An Multiple Regression Analysis Based Color Transform Between Objects Speaker : Chen-Chung Liu 1.
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Transcript of An Multiple Regression Analysis Based Color Transform Between Objects Speaker : Chen-Chung Liu 1.
An Multiple Regression Analysis Based
Color Transform Between Objects
Speaker : Chen-Chung Liu
11
OutlineIntroduction
The proposed algorithm◦Color Objects Extraction Algorithm Using
Multiple Thresholds (COEMT)
◦Color Transform Using Multiple Regression
Analysis (MRA)
Conclusions2
1. Introduction(1/3)Art purpose
3
1. Introduction (2/3)Image analysis (details increasing)
4
1. Introduction (3/3)Image analysis (image simplify)
5
The proposed algorithm
6
Figure 1. The flow chart of the proposed color transformation algorithm.
2.1.Color Objects Extraction(1/17)
Figure 2. Color objects extraction algorithm flow chart.
7
IRGBI DSROI CSSC
RGB2HSI EOAFFSSC OER
IRGBI: Input RGB Color ImageDSROI: Draw Symbols on the Region of InterestCSSC: Capture and Store the Symbols’ CoordinatesRGB2HSI: Transform Image Color Space from RGB to HSISSC: Set Searching Coordinates on HSI imageEOAFF: Extract Object Using Adaptive Forecasting FiltersOER: Output the Extracted Result
Figure 3. Pixels values distribution on different planes.Figure 3. Pixels values distribution on different planes.
2.1.Color Objects Extraction (2/17)
8
(a) original RGB image (b) on R plane (c) on G plane (d) on B plane
(e) on H plane (f) on S plane (g) on I plane (h) on |S-I| plane
2.1.Color Objects Extraction (3/17)
Figure 4. Intensity versus RGB and saturation versus RGB.
9
2.1.Color Objects Extraction (4/17)
Figure 5. The flow chart of EOAFF on HSI domain.
10
SNSS
CAFFSEC CATV
CS on H&I
BSE on S&I
MCSR CR OER
IIMTrue
False
IHFW ,
ISFW ,
tS
tH tI
IIM: Input HSI Image and Markers SNSS: Set New Searching SeedsSEC: Search by Eight-ConnectivityCAFF: Create the Adaptive Forecasting FiltersCATV: Calculate the Adaptive Threshold Vectors
CE on H&I: Color Search on H&I Planes with SLCCABSE on S&I: Bright and Shadow pixels Extraction on S&I Planes with SLCCAMCSR: Merging of CS result and BDE ResultCR: Check Result Whether Have Any SeedOER: Output the Extracted Result
2.1.Color Objects Extraction(5/17)
11
I(1)-I(0)*2(3)I'
S(1) -S(0)*2 (3)S'
H(1)}/2 H(0) {(3)H'
I(5) -I(0)*2 (7)I'
S(5) -S(0)*2 (7)S'
H(5)}/2 H(0) {(7)H'
2.1.Color Objects Extraction(6/17)
12
I(0)}/2 I(1) {(5)I'
S(0)}/2 S(1) {(5)S'
H(0)}/2 H(1) {(5)H'
I(5)}/2 {I(0) (1)I'
S(5)}/2 {S(0) (1)S'
}/2 H(5) H(0) {(1)H'
2.1.Color Objects Extraction(7/17)
13
I(1) -I(5)*2 (2)I'
S(1) -S(5)*2 (2)S'
H(5)}/2 H(1) {(2)H'
I(5) -I(0)*2 (1)I'
S(5) -S(0)*2 (1)S'
H(8)}/3 H(5) H(0) {(1)H'
2.1.Color Objects Extraction(8/17)
14
I(2)}/2 I(1) {(5)I'
S(2)}/2 {S(1) (5)S'
H(2)}/2 {H(1) (5)H'
,81,i I(0), (i)I'
,81,i S(0), (i)S'
,81,i H(0), (i)H'
Filter’s thresholds of hue , saturation , and intensity
2.1.Color Objects Extraction(9/17)
15
otherwiseHiHabs
HHiHabsifH
HHiHabsifH
H
i
mim
MiM
t
),)]0()('[max(
))]0()('[max(,
))]0()('[max(,
81
81
81
otherwiseSiSabs
SSiSabsifS
SSiSabsifS
S
i
mim
MiM
t
),)]0()('[max(
))]0()('[max(,
))]0()('[max(,
81
81
81
otherwiseIiIabs
IIiIabsifI
IIiIabsifI
I
i
mim
MiM
t
),)]0()('[max(
))]0()('[max(,
))]0()('[max(,
81
81
81
the global empirical constants mH =0.008, MH =0.032, mS =0.024, MS =0.048, mI =0.024, and
MI =0.048.
