HISTORY AND BIOMEDICAL APPLICATIONSOF DIGITAL SIGNAL AND IMAGE PROCESSING

Digital Signal and Image Processing Research Grouphttp://dsp.vscht.cz

Ales Prochazka, Senior Member, IEEE, Oldrich Vysata

1. INTRODUCTION

Digital signal processing (DSP) represents a general inter-disciplinary area based upon mathematical analysis of one-dimensional or multi-dimensional data sets that may stand forany physical, engineering, biomedical, acoustic, seismic oreconomical variable measured or observed with a given sam-pling period. Even though applications cover completely dif-ferent areas the mathematical background of their analysis isvery close allowing processing of vectors, matrices or multi-dimensional arrays of observed data in a general way. Digitalsignal processing methods thus form an integrating platformfor many diverse research branches.

Fundamental mathematical methods of signal, image andmulti-dimensional objects processing domains include

• space-frequency and space-scale analysis and multidi-mensional signal decomposition and reconstruction,

• probabilistic, Bayesian and adaptive signal processing,• three-dimensional modelling.

Selected mathematical methods cover basic numerical andstatistical methods, discrete Fourier transform and discretewavelet transform and computational intelligence.

Goals of signal analysis cover the estimation of its char-acteristic parameters either in the time or transform domain.In some cases of signal processing deterministic methodsmay be applied but in many applications statistical and adap-tive methods must be used to compensate for the incompleteknowledge of the real system time variations. Latest applica-tions are devoted to human-machine interactions.

2. DIGITAL SIGNAL PROCESSING EVOLUTION

Historical roots of digital signal processing are very old. Ac-cording to several researchers they date back to the 25th cen-tury BC and they are related to the ”Palermo stone” (Fig. 1)with earliest records of Nile’s floods observed on the timebase of 12 months (naive sampling). Processing of theserecords was concentrated to prediction of floods fundamen-tal for watering fields. ”Nilometers” used later were arabicbuildings with instruments measuring the water level to pre-dict climate conditions and to calculate taxes related to theprosperity of the country.

Fig. 1. Palermo stone (25th cent.BC) with records of the wa-ter level and nilometers on the Rawda Island Cairo (861 AD)

Isaac Newton, 1 Jan. 1643– 31 March 1727

The mathematical fundamentalsof digital signal and image pro-cessing methods are based uponnumerical analysis that predatesthe invention of modern com-puters by many centuries usingworks of famous mathematiciansincluding that of Isaac Newton(1643-1727), Joseph Louis La-grange (1736-1813) and Leon-hard Euler (1707-1783). The

matrix theory introduced in the middle of the 19th century in-corporating ideas of Gottfried Wilhelm Leibnitz (1646-1716)and Carl Friedrich Gauss (1777-1855) forms now one of itsbasic mathematical tools as well.

Jean Baptiste JosephFourier, 21 March 1768 –16 May 1830

The theory of digital signal andimage processing is in manycases closely connected with theFourier representation of func-tions suggested in 1822 by JeanBaptiste Joseph Fourier (1786-1830), functional transforms,matrix theory and numericalmethods including the method ofthe least squares presented in-dependently by Carl FriedrichGauss (1777-1855) and Adrien-

Marie Legendre (1752-1833) in the 19th century.

Marc-Antoine Parseval, 27Apr. 1755 – 16 Aug. 1836

Relation between the space andfrequency domain signal repre-sentation was then studied byMarc-Antoine Parseval (1755-1836). Basic mathematicalmethods were later extendedto many fields including func-tional transforms (Pierre-SimonLaplace, 1749-1827), the es-timation theory and stochasticprocesses introduced by NorbertWiener (1894-1964) in 1949 and

Rudolf E. Kalman (1930-) with applications in various areascovering adaptive filtering problems and spectrum analysis.Many algorithms use properties of the discrete Fourier trans-form and their implementation is enabled by its fast versionpublished by James Cooley (1926-) and John Tukey (1915-2000) in 1965. Modern statistical and Bayesian signal pro-cessing methods are based upon the research of Peter Rayner(1941-), Bill Fitzgerald (1948-2014) and many further re-searchers.

