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Histogram of Gradient Orientation
Dr. Rodrigo Ramele
Computer Vision Techniques applied to EEG Signal Analysis
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Brain Computer-Interfaces
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Motivations
• Clinical and Physician Involvement
Yuste2017, Perdikis2014
• Practical, relevant, and invariant features that convey good-enough information.
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“Can we mimic the physician approach to analyze and discriminate Electroencephalographic signals by automatic processing the shape
of the waveforms ?”
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Waveform-Based Algorithms
• Nowadays clinical EEG still entails a visually interpreted test
• Permutation Entropy• Matching Pursuit• Slope Horizontal Chain Code
• Peak Picking/aEEG/Period Amplitude Analysis/…
Band&Pompe 2002,Mallat 1993,Alvarado-Gonzalez 2016
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Histogram of Gradient orientation
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Histogram of Gradient Orientation
Signal Preprocessing
Signal Segmentation
Signal Plotting
Keypoint Localization
Calculation of Histogram of Gradient Orientation
Signal Segment Localization
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Signal Plotting: Digitalization
(0,0)
(Wx, Hy)
+
+
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Signal Plotting: Interpolation
Bresenham 1965
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Histogram of Gradient Orientation
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Histogram of Gradient Orientation
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Histogram of Gradient Orientation
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Histogram of Gradient Orientation
h(θ, i, j) = ∑p
ωang(∠J(p) − θ) ωij (p − kp) J(p) ωij(v) = ω( 5 vx
Δs St− xi)ω( 5 vy
Δs Sv− yi)
ωang(α) =1
∑r=−1
ω( 8α2π
+ 8r)
St =λ Fs γt
Δs
Sv =ΔμV γ
Δs
Sx × Sy
SvSt
γ
γt
Lowe 2004, Vedaldi 2010
{TrilinearInterpolation ω(z) = max(0,1 − |z | )
Δs = 2 3 (4 + 1)
Sx = ⌊Δs St⌋ + 1Sy = ⌊Δs Sv⌋ + 1
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Histogram of Gradient Orientation
h(θ, i, j) = ∑p
ωang(∠J(p) − θ) ωij (p − kp) J(p) ωij(v) = ω( 5 vx
Δs St− xi)ω( 5 vy
Δs Sv− yi)
ωang(α) =1
∑r=−1
ω( 8α2π
+ 8r)
St =λ Fs γt
Δs
Sv =ΔμV γ
Δs
Lowe 2004, Vedaldi 2010
{TrilinearInterpolation ω(z) = max(0,1 − |z | )
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Histogram of Gradient Orientation
0 45 90 135 180 225 270 315Bin Angles
Num
ber o
f wei
ghte
d gr
adie
nts
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Histogram of Gradient Orientation
1
234
56 7 8
9
101112
13
14 15 1617
181920
21
22 23 24
25
26272829
3031 32
33
343536
37
38 39 40
41
424344
45
46 47 48
49
505152
53
54 55 56
5758
59
128127126
125
124 123 122
121
120119118
117
116 115 114
113
112111110
109
108107
106
105
104103102
101
100
60
61
62 63 64
65
666768
69
70 71 72
73
747576
77
78 79 80
81
828384
85
86 87 88
89
909192
93
94 95 96
97
9899
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The Naive Bayes Near Neighbour
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Naive Bayes Near Neighbour
Boiman2008
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Naive Bayes Near Neighbour
Q
∑i= 1
k
∑h= 1
Class Label 1 Class Label 2
[q(bpc)1 , q(bpc)
2 , ⋯, q(bpc)Q ]
L1 L2
Q
∑i= 1
k
∑h= 1
Template Dictionaries
Query ImageDescriptors
<L̂ = L1
(1) (1)
(1)
(2)
(2)
(3)
(3)
(4)
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The Berger Rhythm
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Alpha Waves Wiggles
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Alpha Waves Wiggles
1 10 20 30 40 50 64
0.5
0.80.9
Channel
Acc
ura
cy
Af3 O1O2 Af40
0.7
Channel
Acc
ura
cy
EPOC Emotiv Consumer Grade EEG Device, 14 subj EEG MI NHS Physionet, Run1 vs Run2, 25 subj
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Mu Rhythm
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Mu Rhythm
Dataset 002-2014 BNCI-Horizon 2020 (Styrl, Scharer et al 2015)
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Mu Rhythm
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P140
0.5
0.7
Participant
Acc
ura
cy
