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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].
![<p>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].</p>](https://knowt-user-attachments.s3.amazonaws.com/4312c8bd-196b-4bf9-a9ba-5a644150e8cd.png)
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.
![<p>The formula [a] represents that the observed signal (Y<em><sub>i</sub></em>) is the sum of the true signal (X<em><sub>i</sub></em>) and additive noise (Z<em><sub>i</sub></em>), where the noise is Gaussian with mean zero and variance σ<sup>2</sup>.</p>](https://knowt-user-attachments.s3.amazonaws.com/e0e34c3f-eafc-4fca-bf8c-8c41b78bfd1f.png)
By averaging N noisy images, temporal filtering reduces the variance of the noise from σ2 to σ2 / N [a].
![<p>By averaging N noisy images, temporal filtering reduces the variance of the noise from σ<sup>2</sup> to σ<sup>2</sup> / N [a].</p>](https://knowt-user-attachments.s3.amazonaws.com/f39b404c-e763-4218-8cc3-edbd28ca499d.png)
