Hiephv - Digital Image Processing - Chapter 1. Gioi Thieu Chung

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1

Hong Vn Hip

B mn K thut my tnh

Vin Cng ngh thng tin v Truyn thng

Email: [email protected]

X l nh

Mc ch

Cung cp cc kin thc c bn v x l nh s

Cung cp cc k nng cn thit gip sinh vin c th vit c cc ng dng x l nh Matlab

C++, C#

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Yu cu

Cc kin thc ton hc Matrix v vector

Xc sut thng k

Cc kin thc v x l tn hiu

K nng lp trnh Matlab

C, C++, C#

Ti liu tham kho Books Digital Image Processing, by: R. C. Gonzalez and R. E.

Woods, 3rd Ed., 2008, Prentice Hall Digital image processing using Matlab by Gonzalez

Journals IEEE Trans. on Image Processing IEEE Transactions on Pattern Analysis and Machine

Intelligence

Conferences ICIP ICIAP CVPR ICPR ICCP ICCV

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nh gi

Thi: 70 %

Bi tp ln: 30 % ti: Tun th 4, 5

Bo v BTL: Tun 15

Chia nhm thc hin: (2 ngi 3 ngi)

Ni dung Chng 1. Gii thiu chung Chng 2. Thu nhn & s ha nh Chng 3. Ci thin & phc hi nh Chng 4. Pht hin tch bin, phn vng

nh Chng 5. Trch chn cc c trng trong

nh Chng 6. Nn nh Chng 7. Lp trnh x l nh bng

Matlab v C

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Chng 1. Gii thiu chung

Khi nim x l nh

Cc vn ca x l nh

Gii thiu mt s ng dng ca x l nh

Matrix v vector

Mt s khi nim c bn

Khi nim x l nh

Khi nim nh

Khi nim nh s

Phn bit nh tnh, nh ng

Khi nim x l nh

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Khi nim nh

Thng tin v vt th hay quang cnh c chiu sng m con ngi quan st v cm nhn c bng mt v h thng thn kinh th gic

Biu din nh v mt ton hc: o F(x, y): trong x, y l ta khng gian 2 chiu

v f l ln ca chi (nh n sc), mu (i vi nh mu)

o Ch : x, y bin thin lin tc v f cng lin tc

Khi nim nh s

nh s l nh thu c t nh lin tc bng php ly mu v lng t ha

pixel

Gray level

Original picture Digital image

f(x, y) I[i, j] or I[x, y]

x

y

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Khi nim nh s (tip)

Khi nim nh s (tip)

Mt nh s thng c biu din nh mt ma trn cc im nh

Trong mi im nh c th c biu din bng 1 bit (nh nh phn)

8 bit (nh a mc xm)

16, 24 bit (nh mu)

nh c biu din nh di dng ma trn cc im nh gi l nh bitmap

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Khi nim nh s (tip)

Mt cch biu din khc ca nh s l di dng vector (nh vector) Khng biu din nh di dng ma trn cc

im nh m hng n i tng trong nh

Thng bao gm cc thnh phn c bn nh hnh trn, ng thng

Circle(100, 20, 20) Line(xa1, ya1, xa2, ya2)

Line(xb1, yb1, xb2, yb2)

Line(xc1, yc1, xc2, yc2)

Line(xd1, yd1, xd2, yd2)

nh bitmap vs nh vector

Vector Biu din cc hnh n

gin

Tnh ton nhanh

ui file: *.EPS, *.AI, *CDR, or *.DWG.

Bitmap

Biu din cc hnh phc tp hn

Tnh ton chm

Hn ch khi zoom, cc php bin hnh

ui file: BMP, JPG

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Phn bit gia nh tnh v chui nh ng (chui nh)

Khi nim x l nh

Nng cao cht lng hnh nh theo mt tiu ch no (Cm nhn ca con ngi)

Phn tch nh thu c cc thng tin c trng gip cho vic phn loi, nhn bit nh.

Hiu nh u vo c nhng m t v nh mc cao hn, su hn.

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Lch s v x l nh

Bt ngun t hai ng dng: nng cao cht

lng thng tin hnh nh v x l s liu

cho my tnh

ng dng u tin l vic truyn thng tin

nh bo gia London v New York vo nm

1920 qua cp Bartlane.

