Sampling

• Rasterization = Sample 2D Positions
• Photograph = Sammple Image Sensor Plane
• Video = Samle Time

Sampling Artifacts(Errors / Mistakes )

Jaggies-sampling in space

Moire Patterns - undersampling images

Wagon Wheel Illusion - sampling in time

Behind the Aliasing Artifacts

Signals are changing to fast (high frequency),but sampled too slowly

Atialiasing Idea : Blurring(Pre-Filtering) Before Sampling

Order : Blurring(Pre-Filtering) first, then sampling

difference between two orders

Frequency Domain:

Higher Frequencies Need Faster Sampling

我们发现：当函数本身很快时，如果采样（虚线函数）过慢，就会导致很大的误差（频率慢的函数自然无妨）

Undersampling Creats Frequency Aliases

High-frequency signal is insufficiently sampled : samples erroneously appear to be from a low-frequency signal.

Filtering = Getting rid of certain frequency contents

Filtering = Convolution = Averaging

Convolution Theorey:

Convolution in the spatial domain is equal to multiplication in the frequency domain .

• In the Spatial Domain: Filter by convolution
• In the Frequency Domain:

1. Fourier Transform
2. Multiply by Fourier transform of convolution kernel
3. Inverse transform

Box Function = "Low Pass" Filter

Sampling = Repeating Frequency Contents

Aliasing = Mixed Frequency Contents

when sampling is low ,frequency is faster, the frequency contents are mixed.

How to reduce Aliasing Error?

Increasing sanmpling rate:

increasing the distance between replicas in the Fourier domain

• Higher resolution displays,fraebuffers
• costly & may need very high resolution

Antialiasing

• Making fourier contents "narrower" before repeating
• Filtering out high frequencies before sampling

Antialiasing By Supersampling(MSAA)

Point sampling : One Sample Per Pexel

Supersampling

1. Take $N\times N$ samples in each pixel

2. Average $N \times N$ samples inside each pixel