Digital Image Processing Lecture 5. Basic intensity transformations. Log transformation. Negative and Log transformations

Transcription

1 Digital Image ocessing Lectue 5 Basic intensit tansomations Histogam ocessing Thesholding. Basic intensit tansomations s T (.-). onzales & Woods: Chate. - Chate Chate Fo aebac : Add to the age numbes above. onzales & Woods lacs ats o the ollowing toics: Thesholding with the least eo Local thesholding Maia Magnusson, Comute Vision Lab., Det. o Electical Engineeing, Linöing Univesit Fig.. Contast stetching Thesholding unction.. Negative and Log tansomations s T s L (.-) Fig.. (.-) s Log tansomation c log (.-) The log tansomation comesses the dnamic ange o images with lage vaiations in ixel value. Fig.. Oiginal mammogam Moe eas to analze ate negative tansomation Fig..5 Fouie tansom Ate Log tansomation

2 owe-law (amma) tansomations. 5 owe-law tansomations o contast enhancement. 6 s c (.-) Oiginal, too bight c=, =. c=, =. c=, =5., too da Fig..6 Fig..9 iecewise-linea tansomations o contast enhancement. 7 Two s to incease the contast Oiginal image and oiginal colo table Lab tas Contast enhancement with. 8 intensit tansomation Oiginal, too low contast Tansomation unction Result, good contast colo table maniulation Fig..

3 Contast enhancement with intensit tansomation In geneal: s x T Suose that we want to incease the contast o the image: 55 s s, (.-), 55, 8, Contast enhancement with colo table maniulation ixel value () Linea tansomation : 6 65: : 66: 9: 9: 55: R B To D/A-convete and uthe to the sceen. Comutation o the histogam o a small image. The nomalized histogam is a DF, a obabilit unction ( ). Image () Histogam h( )= n 6 The histogam o a digital image with intensit levels in the ange [,L-] is a discete unction h( )=n, whee is the :th intensit value and n is the numbe o ixels in the image with intensit. Denote the total numbe o ixels in the image b NM. Then, the nomalized histogam ( )=n /NM is an estimate o the obabilit o occuence o intensit level in the image. age o (aebac )

4 Histogams o da and light images, esectivel. Histogams o low- and highcontast images, esectivel. Fig..6 Fig..6 The CDF ( ) (cumulative distibution unction) o the nomalized histogam ( ) Discete L Continuous L L L. 5 Histogam equalization I the ollowing intensit tansomation is eomed, the histogam will be constant. s T L L d The ga scale is utilized maximall Automatic. 6 Also Lesson (.-) Nomalized histogam beoe Nomalized histogam ate (.-8) d (.-) Fig..8

5 Image to utilize o oo Also Lesson. 7 Histogam equalization. 8 s L s s s s s L L L L d d Fig..6 Beoe Fig.. Ate Histogam seciication. 9 No exam question, howeve. Result om histogam seciication Histogam seciication. Obtain the nomalized histogam () om the inut image and comute s accoding to (.-) Use the seciied z () in (.-) to obtain (z) Obtain the invese tansomation z= - (s) Obtain the outut image b ist equalizing the inut image and then eoming the invese maing z= - (s) s T L d z L t dt z z z T s (.-) (.-) (.-) Beoe Fig.. Ate Fig..5

6 . Examle o the use o histogam seciication in a maste thesis ht Thesholding A gascale image () is thesholded accoding to: g,, i i white T T. (.-) Blac Image Image Image :s histogam Atewads the images can be analzed in a simila wa seciied to image :s histogam g Fig..8 Histogam T The mid-wa o automatic thesholding initialize T, i T T i T i T i T i i i T T / i i : i age 7 o 76 (aebac ). Baes classiie o aussian unctions d x x,, W d,..., m e,, Assign the atten vecto x to the class with the lagest d x. (.-7) (.-8). Lab tas Also Le m m Fig..

7 To ind the otimal theshold. 5 The least eo o automatic thesholding. 6 Not in &W! The nomalized histogam can be witten: Vi loo o a =T such that: initialize T, i i T,, T i,, i T, i : i T Fig.. Lab tas Also Le Ex Histogam Ex Histogam a scale image a scale image With the mid-wa Theshold = 9 With the least eo Theshold = 8 With the mid-wa Theshold= With the least eo Theshold= 87

8 Conclusions o the two s o automatic thesholding Bette esult with the least eo Less comutations with the mid-wa The theshold om the mid-wa can be used as stating theshold o the least eo What is a good stating theshold o the mid-wa? T. 9 Otsu s, idea i (.-) m m m m m B (.-) i L i i (.-5) Find the Otsu theshold * such that B, the between class vaiance, is maximized m i L i i L i m i i i i i (.-6) (.-7). (.-9) Otsu s algoithm, ate equation maniulation Comute the nomalized histogam o the image Comute the cumulative sums Comute the cumulative means m Comute the global mean Comute the between-class vaiance age 77 o 769 (aebac ), i,,,..., L,,,,..., L i i i,,,,..., L i i Obtain the Otsu theshold * o which B is max i (.-) (.-8) L m i i (.-9) i m m B. (.-7) Otsus algoithm o two thesholds B Fig..5 age 755 o 777 (aebac ) m m m m m m a scale image Maximize the between-class vaiance! * *, max, B B L Histogam (.-5) (.-) Image segmented into egions.

9 D Local thesholding. D Local thesholding. A lot o aveaging g g,,,, i elsewhee i elsewhee T T Thesholding Altenative: lalacenegilteing with a lage ilte Lab tas Constuction o a lalacenegilte o local thesholding. 5 Local and global thesholding. 6 diac ave5 lalaceneg lalaceneg diac ave 5 lalaceneg diac ave OBS! In ealit the iltes much be lage! a scale image Note: In this examle, the aveaging whee eomed onl -D Thesholding with a global I n is the stoe width, &W ecommends a size o 5xn o the D aveaging ilte, Thesholding with a local Fig..9