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Temporal filtering involves averaging a sequence of images of the same scene to suppress noise and enhance contrast. It assumes that the scene is unchanging and the noise is mean zero and uncorrelated [a].
What are piecewise constant and piecewise continuous assumptions in temporal filtering?
Piecewise constant means the signal (e.g., pixel intensity) remains unchanged over intervals, like a stationary object in a video. Piecewise continuous allows smooth, gradual changes without abrupt jumps, such as a ball slowly moving across a scene.
What does the formula for noise in temporal filtering represent?
The formula [a] represents that the observed signal (Yi) is the sum of the true signal (Xi) and additive noise (Zi), where the noise is Gaussian with mean zero and variance σ2.
By averaging N noisy images, temporal filtering reduces the variance of the noise from σ2 to σ2 / N [a].