifted butterfly operations results in, for any given input value pair comprising a first input value and a second input value, an output value pair comprising the average of the first and second input values and half the difference between the first and second input value, and
wherein during the computing, a DC basis function is maintained to be flat by applying a set of the lifted butterfly operations initially on the N inputs values and then recursively on low pass outputs of a previous stage, and by arranging the ordered set of operations such that the DC coefficient of the DCT coefficients is substantially equal to the average value of the N inputs values.
7. The method of claim 5 further comprising scaling the DCT coefficients resulting from the first transform pass.
8. The method of claim 5 further comprising applying one or more permutation vectors to locate the same order coefficients in the set of DCT coefficients resulting from the first transform pass.