hiephv - digital image processing - chapter 4_2. phan vung anh_thresholding and region based
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Slide Xu ly anhTRANSCRIPT
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Hong Vn Hip
B mn K thut my tnh
Vin Cng ngh thng tin v Truyn thng
Email: [email protected]
X l nh
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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 4. Phn vng nh
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Hai phng php chnh p dng trong phn vng nh Phng php da trn bin: pht hin bin
Phng php da trn vng nh
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Phn vng nh da trn ngng
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Segmentation
Detect discontinuity
Detect similarity
Edge detection
Gradient operator
Zero crossing (LoG)
Edge linking
edge Hough Transform
Optimal thresholding
Region growing
Boundary thresholding
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Phn vng nh da trn ngng (tip)
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C s Khi i tng v nn c nhm li trong
cc vng
La chn mt ngng T c th phn tch cc vng
im nh p(x, y) o Nu f(x, y) > T p(x, y) thuc i tng
o Nu f(x, y) < T p(x, y) thuc nn
C th c nhiu ngng
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Phn vng nh da trn ngng (tip)
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Ly ngng c th coi l bi ton xc nh hm T: T = T[x, y, p(x, y), f(x, y)]
f(x, y): biu din mc xm ca im nh (x,y)
p(x, y): hm m t thuc tnh cc b ca nh
nh sau ly ngng Hai cp (bi-level)
a cp (multi-level) o
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Phn vng nh da trn ngng (tip)
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Vn : lm sao chn gi tr ngng T thch hp Nu T ch ph thuc f(x, y): php ly
ngng ton cc
Nu T ph thuc vo P(x, y) v f(x, y): php ly ngng cc b
Nu T ph thuc x, y: Php ly ngng thch nghi (adaptive thresholding)
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Phn vng nh da trn ngng (tip)
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Phn vng nh da trn ngng (tip)
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Cc phng php ly ngng Ly ngng cng
Ly ngng ton cc
Ly ngng cc b
Ly ngng thch nghi
Ly ngng da trn kim chng
Ly ngng da trn phn nhm (gom nhm)
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Ly ngng cng
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Ly ngng cng (tip)
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Ph thuc ch quan phn tch histogram
D b nh hng bi nhiu
nh hng bi thay i sng
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nh hng ca nhiu
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nh hng ca sng
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nh hng ca sng
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Nhn xt nh c sng ng u ti cc vng s d
tm ngng hn
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Ly ngng ton cc
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Cch tip cn heuristic Bc 1. Xc nh gi tr khi to ca T
(thng l gi tr trung bnh mc xm nh)
Bc 2. Chia nh thnh 2 vng: G1 (gm cc im nh mc xm >= T) v vng 2 (gm nhng im nh mc xm < T)
Bc 3. Tnh gi tr trung bnh mc xm ca G1 l m1, G2 l m2
Bc 4. Cp nht T = (m1 + m2)/2
Bc 5. Quay li bc 2 n khi no
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Ly ngng ton cc (tip)
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Ly ngng thch nghi
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tng Ngng ton cc b nh hng bi
sng, nhiu
Chia nh nh thnh cc phn, sau p dng tm ngng khc nhau cho tng phn nh o Vn :
Chia nh th no l hp l
Tm ngng cho tng phn nh
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Ly ngng thch nghi (tip)
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Ly ngng thch nghi (tip)
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Ly ngng ti u
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Gi s nh c 2 vng chnh r rt (vng i tng v nn)
Mt im (x, y) trong nh c 2 kh nng H0: Khng thuc vng i tng
H1: Thuc vng i tng
Gi z l gi tr mc xm trong nh (z coi nh bin ngu nhin)
Cc xc sut Xc sut tin nghim: P1= p(1); P2= p(0);
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Ly ngng ti u (tip)
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p1(z): hm mt phn b xc sut ca cc pixel trn i tng
p2(z): hm mt phn b xc sut ca cnn (ch rng ta cha c p1(z) v p2(z))
Hm mt phn b xc sut p(z)
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Ly ngng ti u (tip)
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T l ngng c chn phn vng nh (pixel > T nn v ngc li) Xc sut li khi phn vng cc pixel trn
nn l i tng
Xc sut li khi phn vng cc pixel trn i tng l nn
Xc sut li tng:
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Ly ngng ti u (tip)
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Bi ton t ra l tm T , xc sut li nh nht
Gii, p dng lut leibniz cui cng thu c
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Ly ngng ti u (tip)