Johann Karl AugustRadon, 16 Dec. 1887 - 25May 1956

Research of Johann Karl AugustRadon (1787-1956) formed thebasis of computer tomographyand opened a completely newarea of biomedical image anal-ysis. The following research ofwavelet transform using the firstknown wavelet proposed by Al-fred Haar (1885-1933) in 1909is based upon research of IngridDaubechies (1954-) published in1992 followed by research of

Martin Vetterli (1957-), Nick Kingsbury (1950-) and furtherresearchers extending the principle of uncertainty discussedby Werner Heisenberg (1901-1976). The latest research re-lated to computational intelligence allows the use of computertechnologies for human-machine interaction, robotic systemsand assistive technologies using different biosensors, data fu-sion and wireless communication systems.

3. SELECTED CASE STUDIES

3.1. Polysomnography and Analysis of Brain ActivitiesAnalysis of EEG multichannel signals form the fundamen-tal information source of brain activities. Its de-noising, seg-mentation and signal components classification is often usedfor diagnosis of different diseases and in polysomnography.Age-related changes in the energy and colored noise evolu-tion presented in Fig. 2 can be used to explain learning abilityand intellectual performance changes.

Further EEG analysis can be used to study mental ac-tivities, human-machine interaction and aging. This topic isclosely related also to robotic systems, assistive technologies,analysis of sport activities and computational intelligence.

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FREQUENCY ANALYSIS OF A SELECTED EEG CHANNEL AND FILTER

Frequency [Hz]Stop−band cut−off frequencies: 47 53

Channel

EEG SIGNAL DENOISING

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(a) De-noising of selected EEG channels

20 30 40 50 60 700

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ALL BAND: THE λ COEFFICIENT AGE EVOLUTION Regression Coefficient: −0.0053 [1/year]

Age [years]

Coeff

icient

λ

λ valuesRegression Line95 % confidence bounds

(b) Age-evolution of the colored noise

Fp1 Fp2

F7 F3

Fz F4

F8

T3 C3 Cz C4 T4

T5 P3

Pz P4

T6

O1 O2

(c) AGE RELATED CHANGES OF THE λ COEFFICIENT IN THE ALPHA BAND

(c) Regression

Fig. 2. Age-related changes in the EEG colored noise relatedto the power spectrum 1/fλ distribution.

Fig. 3 presents the percentage distribution of the energyin separate frequency bands related to the whole energy ofeach record with respect to the age of individuals. Resultsobtained confirm the decrease of the energy in bands DELTAand THETA and the relative increase of this energy in bandsBETA and GAMMA over age.

20 40 608

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14

16

18(a) DELTA / B=−0.0133

Age [years]

Band

Energ

y [%]

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16

(b) THETA / B=−0.0179

Age [years]

Band

Energ

y [%]

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18

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Age [years]

Band

Energ

y [%]

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40(d) BETA / B=0.0369

Age [years]

Band

Energ

y [%]

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28

30(e) GAMMA / B=0.0093

Age [years]

Band

Energ

y [%]

Fig. 3. Distribution of relative energy in separate EEG fre-quency bands with respect to the age of individuals and cor-responding correlation coefficientsMares J., Vysata O., Prochazka A., Valis M.: Age-Dependent Complex Noise Fluctuation in the Brain,IOP Science: Physiological Measurement, 34(10):1269-1279, DOI: 10.1088/0967-3334/34/10/1269, 2013

Kopal J., Vysata O., Burian J., Schatz M., Prochazka A., Valis M.: Complex continuous wavelet coherencefor EEG microstates detection in insight and calm meditation, ELSEVIER: Consciousness and Cognition, 30:13-23, 2014

3.2. Classification of Muscle DisordersMuscle activities are followed to detect neurological muscledisorders. Fig. 4 presents typical signals acquired for healthyand neuropathic individuals. Their spectral features allowclassification of negative and positive sets of individuals toenable more precise diagnosis. Neural networks can then beused to combine individual features and to improve sensitivityand specificity measures.

