CODEWITHSUNDEEP
frequencydctcoefficients
t.hicham
t.hicham

Reputation: 45

2D DCT coeficients meaning of a gray scale image

what are the DCT coefficients mean. And what is the difference between a positive and a negative DCT's coefficient for example coeficient 5 and -5. Thanks

Upvotes: 0

Views: 775

Answers (1)

user3344003
user3344003

Reputation: 21627

The DCT is simply a 1-to-1 transformation of the data.

Suppose you have a set of blueprints on paper. You scan them in. Once scanned they are crooked. You use Photoshop or something like it to rotate the image to its aligned to the edges and easier to work with.

The DCT is like a rotation in that it simply makes the image data easier to work with. I have to say that a lot of books make this confusing by adding spectral analysis mumbo-jumbo.

Desirable attributes of the DCT for this purpose are:

  1. That it is a transformation to an orthonormal basis set. If D is the DCT transformation matrix, X is the input and Y is the output so that

    X D = Y

Then there is an inverse matrix Q that gives:

    Y Q = X

And Q is the transpose of D.

Therefore, it is just as easy to go forwards as it is to go backwards with the DCT.

  1. The DCT transformation tends to concentrate the most important image data in one corner of the output matrix. The data at the opposite corner tends to be discardable without noticeably affecting photographic images.

As to your other question, the JPEG input pixels are translated to the range -127 to 128. Your starting values usually have negative values to it's no surprise that you get negative output values. Even if you did have all positive input values you could still get negative output values. There is no real significance between positive and negative values.

Upvotes: 1

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