2.1.Color Objects Extraction(10/17)
Figure 6. An example of the proposed adaptive forecasting filter‘s working.
16
2.1.Color Objects Extraction(11/17)
Figure 7. An example of the proposed scheme.
17
original image union result
CS result BSE result
2.1.Color Objects Extraction(12/17)
18
Figure 8. Test image: Pink hat.
original imagewith seeds
DTS in RGB DTS in HSI proposed scheme
C. C. Liu and G. N. Hu, Color Objects Extraction Scheme Using Dynamic Thresholds (DTS), 2009 Workshop on Consumer Electronics (WCE2009), pp. 1130-1138, 2009.
2.1.Color Objects Extraction(13/17)
19
Figure 9. Test image: Flowers.
original imagewith seeds
DTS in RGB DTS in HSI proposed scheme
2.1.Color Objects Extraction(14/17)
20
Figure 10. Test image: Pottery.
original image with seeds DTS in RGB
DTS in HSI proposed scheme
2.1.Color Objects Extraction(15/17)
21
Figure 11. Test image: Cup set.
original image with seeds DTS in RGB
DTS in HSI proposed scheme
2.1.Color Objects Extraction(16/17)
22
Figure 12. Test image: Sun flower.
original image with seeds DTS in RGB
DTS in HSI proposed scheme
Image Extraction scheme ME RFAE EMM NU MHD Accuracy
Pink hat(325×415)
DTS on RGB 0.0355 0.2549 0.8319 0.8696 4.4061 0.9645
DTS on HSI 0.0079 0.0537 0.0975 0.8629 0.696 0.9921Proposed 0.0079 0.0397 0.0949 0.8615 0.0625 0.9921
Flowers(172×222)
DTS on RGB 0.3726 0.8586 0.9556 4.4272 11.737
1 0.6274DTS on HSI 0.0514 0.1119 0.1835 1.1290 0.1848 0.9486Proposed 0.0186 0.0085 0.0664 0.6315 0.0372 0.9814
Pottery(350×251)
DTS on RGB 0.3140 0.8305 0.9012 1.5588 16.196
0 0.6860DTS on HSI 0.0841 0.2267 0.4983 0.9522 0.4927 0.9159Proposed 0.0160 0.0263 0.0461 0.6720 0.0372 0.9840
Cup set(599×399)
DTS on RGB 0.0621 0.1490 0.6542 1.2389 0.5322 0.9379
DTS on HSI 0.0286 0.0677 0.1874 0.7566 0.2494 0.9714Proposed 0.0066 0.0059 0.0417 0.6214 0.0124 0.9934
Sunflower(768×1024
)
DTS on RGB 0.3716 0.8323 0.9784 1.1597 95.459
6 0.6284
DTS on HSI 0.3795 0.8181 0.9650 1.1492 93.8753 0.6205
Proposed 0.0434 0.0862 0.4841 0.5430 0.0121 0.9566
2.1.Color Objects Extraction(17/17)
23
Table 1. Comparisons of extraction results
Multiple Regression Analysis (1/5)
For data of ordered pairs
We want to predict y from x by finding a function that fits the data as closely as possible.
2.2. MRA_based Color Transform(1/20)
24
),(),...,,(),,( 2211 nn yxyxyx
)(xHy
Multiple Regression Analysis (2/5)MRA is used to find a polynomial function of degree , as the predicting function, that has the minimum of the sum of squares of the errors(SSE) between the predicted values of y and the observed values for all of the n data points .
2.2. MRA_based Color Transform(2/20)
25
k kk xxxy ...2
210
iy),(),...,,(),,( 2211 nn yxyxyx
Multiple Regression Analysis (3/5)The values of , , ,…,and that minimize
are obtained by setting the first partial derivatives ,
,…, andequal to zero.
2.2. MRA_based Color Transform(3/20)
26
0 1 2k
2
1
221010 )]...([),...,,(
n
i
kikiiik xxxySSE
),...,,( 100
kSSE
),...,,( 101
kSSE
),...,( 10 kk
SSE
Multiple Regression Analysis (4/5)Solving the resulting simultaneous linear system of the so-called normal equations:
2.2. MRA_based Color Transform(4/20)
27
n
ii
n
i
n
i
n
i
kikii yxxxn
11 1 1
2210 ...
n
iii
n
i
n
i
n
i
kikii
n
ii yxxxxx
11 1 1
132
21
10 ...
n
ii
ki
n
i
n
i
n
i
kik
ki
ki
n
i
ki yxxxxx
11 1 1
222
11
10 ...