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plit

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V]

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Am

plit

ude [m

V]

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(c) EMG DE−NOISED SPECTRUM

Frequency [Hz]

Normal − Fmax=43 [Hz]Neuropathy − Fmax=6 [Hz]

8.8 8.52 8.24 7.96 7.68 7.40

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1

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Threshold

DISTRIBUTION OF NEGATIVE AND POSITIVE POPULATIONS

TN − True NegativeFP − False PositiveFN − False NegativeTP − True Positive

Criterion

Fig. 4. Typical EMG signals of selected (a) healthy and(b) neuropathic individuals with (c) their smoothed spectraand (d) distribution of their spectral features.

The confusion matrix with results of the two-class clas-sification system for class 1 (positive) and class 2 (negative)values is presented in the following Table.

Trueclass

Predicted ClassNegative Positive Row sum

Negative TrueNegative (TN)

FalsePositive (FP)

TN+FP

Positive FalseNegative (FN)

TruePositive (TP)

TP+FN

Column Sum TN+FN TP+FP

The ROC curve as a plot of true-positive rate versus false-positive rate and our sample’s accuracy results are presentedin Fig. 5. Both these plots represent parametric curves withcriterion values (cr) as their parameters.

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1ROC CURVE (Parameter: criterion)

False Positive Rate P(FP) (1−Specificity P(TN))

True

Pos

itive

Rat

e P

(TP

)

(Sen

sitiv

ity)

Cr=7.955Cr=8.085

Cr=8.215

Cr=8.345

Cr=8.475

True Positive Rate P(TP)=TP/(TP+FN)

False Positive Rate P(FP)=FP/(FP+TN)

Area: 0.88095

0 0.2 0.4 0.6 0.8 140

45

50

55

60

65

70

75

80

85ACCURACY

False Positive Rate P(FP) (1−Specificity P(TN))

Cr=7.955

Cr=8.085

Cr=8.215

Cr=8.345

Cr=8.475

Maximal Accuracy: 82.7778 %

Fig. 5. The ROC curve of EMG Willison rates for the set offeatures in 104 healthy and 76 neuropathic individuals withassociated criterion (cr) values and the accuracy curve indi-cating the optimal criterion that provides the highest proba-bility of the right decisionProchazka A., Vysata O., Tupa O., Yadollahi M., Valis M.: Discrimination of Axonal Neuropathy Using Sensitivityand Specificity Statistical Measures, SPRINGER: Neural Computing and Applications,25(6):1349-1358, DOI: 10.1007/s00521-014-1622-0, 2014

3.3. Machine-Man Interaction and Gait AnalysisDiagnostics of movement disorders including detection ofgait features forms a very important neurological area usingimages and data from different biosensors, accelerometersand camera systems. An example of the MS Kinect use forgait features acquisition is presented in Fig. 6. Image anddepth sensors of this system enable to obtain image framesand detection of joints in the three-dimensional space. Dig-ital filtering and data analysis was then used for detectionof stride length and speed velocity as main features used todetect Parkinson’s disease (Fig. 7).

The spatial modelling using video systems and MS Kinectdevice can be used both for diagnostical purposes and for re-habilitation. This approach has a wide range of applications inmedicine, neurology and engineering using human-machineinteraction and computational intelligence.

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(f) CENTERS

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(g) MAS CENTERS

Walk length [m]

Heigh

t [m]

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(h) DISTANCE BETWEEN LEGS

Walk length [m]

Distan

ce [m

]

Right LegLeft Leg

Mass Centers

x [m]

y [m]

Fig. 6. The 3D modelling presenting (a) MS Kinect sensors,(b), (c) depth sensor map, (d) selected RGB camera frame,(e) 3D skeleton model, (f) evolution of the centers of massand leg centers in the 3D space, (g) evolution of the centers ofmass positions above the horizontal plane, and (h) distancesbetween the leg centers for a selected walk segment

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0.7(a) PD / mean: 0.38

Individual

Stride

Leng

th [m

]

5 10 15

(b) CONTROLS / mean: 0.53

Individual

AVERAGE STRIDE LENGTH

Fig. 7. The average stride lengths of (a) the patients withParkinson’s disease and (b) the reference set of individuals

