Methods in Image Analysis – Lecture 3 Fourier George Stetten, M.D., Ph.D. U. Pitt Bioengineering 2630 CMU Robotics Institute 16-725 Spring Term, 2006 Frequency in time vs. space Classical “signals and systems” usually temporal signals. Image processing uses “spatial” frequency.
George Stetten, M.D., Ph.D.
U. Pitt Bioengineering 2630
CMU Robotics Institute 16-725
Spring Term, 2006
is the Fundamental Frequency
Frequency is no longer the rate of phase change in time, but rather the amount of phase change per sample.
Sampling frequency is 1 cycle per second, and fundamental frequency is some multiple of that.
Sampling frequency is still 1 cycle per second, but now any frequency are allowed because x[n] is not periodic.
or separating dimensions,
Combine with rotation, have arbitrary projection.
Since the Fourier Transform is also separable, the spectra of the 1D Gaussians are, themselves, separable.
For radially symmetrical functions
Parametric function, usually with constant velocity.
Truncate harmonics to smooth.
Product is defined such that rotation by arbitrary angles from arbitrary starting points become simple multiplication.