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gii
Chng ta cn bit p1 v p2, tuy nhin thc t th p1 v p2 l cha bit
gii quyt c 2 cch o C1) Gi s phn b p1 v p2 l cc phn b
Gaussian (khng c gim st)
o C2) Xp x phn b p(z) l cc phn b Gaussian t histogram ca nh (c gim st) sao cho ti thiu ha:
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Ly ngng ti u (tip)
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Phng trnh
Ly lograrit 2 v a phng trnh v
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Ly ngng ti u (tip)
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Ch : c th ly ngng ti u bng cch xp x vi cc hm khc Gaussian Raleigh
Log-normal
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Ly ngng ti u Otsu
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Hm graythresh trong matlab hin ang ci t theo phng php ny
Bi ton Cho nh a mc xm MxN
L mc xm {0, 1, 2, L-1}
ni: s pixel trong nh c mc xm I o MN = n0 + n1 + + nL-1
Histogram chun ha:
Tm ngng t ti u
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Ly ngng ti u Otsu (tip)
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Ly ngng ti u Otsu (tip)
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Vi ngng k, ta c 2 lp pixel
tng: Tm ngng sao cho minimizes the weighted within-class
variance tng t vi vic maximizing the between-class variance
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Ly ngng ti u Otsu (tip)
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Weighed within-class variance
Trong :
w2(t) q1(t)1
2(t) q2 (t) 2
2(t)
q1(t) P(i)i1
t
q2 (t) P(i)i t1
I
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Ly ngng ti u Otsu (tip)
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Class mean
Class variance
1(t) iP(i)
q1(t)i1
t
2(t)iP(i)
q2(t )it1
I
12(t) [i 1(t)]
2 P(i)
q1(t)i1
t
22(t) [i 2(t)]
2 P(i)
q2 (t)it1
I
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Ly ngng ti u Otsu (tip)
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Total variance
V total variance = const
Minimize within-class tng ng vi maximize between-class
2w
2(t) q1(t)[1 q1 (t)][1(t) 2 (t)]
2
Within-class,
from before Between-class, B2(t)
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Ly ngng ti u Otsu (tip)
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Thut ton: Bc 1. Tnh histogram, v xc sut ti mi
gi tr mc xm
Bc 2. Khi to Bc 3. Duyt ln lt cc gi tr ca t t 1
n L-1 o Tnh q1(t); 1 o Tnh
Bc 4. Cp nht ngng t ng vi ln nht
B2(t)
B2(t)
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Ly ngng ti u Otsu (tip)
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Ch c th tnh bng cch qui Khi to:
qui:
B2(t)
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Ly ngng ti u Otsu (tip)
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nh hng ca nhiu n ly ngng Otsu
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nh hng kch thc vng n ly ngng Otsu
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Ci thin ly ngng bng cch kt hp thng tin bin
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Thut ton Tnh gradient hoc laplacian ca nh ban
u
Ly ngng trn nh gradient hoc laplacian loi b cc im nhiu
Nhn nh ban u vi nh gradient hoc nh laplacian xy dng histogram
Ly ngng Otsu ca nh ban u da trn histogram va tm c
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Ci thin ly ngng bng cch kt hp thng tin bin
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Phn vng nh da trn cc thut ton gom nhm
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Mi im nh c i din bi mt vector c trng
Cc c trng c th l Gi tr mc xm Gi tr thnh phn mu sc Cc o cc ln cn (v d gi tr trung bnh
trong ca s chy)
Phn nhm: tin hnh gom cc vector ging nhau vo cng mt nhm
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Phn vng nh da trn cc thut ton gom nhm (tip)
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Cc phng php phn nhm K-means
ISODATA
Thut ton K-means Bc 1. Khi to k tm ca k nhm
Bc 2. Phn loi n im vo k nhm da vo khong cch n cc tm
Bc 3. Tnh li tm ca mi nhm (gi tr trung bnh), quay li bc 2 hoc sang bc 4
Bc 4. Thut ton dng khi tm cc nhm ln i + 1 so vi ln th i khng c thay i
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Thut ton K-means
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Thut ton gom nhm ISODATA
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ISODATA l ci tin ca thut ton K-means
S lng cc nhm c th c iu chnh t ng o Nu 1 nhm qu tn mn tch lm 2 nhm
o Nu 2 nhm qu gn nhau gp vo mt nhm
Tnh khong cch t tt c cc phn t n tt c cc tm a ra quyt nh gom nhm hay tch nhm
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Phn vng nh trc tip da trn min nh
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Gi s R biu din vng ca ton nh, chng ta c th chia R ra thnh nhiu vng con khc nhau R1, R2, , Rn tha iu kin:
RRa
n
i
i
1
)(
(b) Ri l mt vng lin thng, vi mi i = 1, 2, , n.
(d) P(Ri) = TRUE, vi mi i = 1, 2, , n.
(e) P(Ri Rj) = FALSE, vi mi i j
(c) Ri Rj = , i j.