Prochazka A., Vysata O., Valis M., Tupa O., Schatz M., Marık V.: Use of the Image and Depth Sensors of theMicrosoft Kinect for the Detection of Gait Disorders, SPRINGER: Neural Computing and Applications, 2015

3.4. Segmentation and Dental Arch AnalysisSegmentation of dental arch components using digital recordsof plaster cast models plays an important role in the orthodon-tic treatment. Selected light conditions are used for the dataacquisition to provide more clearly defined contours of theimage components. The preliminary stage of the data pro-cessing uses the Circular Hough Transform (CHT), digital de-noising, and a separation of the orthodontic objects from theirbackgrounds employing Otsu’s thresholding method. The re-gion growing method using multiple seed points in a convex-hull is then applied. The proposed general method identifiesthe common boundary of two neighbouring and overlappingorthodontic objects with results enabling the efficient segmen-tation of digital data and their analysis through the computernetwork. Fig. 8 present selected results of this process allow-ing further evaluation of dental arch parameters.

(a) PROPOSED METHODSEGMENTATION

(b)EDGE &MORPHOLOGYSEGMENTATION

(c) MARKER CONTROLLEDWATERSHED

SEGMENTATION

Fig. 8. Comparison of the segmentation process using(i) the proposed method, (ii) morphology segmentation, and(iii) marker controlled watershed transform

Image registration forms another important area allowingto evaluate the progress of the treatment using digital modelsobtained either by digitalization of plaster casts or acquiredthrough magnetic resonance systems. Fig. 9 presents an ex-ample of such an analysis during the treatment.

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48INITIAL FEATURE PLOT

Distance 3−3 [mm]

Distan

ce 5−5

[mm]

Given Data: RC=0.57Regression Line: CC=0.64

25 30 35 40 4532

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48FINAL FEATURE PLOT

Distance 3−3 [mm]

Distan

ce 5−5

[mm]

Given Data: RC=0.7Regression Line: CC=0.8

Fig. 9. Spatial location of teeth centers detected by the two-camera system and used for evaluation of the correspondingteeth distances, together with their approximation plane be-fore and after its rotation into the horizontal position for theexamination (a) before the treatment and (b) after the treat-ment with distances between selected teeth

Prochazka A., Kasparova M., Yadollahi M., Vysata O., Grajciarova J.: Multi-Camera Systems Usefor Dental Arch Shape Measurement, SPRINGER: The Visual Computer, DOI: 10.1007/s00371-014-1029-z, 2014

Yadollahi M., Prochazka A., Kasparova M., Vysata O.: The Use of Combined Illumination in Segmentationof Orthodontic Bodies, SPRINGER: Signal, Image and Video Processing, SIViP, 9:243-250, 2015

3.5. Spatial Modelling in OrthodontiaDigital modelling plays and important role in the orthodon-tic treatment replacing classical plaster casts by they digitalmodels. Digitalization of plaster casts are performed either bythe 3D scanning or by processing of their stereophotos allow-ing to use numerical methods for evaluation of specific mea-sures of dental arch. To detect individual image componentsit was necessary to apply image de-noising and segmenta-tion methods including watershed transform, region growingand Hough transform to evaluate distances between individ-ual teeth before and after the treatment according to Fig 10.The 3D scanner allows to construct the digital model accord-ing to Fig. 10 as well.

Fig. 10. Image processing and spatial digital modelling meth-ods in the orthodontic treatment

Fig. 11 presents the system of two cameras located at aselected distance c to follow a specific point C on the plas-ter cast in the three-dimensional space. Cameras A and Btogether with the object C form a triangle allowing to deter-mine its spatial coordinates and distances between selectedobjects as well.