M ha d liu nh khi phc nh

Thi gian truyn nh: T 1 tun 3 ting

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Lch s v x l nh

Anh s c tao ra vao nm 1921 t

bng ma hoa cua mt may in in tin.

(McFarlane)

Anh s c tao ra vao nm 1922 t card

uc l sau 2 ln truyn qua ai Ty

Dng.

Mt vai li co th nhin thy c.

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19

Lch s v x l nh

Anh 15 cp xam c truyn t Lun n n New York, nm 1929. (McFarlane)

Trong khoang thi gian nay, ngi ta chi noi n anh s,

ch cha cp gi n x ly anh s, vi mt ly do n gian:

may tinh cha co.

H thng u tin c kha nng m ha

hnh anh vi mc xm l 5 v tng ln 15

vo nm 1929

20

Lch s v x l nh

Nm 1964, nh mt trng c a v tri t thng

qua cc my chp ca tu Ranger 7 ca Jet Propulsion

Laboratory (Pasadena, California) cho my tnh x

l: Chnh mo.

Anh u tin cua mt trng c chup bi tau

vu tru My Ranger 7, vao 9 gi 09 phut sang

ngay 31/7/1964 (ngun: NASA)

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Lch s v x l nh

Song song vi cac ng dng trong kham pha khng gian, cac k thut x ly nh cng a bt u vao cui nhng nm 1960 va u nhng nm 1970 trong y hc, theo doi tai nguyn trai t va thin vn hc.

n nay x l nh a c mt bc tin di trong nhiu ngnh khoa hc, t nhng ng dng n gin n phc tp.

M hnh h thng x l nh

Nhn t pha ngi dng

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M hnh h thng x l nh

Cc giai on trong x l nh

Camera

Sensor

Thu nhn

nh S ha

Phn tch

nh

i snh

Nhn dng

H

quyt nh Lu tr

Lu tr

M hnh h thng x l nh

Image Acquisition

Discretization/Digitization

Quantization

Compression

Image enhancement

and restoration

Image Segmentation

Feature Selection

Image Representation

Image Interpretation

Phn on nh: phn tach cac i tng trong nh

Rt trch nhng c trng ca nh

Biu din (gan nhan) nh da vao c trng nh

Nhn dng, gii thch

Thit b cm bin thu nhn nh

Lng t ha, nn nh

Nng cao cht lng nh ( tng phn, nhiu,)

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Cc cp trong x l nh

Level 0: Image acquisition (thu nhn nh, ly mu, lng t ha, nn)

Level 1: Image to Image (tng cng nh, khi phc nh, phn on nh)

Level 2: Image to parameter (trch chn c trng: feature extraction, feature selection)

Level 3: Parameter to decision (recognition, interpretation)

M hnh h thng x l nh

Nhng vn cn gii quyt (cn hc)

Image

Acquisition

Image

Enhancement

Image

Restoration

Image

Compression

Image

Segmentation

Representation

& Description

Recognition &

Interpretation

Knowledge Base

Preprocessing low level

Image

Coding

Morphological

Image Processing

Wavelet

Analysis

High-level IP

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Cc vn ca x l nh

Thu nhn nh, s ha nh (image aquisition) H thng chp nh, tn hiu nh H thng s ha nh: Cc phng php ly

mu, lng t ha

Ci thin nh, khi phc nh, lc nhiu (tin x l image pre-processing) Cc php x l im nh

Cc php x l trn min khng gian

Cc php x l trn min tn s

Cc vn ca x l nh Phn tch nh Trch chn c trng (feature extraction)

Biu din, m t nh (image representation, image description)

Phn lp nh (image classification)

Nhn dng nh (image recognition)

M ha, nn nh Cc phng php nn nh, cc chun nn nh

Truyn thng nh

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X l nh v cc lnh vc lin quan

Phn bit mt s khi nim Image formation: object in image out (level 0)