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Phn vng nh trc tip da trn min nh (tip)
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P(Ri) l mt hm logic c nh ngha trc trn cc im nh trong tp Ri v l tp hp rng.
iu kin (a) m bo vic phn vng l hon ton, mi im nh phi thuc vo mt vng no .
iu kin (b) R l mt vng lin thng.
iu kin (c) m bo cc vng phi ri nhau.
iu kin (d) m bo cc im nh trong vng phi tha mt tnh cht P no .
iu kin (e) m bo hai vng khc nhau v tnh cht P c nh ngha trc
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Phn vng nh trc tip da trn min nh (tip)
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p dng khi nh c nhiu nhiu vic pht hin bin phc tp hoc khng th pht hin chnh xc
Tiu chun xc nh tnh ng nht ca min ng vai tr rt quan trng
Mt s tiu chun tnh ng nht Theo gi tr mc xm
Theo mu sc, kt cu nh
Theo hnh dng, theo m hnh
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Phn vng nh trc tip da trn min nh (tip)
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Mt s phng php Phng php lan ta vng (gia tng vng
region growing)
Phng php phn chia v kt hp vng
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Phng php lan ta vng
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Bt u ti nhng im ht ging
Pht trin vng bng cch thm vo tp cc im ht ging nhng im ln cn tha mn mt tnh cht cho trc (nh cp xm, mu sc, kt cu) Tha mn hm P
4 ln cn
8 ln cn
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Phng php lan ta vng
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Tiu chun:
1. Gi tr sai khc
tuyt i gia cc
im nh phi nh
hn 65
2. Cc im nh phi
l 8 ln cn vi
nhau v c t nht
mt im nh nm
trong vng
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Phng php lan ta vng (tip)
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V d: Phn vng p dng lan ta vng cho nh sau (s sai khc < 3, seed point l nhng im c gi tr ln nht)
0 0 1 2 5 7 1 0 1 1 1 1 1 0
0 0 1 6 6 7 1 0 0 0 0 0 0 0
0 1 2 1 2 1 1 0 0 7 7 7 1 1
1 2 1 1 1 2 0 0 0 6 6 7 1 1
1 2 7 6 6 6 5 5 1 6 7 7 1 1
2 3 1 1 1 6 6 1 1 6 6 7 1 1
0 0 0 1 1 1 1 1 1 6 6 7 1 1
0 0 0 0 0 0 1 1 0 0 0 0 1 1
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Phng php lan ta vng (tip)
0 0 1 2 5 7 1 0 1 1 1 1 1 0
0 0 1 6 6 7 1 0 0 0 0 0 0 0
0 1 2 1 2 1 1 0 0 7 7 7 1 1
1 2 1 1 1 2 0 0 0 6 6 7 1 1
1 2 7 6 6 6 5 5 1 6 7 7 1 1
2 3 1 1 1 6 6 1 1 6 6 7 1 1
0 0 0 1 1 1 1 1 1 6 6 7 1 1
0 0 0 0 0 0 1 1 0 0 0 0 1 1
Cc im nh ht ging
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Phng php lan ta vng (tip)
0 0 1 2 5 7 1 0 1 1 1 1 1 0
0 0 1 6 6 7 1 0 0 0 0 0 0 0
0 1 2 1 2 1 1 0 0 7 7 7 1 1
1 2 1 1 1 2 0 0 0 6 6 7 1 1
1 2 7 6 6 6 5 5 1 6 7 7 1 1
2 3 1 1 1 6 6 1 1 6 6 7 1 1
0 0 0 1 1 1 1 1 1 6 6 7 1 1
0 0 0 0 0 0 1 1 0 0 0 0 1 1
Pht trin vng.
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Phng php phn chia v kt hp vng
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tng: Xc nh mt lut P(Ri) m mi vng phi
tha mn
Mt vng Ri s c chia thnh cc vng nh hn nu P(Ri) = FALSE
Hai vng Ri v Rj s c gp vo nhau nu P(Ri Rj) = TRUE
Thut ton dng khi khng chia v gp c na
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Phng php phn chia v kt hp vng (tip)
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C nhiu k thut tch v hp vng Xem xt k thut tch v hp vng theo cu
trc cy t phn
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K THUT TCH VNG V HP VNG T PHN
P(Ri) = TRUE nu c t nht 80% cc im trong Ri c tnh cht |zj m| 2i.
Trong :
zj: l cp xm ca im nh th j trong vng Ri.
m: l gi tr trung bnh ca vng Ri.
i: l lch chun ca cc cp xm trong Ri.
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TNH LCH CHUN
Khi cc vng c gp: tt c cc pixel trong vng nhn gi tr trung bnh ca vng
Phng sai:
lch chun:
1
1
2
2
n
zzn
j
j
1
1
2
n
zzn
j
j