β2(k)

Camera: B[xa,0,0]

β1(k)

Axis xc

a2(k)

a1(k)

SPACE OBJECT DETECTION

C[xC

(k),yC

(k),zC

(k)]

b1(k)

α1(k)

Camera: A[0,0,0]

α2(k)

b2(k)

Axis y

Axis

z

Fig. 11. Digital cameras used for tracking an object in spaceand the determination of its coordinates in the selected coor-dinate system at specified time instants

Kasparova M., Prochazka A., Grafova L., Yadollahi M., Vysata O., Dostalova T.: Evaluation of Dental MorphometricsDuring the Orthodontic Treatment, BioMedical Engineering OnLine 2014, 13:68, pp. 1-13, 2014

3.6. GPS Data Processing in Sport ActivitiesThe monitoring of data from Global Positioning System(GPS) receiver and remote sensors of physiological data al-low evaluation of cross-correlations between the heart rateand the altitude gradient during cycling. The data acquiredduring 15 identical cycling routes, each 140 km long, in-cluded more than 4 600 segments of length 60 s. Generaldigital signal processing methods used included mathemati-cal tools to reject gross errors, digital filtering of noise signalcomponents, and estimating cross-correlations between theposition data and the physiological signals. The results of aregression between GPS and physiological data include theestimate of the time delay between the heart rate change andgradient altitude of about 7.5 s.

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CYCLING ROUTE FROM WINDSOR TO OXFORD

Longitude

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OXFORD

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Speed [km

/h]

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Altitude [m

]

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120

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Heart

Rate

[bpm

]

Fig. 12. The cycling route and (a) the speed, (b) the altitude,and (c) the heart rate recorded with the sampling Ts=0.5s

Fig. 13 presents the correlation of more than 4 600 seg-ments 60 s long observed during 15 cycling routes fromWindsor to Oxford with corresponding regression lines and95 % confidence bounds. The regression coefficient of theheart rate versus the speed has a negative value, while that ofthe heart rate versus the altitude gradient is positive.

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(a) HEART RATE RELATED TO SPEED / CorrCoef: −0.14

Speed [km per hour]

Hea

rt R

ate

[bpm

]

Given dataRegression line / RC=−0.2995 % confidence bounds

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(b) HEART RATE RELATED TO SLOPE / CorrCoef: 0.38

Slope [%]

Hea

rt R

ate

[bpm

]

Given dataRegression line / RC=1.7895 % confidence bounds

Fig. 13. Plot of the heart rate versus (a) speed and (b) altitudegradient for more than 4 600 segments 60 s long observedduring cycling routes from Windsor to Oxford

Prochazka A., Vaseghi S., Yadollahi M., Tupa O., Mares J., Vysata O.: Remote Physiological and GPS Data Processingin Evaluation of Physical Activities, SPRINGER: Medical & Biological Engineering & Computing, 52:301-308, 2014

3.7. Computational Intelligence in Retina AnalysisComputational intelligence and methods of digital signal pro-cessing form very useful tools for analysis of retinal images,their enhancement and analysis to monitor changes during thetreatment. After the appropriate image registration it is possi-ble to analyze blood-vessel trees and their specific structuresto find retina disorders. The proposed graphical user interfacewas used for analysis and monitoring of the set of 20 patients(Fig. 14) observed during the treatment using the optical co-herence tomography.

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Fig. 14. The set of retina images of 20 patients at the begin-ning of their treatment

Fig. 15 present the principle of image registration. Fea-tures obtained by further methods were then analysed by se-lected statistical methods to compare features obtained and topropose the method for classification of healthy and diseasedpatients. The accuracy achieved was 79 %.

Fig. 15. Principle of image registration for the base and inputimages using selected fixed points

Prochazka A., Vysata O., Vavrycukova J., Cejnar P., Pavelek Z., Lhotska L.: Registration and Analysis of Retinal Imagesfor Diagnosis and Treatment Monitoring, in Proceedings of the International Workshop on Computational Intelligence forMultimedia Understanding (IWCIM), Paris, France, DOI: 978-1-4799-7971-4/14, 2014

4. MATHEMATICAL METHODS

The digital signal processing forms an integrating environ-ment for many biomedical and engineering areas as it allowsthe use of similar mathematical methods for analysis and pro-cessing of observed multidimensional and multichannel sig-nals and data fusion of information obtained.