Image processing (level 0, 1) Image in image out

Image analysis (level 1, 2) Image in features out

Computer vision (level 2, 3) Image in interpretation out

Computer graphic Number in image out

Visualization Image in representation out

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Cc ng dng ca x l nh

X l nh v tinh, nh vin thm

Thin vn, nghin cu khng gian, v tr

Thm d a cht

Lnh vc y t

Robot, t ng ha

Gim st, pht hin chuyn ng

Image v video retrieval

Cc ng dng ca x l nh

Bc x ph in t ca nh sng

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Cc ng dng ca x l nh

nh Gamma

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Cc ng dng ca x l nh

nh Gamma a b

c d

nh phng x

(a) Qut b xng

(b) Chp PET (Positron Emission Tomography)

nh thin vn

(c) Chm sao thin nga

nh phn ng ht nhn

(d) S bc x tia Gamma t l phan ng

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35

Cc ng dng ca x l nh (tip)

nh tia X (nh X-Quang)

H thng may chp anh X-Quang

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Anh X-Quang chp lng ngc Anh X-Quang chp ham mt

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H thng may chp anh ct lp CT

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nh tia X

Anh chup ct lp CT

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nh trong di cc tm a c

d

(a) Trng binh thng

(b) Trng bnh than

(c) Chm sao thin nga

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nh hng ngoi

Anh hng ngoi chp u con mo

Anh hng ngoi chp u con cho

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nh hng ngoi

Anh hng ngoi chp b mt trai t. Nhng ni co nh sng mnh la nhng ni co ngun nhit ln.

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nh hng ngoi

Anh hng ngoi chp khng gian trn b mt trai t. Anh nay cho bit lng hi nc tich t trong khng gian, phc v cho vic d bao thi tit.

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Trong vng nh sng nhn thy Ci thin nh


Gim nhiu

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Nhn dng ch vit

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Gii thiu mt s h thng retrieval

Google image similarity

IMARS http://www.alphaworks.ibm.com/tech/imars

MediaMill http://www.science.uva.nl/research/mediamill/demo/

crossbrowser.php

Demo1

Demo2

CuVid http://apollo.ee.columbia.edu/cuvidsearch/login.php

Video summarization

Matrix v vector

Cc php x l nh thc cht l cc php tnh ton trn cc ma trn v cc vectors

review li mt s khi nim trong ton hc v matrix v vector

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Mt s khi nim Khi nim ma trn:

m: dng, n ct

A l vung (square) nu m = n

A l ma trn ng cho (diagonal): nu cc phn t khng nm trn ng cho = 0, c t nht mt phn t trn ng cho 0

A l ma trn n v (identity - I): nu diagonal v cc phn t trn ng cho u = 1

Mt s khi nim (tip) =

Ma trn chuyn v (transpose): dng ct, ct dng, k hiu:

Ma trn vung A i xng (symetric) nu A =

Ma trn nghch o (Inverse): X l inverse ca A nu: XA = I v AX = I

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Mt s khi nim (tip)

Vector ct (column vector) l ma trn mx1

Vector hng (row vector) l ma trn 1xm

Cc php tnh trong ma trn

A, B cng kch thc m x n C = A + B C kch thc m x n v = +

D = A B D kch thc m x n v = -

A(m, n); B(n, q)

C = AB C kch thc m x q v

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Cc php tnh trong ma trn

Cho 2 vector a, b cng kch thc

Tch v hng 2 vector (inner product dot product) c nh ngha nh sau

Khng gian vector (vector spaces)

Khng gian vector c nh ngha l mt tp vector V v tha mn cc iu kin sau y iu kin A o 1. x + y = y + x vi mi vector x v y trong khng

gian

o 2. x + (y + z) = (x + y) + z

o 3. Tn ti duy nht vector 0: x + 0 = 0 + x = 0

o 4. x + (-x) = (-x) + x = 0

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Vector spaces (tp)

iu kin B 1. c(dx) = (cd)x vi mi s c, d v vector x

2. (c + d)x = cx + dx

3. c(x + y) = cx + cy

iu kin C 1x = x

Vector spaces (tip) T hp tuyn tnh (linear combination) ca

cc vectors: 1, 2, ,

Vetor v gi l ph thuc tuyn tnh (linearly dependent) ca cc vectors 1, 2, , nu v c th vit l t hp tuyn tnh ca tp vector ny. Ngc li v l c lp tuyn tnh ca tp vector trn (linearly independent)

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Vector spaces (tip)

