Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
Finding Heart Rate From Web-cam Images by
Application of Independent Component Analysis
Michael Mason
Colorado School of Mines
mimason@mines.edu
December 1, 2014
1/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
Overview
1
Introduction
2
Descriprion of Independent Component Analysis
The Problem
Theory
Practice
3
Application for Pulse Measurement
2/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
Remote Measurement of Pulse
Goal
To be able remotely detect a persons heart rate.
Past work
The remote detection of heart rate and other physiological
indicators has been a subject of interest for some time. This
technology is particularly suited for remote health-care applications
due to the proliferation of the necessary hardware(a web-cam).
This project was inspired by the work of the MIT CSAIL
Laboratory and by Poh et al and their use of blind source
separation for the afore mentioned task.
3/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
The Cocktail Problem
4/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
The Cocktail Problem specifics
Same number of microphones as there are guests
Could have more microphones than guests
Square matrices easier to work with
No echoes
No time delay in recording
5/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
The Solution
Independent Component Analysis
6/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
Assumptions
Independent sources
Justifies use of central limit theorem
The sum of independent random variables is generally more Gaussian than any
of the individual random variables
Sources have non-Gaussian
distribution(except 1)
Allows ICA to go further than PCA
Instantaneous, error-free
measurement
Not accounted for
For Gaussian variables,being uncorrelated
is equivalent to being independent
If there is one more recording than
source, the final source could be thought
of as a Gaussian error ”source”
7/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
Assumptions cont.
Recordings represent a linear
combination of sources
x = As
A is an unknown mixing matrix, x contains your measurements at some point
in time, s is the value of the sources
8/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
Blind Source Separation
We have x in :
x = As
But, both s and A are unknown. We want to estimate an
de-mixing matrix B:
B = A−1
(1)
(2)
To do this, we pick the rows of B s.t. the signals Bx are maximally
non-Gaussian
9/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
Measuring Non-Gaussianity
Kurtosis
Kurtosis, denoted γ2 , defined:
µi = E[(X − µ)i ]
µ4
γ2 = 2 − 3
µ2
(3)
is zero for Gaussian distributions. Maximizing kurtosis maximizes
non-Gaussianity. This is computationally cheap but very sensitive
to outliers in the measured signal.
10/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
Measuring Non-Gaussianity cont.
Entropy
Entropy, defined as:
X
P(X = ai )log2 (P(X = ai ))
(4)
i
is maximal for the Gaussian distribution, so minimizing entropy is
equivalent to maximizing non-gaussianity. This is much more
robust but it is computationally expensive
11/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
Limitations
Can not determine amplitude(and sign) of signal
Sources must be independent
Cannot have more than one Gaussian source
12/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
The Problem
Theory
Practice
ICA Algorithm
1
whiten data
2
choose number of independent components to find, m
3
choose initial mixing vector wj
4
optimize w for wjT x to be maximally non-Gaussian
ensure wj is orthogonal to all previously found wi (e.g with
Gram-Schmidt) at every step
5
repeat steps 3 and 4 until m components have been found
13/20
Michael Mason
Finding Heart Rate With ICA
Some Signals
14/20
Some “Recordings”
15/20
Comparison with Extracted Signals(right)
16/20
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
Approach
To obtain a pulse rate measurement follow these steps:
1
2
capture a color video of a face
sum each color channel over all pixels
these 3 sums serve as the recorded signals at that point in time
3
perform ICA on the recorded signals and look for an extracted
source which is correlated with pulmonary signals
4
extract pulse from the periodogram of source
17/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
Results
Poh et al
Able to determine pulse rates very accurately and in real time.
99% accuracy when compared to a finger pulse monitor
myself
Able to find independent components in real time, but none of
them had a strong pulmonary signal. Furthermore, the nature of
the ICA algorithm does not guarantee an order to the sources, so
there was little consistency between samples.
18/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
References
A. Hyvärinen et al, Independent Component Analysis NY, John
Wiley and Sons, 2001.
Poh , M.-Z., McDuff, D.J., and Picard , R. W. 2010.
Non-contact, automated cardiac pulse measurements using video
imaging and blind source separation. Opt. Express 18, 10,
1076210774.
19/20
Michael Mason
Finding Heart Rate With ICA
Introduction
Descriprion of Independent Component Analysis
Application for Pulse Measurement
Questions?
20/20
Michael Mason
Finding Heart Rate With ICA