CS 450: Level operations - Part 1

CS 450: Level operations - Part 1 includes point processing; adding a constant; amplification, linear level operators; negative; thresholding; quantization; logarithm; exponential; contrast enhancement;...
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CS 450: Level operations - Part 1CS 450 Level Operations - Part 1 1 Point Processing Simplest kind of enhancement: point operations. Process each point independently of the others. All you can do is remap the sample’s value: b0 = f (b) where • b is the value at the point in question • b0 is the new value in the processed result • f is a level operationCS 450 Level Operations - Part 1 2 Adding a Constant Simplest level operation: f (b) = b + c for some constant c. c>0 Brighter Image cCS 450 Level Operations - Part 1 3 Amplification (Gain) Another simple level operation is amplification (multiplication): f (b) = ab where • b is the input signal level • a is the amplification gain a>1 amplifies the signal (louder/more constrast) aCS 450 Level Operations - Part 1 4 Linear Level Operators Linear operators combine gain (multiplication) and offset (addition): f (b) = ab + c a is the gain c is the offsetCS 450 Level Operations - Part 1 5 Negative Computing the “negative” of the signal: f (b) = −b Or, to keep range positive: f (b) = bmax − b where b ∈ [0, bmax ] This is simply a line with slope = −1.CS 450 Level Operations - Part 1 6 Thresholding Thresholding a signal:   1 if b > T f (b) =  0 otherwise for some intensity threshold T .CS 450 Level Operations - Part 1 7 Quantization Quantization is choosing different finite values to represent each value of a (possibly analog) input signal. Quantization is usually monotonic: b1 ≤ b2 implies f (b1 ) ≤ f (b2 ) Quantization can be thought of as multi-level thresholding:    q1 if bmin ≤ b < T1       q if T1 ≤ b < T2  2 f (b) = q3 if T2 ≤ b < T3     ..   .    qn if Tn−1 ≤ b ≤ bmaxCS 450 Level Operations - Part 1 8 Logarithm Used to consider relative changes b1 /b2 instead of absolute ones b1 − b2 . f (b) = log b Useful when the dynamic range is large. Examples: • Apparent Brightness • Reichter Scale • Human VisionCS 450 Level Operations - Part 1 9 Exponential Can be used to “undo” logarithmic processing: f (b) = ebCS 450 Level Operations - Part 1 10 Contrast Enhancement Any time we use level operations to make one level more distinguishable from another we call it contrast enhancement. If number of levels stays fixed, contrast enhancement means trading off decreased contrast in one part of our signal range for increased contrast in a range we’re interested in. If we plot our level operation as a function, • all sections where the slope is greater than one increase the contrast in that intensity range. • all sections where the slope is less than one diminish the contrast in that intensity range.CS 450 Level Operations - Part 1 11 Windowing Windowing is contrast enhancement of one part of the signal range. Example: mapping [0,4095] input to [0,255] display The simplest mapping is 256 f (b) = b = b/64 4096 Supposed that we’re interested mainly in the range [500,2000]. Better mapping:     0 if b < 500 f (b) = 256(b − 500)/(2000 − 500) if 500 ≤ b < 2000 ...