2020年3月13日星期五

Image aliasing (Moire pattern)

Image sampling and quantization are necessary steps in digital image acquisition and storage.

According to Nyquist's sampling law:

An analog signal can be perfectly reconstructed form its samples as long as the sampling frequency is at least twice the amount of the maximum frequency component present in the analog signal.

That is, the sampling frequency is at least twice the highest frequency in the analog signal. Otherwise, aliasing will occur.




The so-called aliasing, that is, the high-frequency signal that is higher than half of the sampling frequency is mapped to the low-frequency portion of the signal and superimposed with the original low-frequency signal, which affects the integrity and accuracy of the signal. As shown below:


(Image Source: Gonzalez, R. C., Woods, R. E., & Eddins, S. L. (2004). Digital image processing using MATLAB. Pearson Education India.)

This is a schematic diagram of the aliasing effect. The black rectangles with regularly distributed dots in the figure represent photosensitive devices. The white dots represent sampling points, and the black stripes inclined at an angle represent the sampled image. In the superimposed part of the them, you can clearly see several thicker stripes. These stripes are called Moirés pattern. Moirés pattern do not exist in the original image and are the result of aliasing.

The following picture is the same:


(Image Source: Gonzalez, R. C., Woods, R. E., & Eddins, S. L. (2004). Digital image processing using MATLAB. Pearson Education India.)

The low-frequency white fringes are the product of the aliasing effect.

For this case, the "solution" for sampling in the spatial domain is to reduce the frequency of the image / use a higher resolution sensor, or to optically process the image before acquiring it with the sensor.

Reference:
Gonzalez, R. C., Woods, R. E., & Eddins, S. L. (2004). Digital image processing using MATLAB. Pearson Education India.

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