I don't understand your numbers. A 5mp image uncompressed takes up 15 MB, assuming 3 8-bit colour channels. I'm not sure how RAW works, I assume its uncompressed, and I know some cameras give you 16-bits per channel, which would suggest a 30MB image, how did you end up with a 4.3 MB file? And how on earth did you manage to create a 100 MB jpeg from that?! I'm not sure what you mean by maximize the resolution and colour depth either, could you please explain?

So, at what point would the number of terms in the fourier transformation of a group of pixels constitute more numbers than would be required to store the group of pixels directly in the first place?

never. the number of points in a fourier transform* are actually half as many as are in the original data, but in complex number format. the amount of information is preserved. however, the compression schemes throw out terms that have relatively low amplitude.

taks

PS: technically, since we're talking pixels, this is the discrete-time fourier transform implemented as a fast fourier transform to save computations.

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goodbye richard pryor :(...

Short version: Taks is correct

Long version: Fourier transforms take arrays of complex numbers as their input, and give you arrays of complex numbers back as the output. The 'imaginary' value of a pixel doesn't really mean much, so in the case of image compression, it is set to zero for each pixel before being passed to the FT.

However, when you get your Fourier-transformed data back, the samples have both real and imaginary components that are non-zero, and both are required to reconstruct your image. In effect, for signals that only have real components, the Fourier Transform actually gives you back twice as much meaningful information as you put in.

The reason that a perfect representation of an image can be given by a Fourier transform of the same size is that the last half of the signal is a reflection of the first - the frequency spectrum is 'mirrored' about the sample in the transform that represents half the sampling frequency, and this information can be thrown away.

Sure.

RAW is the digital information read right off the image chip before it's gone through any processing whatsoever. The size is about 4.3Mp. Even the highest-resolution JPG files that would have been build from that RAW file using the camera's on-board processors, would be only around a couple Mp.

RAW is not tecnically "uncompressed." Truth be told, it's losslessly compressed. 100% of the original information is still there, just like PKZIPPing a Word document. JPEG, by comparison, is good, but is lossy - you loose resolution. The more you compress, the more you loose. The problem is, once you compress the info, you can't get it back using JPEG, you can't get it back due the its recursive algorithms. Assumptions are made from the data points, interpixels are created, and you wind up with a good-looking, but smaller version of the file.

When you process a RAW file in Adobe CS, you do so at a much higher resolution than you do so in the camera. This produces a much smoother surface for interpixellation, generating far more accurate results, less effects, and a much larger file.

The end result is a huge file, more than 100Mb, and suitable for flawless 8x10s! (provided you made no flaws during the shooting).

a fourier transform, btw, is nothing more than a linear transformation from one vector space (time representation) to another (frequency representation). any linear transformation (one to one) preserves information.

taks

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goodbye richard pryor :(...