JPEG compression algorithm | Fourier transformation | Hoffman Encoding

JPEG compression algorithm steps:

Step 1: Convert RGB --> YUV

Because of two important features of human vision: Human vision is not sensitive to sharp changes in the edge, human eyes are sensitive to the brightness information of the image, and the color resolution is weak; A large amount of data bit can be used to describe the brightness of an image, and a small amount of information can be used to describe the color of an image (the concept of Hoffmann coding ). Therefore, the first step in image compression is to convert the image description method (RGB) to (YUV ). Conversion formula:

Y 0.3 0.59 0.11 R
U =-0.15-0.29 0.44g
V 0.61-0.52-0.096 B

 

1.Harmonic Motion:

Is the simplest periodic motion, represented by the sine function y = Asin (ω T + θ) and Cosine Function Y = ACOs (ω T + θ. Y is called the displacement of vibration, and A is calledAmplitude, ω T + Phi or ω T + θ is calledPhase, Phi and θ are calledInitial Phase. T = 2PI/ω is called Simple Harmonic VibrationCycle, F = 1/T is calledFrequency.

2.Synthesis of Harmonic Vibration:

Any complex Periodic Vibration can be regarded as a simple harmonic vibration synthesis from the frequency to an integer multiple. The vibration with the lowest frequency is calledFundamental WaveThe cycle and frequency of the fundamental wave are the same as those of the combined vibration.

3.Time domain and frequency domain:

The function that uses time t as the independent variable and displacement X as the dependent variable is calledTime Domain FunctionsThat is, the vibration waveform. The coordinate system with the frequency as the abscissa and the displacement as the ordinate is calledFrequency DomainThe function described above is calledFrequency Functions.

4.Fourier transform:

Transform the time domain to the frequency domain, which is called FourierPositive transformationThe transformation from the frequency domain to the time domain is called FourierInverse Transformation. Fourier analysis provides a complete method for obtaining frequency domain information.Frequency, amplitude, and phaseTo describe the vibration waveforms in the time domain.

5. If the waveform in the time domain increases rapidly, it means that the wave contains a high frequency.
6. Discrete Fourier TransformationDFT, Short for Fast Fourier TransformationFFT. FFT is a new technology used in the process of Discrete Fourier transformation.

-------------------------------

Fourier transformation is used in JPEG image format, so we can extract this article for further study.

Supnumb

2007-07-28

-------------------------------

Today (07-29), I read all the materials I can find on hand and studied the format and Compression Algorithm of JPEG files, I plan to edit this article into a concise introduction to the JPEG file format.

Supnumb

2007-07-29