Multiple Regression Analysis (5/5)The matrix form solution be
where
2.2. MRA_based Color Transform(5/20)
28
YXXX TT
k
1
2
1
0
:
,
...1
:::::::
...1
...1
...1
2
3233
2222
1211
knnn
k
k
k
xxx
xxx
xxx
xxx
X .
.
.
.2
1
ny
y
y
Y
2.2. MRA_based Color Transform(6/20)
29Figure 13. Target object .
2.2. MRA_based Color Transform(7/20)
30Figure 14. Source object .
Best fitting functions
2.2. MRA_based Color Transform(8/20)
31
Red Green Blue
Figure 15. The curves of degree1, 5, and 9 best fitting functions.
2.2. MRA_based Color Transform(9/20)
32
Figure 16. The color transfer results corresponding to the variation in the degree of best fitting polynomials.
2.2. MRA_based Color Transform(10/20)
33
L* a* b*
Figure 17. The box-plots of L*, a*, and b* for the target, source, and color transferred objects in Figure 11.
CIELAB L* a* b*
MEAN STD MEAN STD MEAN STD
Dress150.430
4
51.4691
7
106.423
6
8.97858
9
117.770
9
5.47792
5
chrysanthemum215.671
1
39.2809
4
124.722
2
7.94416
2
200.105
7
26.2307
9
Degree 1217.829
2
31.3322
5
123.691
6
8.80164
8
195.963
1
28.1982
3
Degree 2220.721
5
36.3131
7
125.550
2
10.5864
8
196.376
9
30.1589
7
Degree 3 220.22735.1729
5
127.664
9
10.9081
5
196.602
9
29.9496
7
Degree 4220.203
4
33.8926
9
126.890
6
11.9964
5
196.317
1
30.0778
9
Degree 5220.272
733.9665
126.950
8
11.8242
7
196.553
6
29.7591
8
Degree 6220.278
1
33.7996
2
126.995
1
11.8225
9
196.376
6
30.0007
5
Degree 7220.398
833.6955
127.098
5
11.9772
4
196.568
1
29.8268
3
Degree 8221.886
7
30.2697
1
126.462
9
11.0972
2
197.157
7
29.2396
2
Degree 9222.843
7
29.3369
2
125.709
7
11.8568
3
193.991
3
29.5341
3
2.2. MRA_based Color Transform(11/20)
34
Table 2. The measurement metrics for the target, source and color transferred objects in Figure 17 (1/2)
CIELAB C* H* E*
MEAN STD MEAN STD MEAN STD
Dress 158.7859.69240
1
42.0409
8
1.43258
2
221.787
1
37.3548
2
chrysanthemum236.502
4
20.3878
7
32.3032
94.79458
321.949
2
27.4735
3
Degree 1232.656
321.0893
32.7115
3
5.44170
1
320.265
6
20.8540
4
Degree 2234.177
7
22.5643
5
33.0888
3
5.88526
6
323.778
1
23.5091
2
Degree 3235.451
7
23.0103
8
33.4690
8
5.70499
3
324.393
3
21.7474
3
Degree 4234.875
3
22.8860
2
33.3507
7
5.92635
1
323.891
4
20.5603
4
Degree 5235.065
1
22.7958
4
33.3198
4
5.80953
1
324.087
9
20.3967
5
Degree 6234.962
522.8892
33.3619
5
5.87509
8
323.999
9
20.4977
8
Degree 7235.160
7
22.9257
6
33.3475
7
5.81623
5
324.225
4
20.3704
8
Degree 8235.195
9
22.9131
533.1205
5.52175
2
325.013
5
18.9275
9
Degree 9232.150
7
23.5463
7
33.3893
8
5.61041
9
323.509
7
17.6013
5
2.2. MRA_based Color Transform(12/20)
35
Table 2. The measurement metrics for the target, source and color transferred objects in Figure 17 (2/2)
The target RGB color image is a girl in a blue dress (350×350 pixels).
The source color images with different sizes.
2.2. MRA_based Color Transform(13/20)
36
Image Size (pixel)
Blue Roses 528×458
Wool Hat 450×377
Potted Plant 750×1000
Amber 399×354
Carnation Flower 640×480
The extraction procedure lasted between 3 and 25 seconds, and the color transferring procedure lasted about 0.03 seconds.
2.2. MRA_based Color Transform(14/20)
37
2.2. MRA_based Color Transform(15/20)
38
Figure 20. Examples of color transferring between objects with the proposed multiple regression analysis algorithm (1/2).