Let us have the data sequence {x(n)}N−1n=0 of N val-

ues observed with the sampling frequency fs standing forthe (biomedical) signal or an image in case that data valuesare represented by vectors. Then it is possible to detect itsfrequency components by its discrete Fourier transform

X(k) =

N−1∑

n=0

x(n) exp(−j kn 2 π/N) (1)

for k = 0, 1, 2, · · · , N . Alternatively the wavelet transformcan be used for signal or image decomposition.

Signal de-noising and enhancement must be applied inthe next stage in most cases. In the simplest case and time-domain processing it is possible to use finite or infinite im-pulse response digital filters of the M th order in the time do-main to evaluate a new sequence

y(n)=−M∑

k=1

a(k) y(n−k)+

M∑

k=0

b(k) x(n−k) (2)

for n = M,M + 1, · · · , N . Alternatively it is possible to usefrequency domain filtering or thresholding of wavelet coeffi-cients and signal reconstruction.

Signal segmentation, selection of features, their classifi-cation and evaluation of results is the most common problemof signal processing both in medicine and engineering.

Let us have a matrix PR,Q of R features/attributes pj

(stride length, walking speed, age, . . . ) for each separate in-dividual j=1, 2, · · · , Q. Let us define further the associatedrow vector t1,Q that specifies the class ck, k = 1, 2, · · · ,Mof each individual selected from the given set of M classes.During the following learning process, a function that trans-forms the space of features PR,Q into the vector t1,Q speci-fying the classes is estimated.

The goal of the probabilistic classification is to find theestimate of class ck of the unknown instance p:

ck = maxc1,c2,··· ,cM

(P (ck|p)) (3)

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it S

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/s]

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Parkinson’s diseaseControl Set1 (age−matched)Control Set2 (students)

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Parkinson’s diseaseControl Set1 (age−matched)Control Set2 (students)

Fig. 16. Bayesian decision boundaries of individual classes(1-Parkinson’s disease set, 2-first controls (age-matched), 3-second controls (students)) and selected attributes: x1-stridelength [m], x2-gait speed [m/s], x3-age [years]

Negative Set

Positive Set

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HISTOGRAMS OF TWO POPULATIONS

Criterion

Threshold

TN − True NegativeFP − False PositiveFN − False NegativeTP − True Positive

Fig. 17. Stride length analysis for objects with Parkinson’sdisease (positive set) and age-matched controls (negative set)

Fig. 16 presents an example of such a classification. The re-ceiver operating characteristic (ROC) curves can be then usedas an efficient tool for evaluation of classification results. Theselected classifier finds in the negative set:

• TN, FP - number of true-negative and false-positive in-dividuals in the negative set,

• TP, FN - number of true-positive and false-negative in-dividuals in the positive set.

The associated performance metrics can then be used to eval-uate the true positive, the true negative rate and accuracy.

The alternative approach is based upon supervised classi-fication process using the two layer neural network structurewith sigmoidal transfer functions F1, F2 that evaluates net-works output A2 by relations

A1S1,Q = F1(W1S1,R PR,Q, b1S1,1), (4)

A2S2,Q = F2(W2S2,S1 A1S1,Q, b2S2,1). (5)

for the associated vector of target values TS2,Q. During theevaluation process coefficients W1,b1,W2,b2 are opti-mized to have networks output as close as possible to targets.

Classification systems in medicine include in most cases(i) the selection of characteristic features acquired by differ-ent biosensors, (ii) the learning process to allow their clas-sification, and (iii) proposal of the diagnosis of an unknownindividual with as high probability as possible.

More detail analysis allow correlation of these featureswith further environmental variables, control of robotic sys-tems and the use of assistive technologies including rehabili-tation.

5. CONCLUSION

The digital signal and image processing joins different re-search topics and in this way it follows ideas of GottfriedWilhelm Leibniz (1646-1716), German mathematician andphilosopher, who wrote papers about philosophical aspectsof differentiation and integration of sciences. G. Leibnitz dis-cussed problems of too specialized disciplines and problemsof scientists who lost abilities to communicate together. Fromthis point of view the digital signal and image processingforms an integrating platform allowing to use similar math-ematical tools for analysis of completely different problemsusing general mathematical tools for data processing.