QUANTIZATION. Outlines. Joseph RONSIN. Definition Scalar quantization. Vector quantization. Definition Distortion Non uniform quantization

Transcription

1 QUANTIZATION by Joseph RONSIN Outlnes Scalar quantzaton Dstorton Non unform quantzaton Vector quantzaton

2 Quantzaton 3 : Dscretsaton of color space One value for a set of values on an nterval Defnng number of ntervals Depends on dsplay (physcal factors) Depends on human vsual propertes (SVH) x Contnuous ampltude Quantzaton Y = Q(x) Dscrete values Quantzaton Topcs: Acquston Processng: reducton of number of grey levels or colors nsde orgnal mage Mnmal Dstorson 4 Interest Reducton of number of bts Dsplayng a pcture wth N bts on a dsplay wth M<N bts Quantzaton types Scalar (lnear or not) Vectoral

3 Type of mages Dfferent Quantzatons and correspondng types of mages bnary I(x,y) { 0,1 } black whte Monochrome or grey I(x,y) [ a, b ] often a = 0 et b = 55 black whte 5 color RVB I(x,y) = I r (x,y) I v (x,y) I b (x,y) Outlnes Scalar quantzaton 6 Dstorton Non unform quantzaton Vector quantzaton

4 Scalar Quantzaton : 7 Quantzaton levels q -1 q q +1 Output Qx d -1 d d +1 decson thresholds Input X Q ( x ) q d x 0 mn d x L max f d x d 1 wth 0,..., L 1 x x, x mn max Scalar Quantzaton Other representaton: Quantzaton Characterstc 8 Unform Quantzaton N reconstructon levels Q(x) Output q N/ q d d +1 d N/-1 X : Input

5 Impossble d affcher l mage. Dstorson Measure of dstorson: objectve crteron 9 For an orgnal mage MxN represented wth B bts dynamc of symbols : B -1 = L x,j and y, pxels of orgnal mage and quantzed mage MSE (Mean Square Error) 1 MSE MN M N 1 j1 x j y j PSNR (Peak Sgnal-to-Nose Rato) PSNR 0log 10 L MSE Non unform leads to ntervals of dfferent szes Adaptaton to dstrbuton of values to quantze Optmal Quantzer Objectve: Fnd best d and q hypothess: optmsaton crteron probablty densty p(x) Crteron of Mean Square Error Non unform Quantzaton Mnmzaton of MSE non unform probablty densty non lnear quantzaton 10

6 Impossble d affcher l mage. Non unform Quantzaton MSE Mnmzaton MAX Quantzer reconstructon levels: centroïds of areas defned by p(x) and decson regons d 1 d decson thresholds d : n the mddle of lmt values of ntervals Symetry wth 0 ( x q ) p( x) dx 0 0 q q d d d 1 et L 1,,..., 0 L 1,,..., 1 L q q 11 Outlnes Scalar quantzaton 1 Dstorton Non unform quantzaton Vector quantzaton

7 Vector Quantzaton Prncpe / example 4 color Image Symbols 00 / 01 / 11 / 10 4 color Image Image: Symbols 0/ VECTOR QUANTIZATION Bnary Dctonnary Q = Index choce for the nearest one of current regon Resultng number of bts Let: Image : matrx MxN I(x,y) [ L mn, L max ] Necessary number of bts for representaton of grey levels n L s K 14 So for scalar quantzaton: L = K Total number of bts: b = M x N x K Then for vector quantzaton: blocks m x n p blocks to code M : dctonary sze b = p x log (M)

8 Bblographe [1] Véronque Coat, Cours et supports de cours, INSA Rennes [] Max Mgnotte, "Tratement d'mages Introducton", support de cours, Unversté de Montréal [3] Grégory Bzarr, "Etude des mécansmes de dégradaton du lumnophore", thèse de doctorat, décembre 003 [4] Sofane Laran, "Percepton et nterprétaton de sectons et blocs ssmques: oculométre et analyse d'mages", Thèse de l'ujf, Mathématques Applquées, Grenoble, 4 Octobre 000. [5] [6] Adelson, «E.H. Lghtness Percepton and Lghtness Illusons». In The New Cogntve Neuroscences, nd ed., M. Gazzanga, ed. Cambrdge, MA: MIT Press, pp , (000). [7] Perre Kornprobst, Cours et supports de cours, INRIA [8] M. Burel, C. Obert, «DICOM Quantfcaton vectorelle», 005 [9] Perre MATHIEU, Cours, DEA ARAVIS, Polytech Nce-Sopha 15 MAX Quantzer Decson thresholds and reconstructon Levels for MAX s quantzer Unforme Gaussen Laplacen Raylegh 16 bts d r d r d r d r

9 MAX Quantzer 17 Unforme Gaussen Laplacen Raylegh bts d r d r d r d r ² 18 END