C3
Cz
C4
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P140
0.5
0.7
Participant
Acc
ura
cy
C3
Cz
C4
Baseline vs. Hand Movement Baseline vs. Feet Movement
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Mu Rhythm
Niedermayer’s book 2010
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P300 Waveform
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P300 Waveform: Single Trial Detection
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P300 Wave
•Dataset I - P300 ALS Public Dataset• 8 subjects, 8 channels, Fs=256 Hz, 7 words, 5 letters, ISI-0.125 s, 10 epochs
•Dataset II - P300 for Healthy Subjects•Dataset III - P300 Pseudo-Real Dataset
• 8 subjects, 4 active, 4 passive•Dataset IV - P300 Dataset IIb BCI Competition II (2003)
• 1 subject, 64 channels, Fs=240 Hz, 73 trials, 42/31, ISI=0.25 s, 15 epochs
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P300 Wave: Dataset I
κ
2 4 6 8 10Intensification Sequences
0
30
70
90
Perc
ent C
orr
ect
12345678
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P300 Wave: Waveform Dictionary
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
0 0.5 1.0-505
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P300 Wave: Dataset I & II
Riccio 2013, Mak 2012, Nijboer 2009
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P300 Wave: Dataset I & II
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P300 Wave: Dataset III
0 50 100 150 200 250-10
-8
-6
-4
-2
0
2
4
6
8
10
Mic
rovolts
Multichannel ERP Template
Ouyang 2017, Verleger 2000
https://codeocean.com/capsule/5299343/tree/v2
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P300 Wave: Dataset III
Experiment 1: Letter identification, 2: jitter noise, 3: P3 peak amplitude noise
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P300 Wave: Dataset III
Dataset IV - P300 Dataset IIb BCI Competition II (2003)
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Signal Segment Localization
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Signal Segment Localization
Devuyst 2010
Signal Segment Localization
• K-Complexes are Sleep Research Graphoelements
• Biomarkers to determine transition from REM to Stage 2
• PSR: Polysomnography Recordings• Very long recordings.
• - Agreement Score between experts: 67%
• Asynchronous/ Self-pace BCIs
κ
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Signal Plot Keypoint Detector
• SIFT: Scale Invariant Feature Transform
• FAST: Features from Accelerated Segment Test
• SURF: Speeded-Up Robust Features
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Scale Space Detection
Iijima 62Otsu 81Witkin 83
Koenderink 84
Lindeberg 94
Lowe 04
Holmstron 13
P300
Viergever 97
Viergever 97, Lindeberg 2010
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Scale Space Detection
Viergever 97, Lindeberg 2010
Iijima 62Otsu 81Witkin 83
Koenderink 84
Lindeberg 94
Lowe 04
Holmstron 13
P300
Viergever 97
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Multichannel Representation
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HIST Multichannel Representation
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HIST Multichannel Representation
Van de sande 2010
HIST
HIST
EnsembleClassifier
Fusion HIST Classifier
ConcatenateDescriptors
MultichannelHIST
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HIST Multichannel Representation❖ Motor Imagery
❖ Laplacian Electrode Configuration
Wolpaw 2012
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HIST Multichannel Representation
h(θ, i, j) = ∑p
ωang(∠J(p) − θ) ωij (p − kp) J(p)
Steyrl 2016
Cz
C3
C4
Pz
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HIST Multichannel Representation
h(θ, i, j) = ∑p
ωang(∠J(p) − θ) ωij (p − kp) J(p)
Steyrl 2016
Cz
C3
C4
Pz
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Conclussions❖ Good performance when waveforms can be visually detected.
❖ Objective metric for waveform shapes.
❖ Stability of the shape of the P300 waveform.
❖ The intelligible property of this feature extraction method could be valuable in clinical settings.
❖ Scale Space Theory could have a revival in terms of finding 1-D signal features.
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Some follow-up
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Thanks !