Image Processing (Computer Vision) Inverse Photography. Vision in Nature. Image Processing: 2003/2004. See the Big Picture.

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1 Image Processng Computer Vson Inverse Photography World Pctures/Vdeo Photography Image Processng Computer Vson Pctures/Vdeo Somethng Vson n Nature Only smart organsms see! Plants do not have eyes Vsual recognton s an early development process Babes recognze and track the mother very early Most o the bran s nvolved n vson processng Panoramc Mosacs Eercse n stereo years ago See the Bg Pcture Image Processng: 3/ Teacher: Shmuel Peleg <peleg@cs.hu.ac.l> Assstant: Ale Rav-Acha <ales@cs.hu.ac.l> Ozer Horaa:?? <??@cs.hu.ac.l> Tetbook: Gonzalez & Woods Dgtal Image Processng nd Ed. Addson Wesley. Jan Pratt Roseneld. Epected Work: Wrtten Eercses ndvdual computer eercses MATLAB Gradng: Eams: -%; Eercses: 3-% VB- Relevant Courses א-ב - Computer Vson Semnar Sundays א Lschnsk Computer Graphcs Math. Methods n Computer Vson & Graphcs א Werman ב Werman Computer Vson ב Peleg Image Sequence Analyss Image Formaton Lght s emtted by lght source Lght s relected rom obects Relected lght s sensed by eye or by camera Intensty I L r r relectance Lght

2 The Human Eye. World to Retna Proecton The Retna Colors - Electromagnetc Radaton Eye senstvty Rods B / W Cones Color Nerves LIGHT Cosmc Rays X Rays UV Vsble IR Mcrowave Vsble Lght Range: 3-8 nm Mamum Sun Energy: nm Best Atmospherc Transmttance: Vsble Range TV/Rado Mach Bands Spatal Senstvty Response Center o cell Mach Bands Sgnal Locaton on Retna

3 Vsual Illusons Dual Interpretatons What s That? Image Dgtzaton.3 Transormng the 3D world nto D mage Perspectve Proecton Optcs Samplng the Image Plane Fnte number o Pels Quantzng the color/gray-level Fnte number o colors Perspectve Proecton.. Transormng the 3D world nto D mage Contnuous Perspectve Proecton optcs y X Z y Y Z y Y Y X X z y y yz XYZ Z yz Z Dgtal Pctures A Matr o numbers B/W A Matr o trplets RGB Color etc

4 Image Samplng Color/Grey-level Quantzaton Samplng the Image Plane Quantzng the color/gray-level Fnte number o Pels Fnte number o colors Levels Orgnal Reduce by Reduce by Levels Levels CIE Chromatcty Dagram 93 Color Spaces. Cyan Blue Magenta Whte Green Black Red Y - Lumnance Levels Reduce by 3 Yellow. R Y.99.8 I.9..3 G Q..3.3 B Color Quantzaton bts/pel - 8 bts/color - Colors 8 bts/pel - colors bts or R-G-B Optmal Quantzaton - Look Up Table LUT LUT can be or RGB or or YUV LUT k L R L Rk R G L G L Gk B L B L Bk L R L G L B Quantzaton Error LUT k R L R L Rk G B L G L Gk L B L Bk L R L L G B I pel p wth color rgb s coded by k a possble quantzaton error or p s: Ε p r Rk + g Gk + b Bk The total error ntroduced by a LUT s: Ε Ε p p

5 The Hstogram Hstogram - Eample Frequency countng o gray levels Frequency Gray-Level In the lmt o contnuos ntenstes: a contnuous probablty dstrbuton pg Unorm Quantzaton z z Z z k Optmal Quantzaton.. z z Z z k 8 Create a LUT {q q k- }: Borders o sectons: z z z z k- Each [z - z ] represented by q Unorm Quantzaton: q z + z + / z z zk z + / k 8 Mnmze the error: Soluton Prove!: q z+ z p z dz z z+ z p z dz k z+ z z q z q + q p z dz Operaton wth LUT. Stretch 3 Threshold 3 Negatve Hstogram Equalzaton Equal usage o all gray levels # Pels at level Hstogram Gray Level # Pels < level Normalzng to range.. N Pels Range.. K- n # pels at k N s k n s k Cumulatve Hstogram Gray Level Relatve Gray Level r K

6 8 / / Orgnal Hstogram 3/ 3 Gray Level / / / / Seres3 Seres Seres Equalzed Hstogram 3 8 Gray Level Seres Hstogram Equalzaton cont. N Pels Range.. K- Normalzed Cumulatve Occurrence: For every orgnal level : Change ts gray level to n # pels at N s n S K Stretch gray levels back to [.. K-] Equalzaton Eample Grey Level k Normalzed r # Pels n Normalzed n/n Cumulatve Appro Result / / 3.. 3/ 3 / 8.. / 3 3/..8 / / / /..9 /.3.98 / 8.. Total: 9 # o Pels Orgnal Hstogram Relatve # Pels Equalzed Hstogram Eamples or Equalzaton Adaptve Hstogram Equalzaton Derent regons n a sngle mage Eample: Con on whte paper Poor result or Hstogram Equalzaton Do the cons and paper separately How to segment? Compute hstogram n local regons around each pel Adaptve Equalzaton For each pel Compute Hstogram n Neghborhood Transorm only the center pel Go to net pel -D Dscrete Convoluton h g n k k g k g h k g k 3 g3 k h k g k 3 g k

7 D Dscrete Convoluton -D Dscrete Convoluton g 9 g 8 g g g g h g p p p 3 p p p p 8 p p 9 g 3 g g h 9 p g h n m k l k l g k l Queston: What s the complety o convoluton Convolutons: Smoothng Q: What s the average gray level ater convoluton? Smoothng 9 Convolutons: Edge-Detecton Q: What s the average gray level ater convoluton? Edge Detecton Orgnal Image Corrupted Image Fltered Image Orgnal Blood Image Edge Map Convoluton Contnuous g a g a da g a g a da g-a g-a a g a a ga / / *g a g a

8 8 Propertes o Convoluton Commutatve: * g g * Transtve: *g * h * g * h Assocatve: *g + h * g + * h Medan Flterng Replace the value o a pel wth the MEDIAN o ts neghborhood Depends on the denton o neghborhood Nose Cleanng Averagng / Smoothng - Loss o Detal Medan - Blockness Mn Ma Mn/Ma etc. Compare: Average Medan An Appromaton to Dervatves y Laplacan y + Equaton: + Convoluton: Subtractng the Laplacan:

9 Subtractng The Laplacan ' '' '' 9