2.2. MRA_based Color Transform(16/20)
39
Figure 21. Examples of color transferring between objects with the proposed multiple regression analysis algorithm (2/2).
Performance measures function:
2.2. MRA_based Color Transform(17/20)
40
22 *)(*)(* baC
222 *)(*)(*)(* baLE
/*))/*(2arctan180(* abH
*}*,*,*,*,*,{,/)(1
EHCbaLXNjXXN
j
st XXX
)/|(|100(%) sXXX
2.2. MRA_based Color Transform(18/20)
41
CIELABL* a* b*
MEAN STD MEAN STD MEAN STD
Blue dress150.430
451.4691
7106.423
68.97858
9117.770
95.47792
5
Blue roses144.574
341.9283
9134.401
713.1304
274.8278
16.13991
Wool hat156.117
740.6513
8106.235
613.2233
6162.011
222.8879
3
Potted plant145.215
937.9356
399.2557
99.78578
7171.883
414.5488
3
Amber145.216
336.4920
2108.842
721.2677
3173.322
914.3342
9
Carnation 147.322
940.4143
6150.093
433.0741
80.18154
19.15783
CIELABC* H* E*
MEAN STD MEAN STD MEAN STD
Blue dress 158.7859.69240
142.0409
81.43258
2221.787
137.3548
2
Blue roses154.988
78.62681
460.8049
36.87635
7214.632
526.2399
Wool hat195.139
912.3608
533.6504
7.001189
252.3068
24.4726
Potted plant199.036
59.35587
230.1465
94.36541
1248.277
624.2501
8
Amber205.627
616.2058
732.0184
5.473507
253.6519
25.00947
Carnation 171.544
631.4717
761.4555
27.18140
1229.262
934.5528
2
Table 3. The measurement metrics for the target and source objects in Figures 20,21
2.2. MRA_based Color Transform(19/20)
42
CIELABL* a* b*
MEAN STD MEAN STD MEAN STD
Blue roses163.318
555.6394
9128.507
417.0255
790.4183
731.5838
Wool hat188.812
639.3171
1126.217
512.7337
7130.383
311.1928
4
Potted plant162.481
453.2363
1102.419
123.9186
7162.492
421.2341
5
Amber168.295
352.2510
7142.565
116.4569
6164.566
21.28246
Carnation 169.981
447.7605
6185.628
633.0194
6102.968
516.2365
4
CIELABC* H* E*
MEAN STD MEAN STD MEAN STD
Blue roses160.051
818.9847
655.3171
510.5985
1231.989
343.8929
2
Wool hat181.843
512.2898
344.0244
93.45239
7264.100
625.7869
7
Potted plant194.418
810.8495
232.2716
68.74632
7257.289
330.8681
3
Amber218.257
622.2291
240.9812
94.04682
1280.646
420.5305
4
Carnation 214.366
121.4830
960.2257
88.36698
2277.923
118.6482
1
Table 4. The measurement metrics for the color transferred target objects in Figures 20, 21
CIELAB ΔL* ΔL*(%) Δa* Δa*(%) Δb* Δb*(%)Blue roses 18.7442
211.4770
95.89427 4.58671
515.5905
717.2427
Wool hat 32.69487
17.31605
19.98188
15.83131
31.62791
24.25764
Potted plant 17.26554
10.62616
3.163266
3.088552
9.391059
5.779385
Amber 23.07898
13.71338
33.7224 23.65404
8.756862
5.321186
Carnation 22.6585 13.32999
35.5352 19.14317
22.78695
22.13002
2.2. MRA_based Color Transform(20/20)
43
CIELAB ΔC* ΔC*(%) ΔH* ΔH*(%) ΔE ΔE*(%)Blue roses 5.06312
13.16342
65.48777
89.92057
317.3568
47.48174
3Wool hat 13.2963
97.31199
510.3740
923.5643
511.7937
54.46563
Potted plant 4.617675
2.375117
2.125071
6.584944
9.011727
3.502566
Amber 12.63007
5.786773
8.962891
21.87069
26.99445
9.618671
Carnation 42.82152
19.97588
1.229737
2.041878
48.66021
17.50852
Table 5. The absolute difference in measurement metrics of the transferred target-object from the source object in Figures 20 and 21
Simple, effective and accurate in color transferring between objects.
Details of target object can be changed by the color complexity of source object.
Time consumption is independent of the number of bins selected and the degree of regression.
Dynamic ranges of colors of objects don’t have any restriction.
Conclusions
44
45
Thank YouQuestions and Comments