Reiss, "The Revised Fundamental Theorem of Moment Invariants", IEEE Trans.
Hu introduced the concept of moments of images into the pattern recognition field in 1962 .
For decades, researchers have extended the concept of moments in various ways.
The excellence of moments is that we can construct invariants of images from them for object recognition.
We encapsulate the image function by another function in the definition of moments.
Moment 5 retains the registral positions of Moment 4 but--in transformation--reorders the pitches, exposing additional symmetries, integrating the result into the motivic web together with a new pitch, G[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII].
Moment 12 is a transformation of Moment 1 and something of a new beginning as well.
Moment 16--the midpoint of the work--transforms the conclusion of Moment 15, unifies it with a registrally transposed, rhythmically transformed Moment 1 (the "return of the non-identical"
Its thesis--the initial four pitches B A G# G--invokes Hexachord 1; the unmistakable G-string registration discloses a partial return of Moment 2.
Moment 19 integrates the B of Moment 18 with a registral displacement of its B [MUSICAL NOTES NOT REPRODUCIBLE IN ASCII] together with pitches C, B and F, last heard together in Moment 6.
This crucial D[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII] is sustained at the end of Moment 22.
As the octatonic collections move to the foreground they generate intricate, symmetrical structures in relatively narrow registral bands in Moments 21-3, the preponderance of Moment 25, and all of Moment 26.
Moment 21 continues the octaronicism of Moment 17, and encapsulates Oct A in the Oct B tetrachord B D[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII] E G.