Tp vector c s (basis vector set) trong khng gian V cho php to ra vector v bt k trong khng gian V d: khng gian vector 3, vector

C th c to bng t hp tuyn tnh ca 3 vectors c s:

Chun ca vector (vector norm)

Vector norm ca vector x : k hiu cn tha mn cc iu kin sau

Cng thc tnh chun ca vector c nhiu, cng thc hay dng: 2-norm (khong cch Euclidean)

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Quan h gia 2 vector Cosin

Suy ra cch tnh khc ca tch v hng

(inner product)

2 vector gi l trc giao (orthogonal) vi nhau nu v ch nu tch v hng = 0

2 vector gi l trc chun (orthonormal) nu Chng trc giao Norm ca mi vector = 1

Quan h gia cc vectors

Tp cc vector l trc giao nu mi cp 2 vector trc giao tng i mt

Tp cc vector l trc chun nu mi cp 2 vector trc chun tng i mt

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Tnh cht ca vector trc giao

Nu l tp vector trc giao hoc trc chun, th vector v bt k c th c biu din bng t hp tuyn tnh ca cc vector trc giao trn

Tr ring vector ring (Eigen values - eigenvectors)

Cho ma trn vung M, nu tn ti mt s v vector e sao cho:

Th: gi l tr ring ca ma trn M

e: l vector ring ng vi tr ring

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Eigenvalues v eigenvectors (tip)

Cng thc tnh: Da trn biu thc

Trong : det l nh thc

V d: Tm tr ring, vector ring ca ma trn sau:

Eigenvalues v eigenvectors (tip)

Gii:

Vi = 3, tm vector ring tng ng

x = y,

Suy ra: = 1 and = 3

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Tnh cht ca eigenvalues v eigenvectors

Ma trn vung A (m x m) c m eigenvalues phn bit th m eigenvectors tng ng s trc giao vi nhau

M l ma trn vung i xng, A l ma trn c cc hng l cc vector ring ca ma trn M th (nu ma trn vung i xng th cc vector ring s trc chun - orthonormal)

.


M l ma trn vung i xng, A l ma trn c cc hng l cc vector ring ca ma trn M.

D l ma trn ng cho, vi cc phn t trn ng cho l cc tr ring (eigenvalues) ca ma trn M

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A l ma trn vung

.

Mt s khi nim c bn

im nh (pixel)

phn gii (resolution)

Mc xm (gray scale)

Ln cn (neighbors)

Lin thng (conectivity)

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Mt s khi nim c bn (tip)

Pixel: Picture element l n v nh nht cu to nn nh s Mi pixel c ta (x,y) v gi tr cng

sng hoc mu sc ti im

phn gii ca nh: S pixel c trong nh to nn bc nh Thng ghi di dng: m x n o m: s pixel trn chiu rng nh

o n: s pixel trn chiu cao nh

phn gii cng cao, nh cng sc nt


phn gii (resolution)

a b c

d e f

(a) 1024 1024

(b) 512 512

(c) 256 256

(d) 128 128

(e) 64 64

(f) 32 32

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Mc xm (gray)

Mc xm l kt qu ca vic m ho ng vi mt

cng sng ca mi im nh vi mt gi tr s.

Thng thng nh c m ho di dng 16, 32,

64 hay 256 mc.

V d: ti im nh ta (20, 40) c mc xm l

60, ti im nh ta (30, 40) c mc xm l 23,

...

Mt s khi nim c bn (tip) Ln cn (neighbours)

Mt im nh p ti ta (x, y) c

o 4 ln cn ngang - dc ca p: K hiu l N4(p)

(x+1,y), (x-1,y), (x,y+1), (x,y-1)

o 4 ln cn cho ca p: K hiu l ND(p)

(x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1)

o 8 ln cn ca p: K hiu N8(p)

l s kt hp ca N4(p) v ND(p)

(x+1,y), (x-1,y), (x,y+1), (x,y-1),

(x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1)

x

x p x

x

x x

p

x x

x x x

x p x

x x x

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Lin thng: Cc im trong nh gi l lin thng vi nhau nu L ln cn ca nhau

V c cng gi tr mc xm

Documents

Hiephv - Digital Image Processing - Chapter 1. Gioi Thieu Chung