Image Sampling

Image Scaling

Image sub-sampling

Image sub-sampling

Even worse for synthetic images

Sampling and the Nyquist rate

	Aliasing can arise when you sample a continuous signal or image
		occurs when your sampling rate is not high enough to capture the amount of detail in your image
		Can give you the wrong signal/image—an alias
		formally, the image contains structure at different scales
			called “frequencies” in the Fourier domain
		the sampling rate must be high enough to capture the highest frequency in the image
	To avoid aliasing:
		sampling rate ≥ 2 * max frequency in the image
			said another way: ≥ two samples per cycle
		This minimum sampling rate is called the Nyquist rate

2D example

Subsampling with Gaussian pre-filtering

Subsampling with Gaussian pre-filtering

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Slide 11

Some times we want many resolutions

Gaussian pyramid construction

Image resampling

	So far, we considered only power-of-two subsampling
		What about arbitrary scale reduction?
		How can we increase the size of the image?

Image resampling

	So far, we considered only power-of-two subsampling
		What about arbitrary scale reduction?
		How can we increase the size of the image?

Image resampling

	So what to do if we don’t know

Resampling filters

	What does the 2D version of this hat function look like?

Bilinear interpolation

	A simple method for resampling images

Things to take away from this lecture

	Things to take away from image processing lecture
		An image as a function
		Digital vs. continuous images
		Image transformation:  range vs. domain
		Types of noise
		LSI filters
			cross-correlation and convolution
			properties of LSI filters
			mean, Gaussian, bilinear filters
		Median filtering
		Image scaling
		Image resampling
		Aliasing
		Gaussian pyramids
		Bilinear interpolation