Reading Circular Analogue Gauges using Digital Image Processing

Jakob S. Lauridsen1, Julius A. G. Grassmé1, Malte Pedersen1, David Getreuer Jensen2,Søren Holm Andersen2 and Thomas B. Moeslund1

1Section of Media Technology, Aalborg University, Denmark2EnviDan, Aalborg, Denmark

Keywords: Computer Vision, Circular Analogue Gauge, Gauge Reading Principal Component Analysis, ExpectationMaximization, Digital Time Series, Parametric Object Classification.

Abstract: This paper presents an image processing based pipeline for automated recognition and translation of pointermovement in analogue circular gauges. The proposed method processes an input video frame-wise in a mo-dule based manner. Noise is minimized in each image using a bilateral filter before a Gaussian mean adaptivethreshold is applied to segment objects. Subsequently, the objects are described by a set of proposed featuresand classified using probability distributions estimated using Expectation Maximization. The pointer is clas-sified by the Mahalanobis distance and the angle of the pointer is determined using PCA. The output is a lowpass filtered digital time series based on the temporal estimations of the pointer angle. Seven test videos havebeen processed by the algorithm showing promising results. Both source code and video data are publiclyavailable.

1 INTRODUCTION

Analogue pointer-type dials are widely applied inboth industrial and personal products where informa-tion such as pressure or speed is displayed. This in-cludes old waste water pumping stations, which canhave analogue pressure gauges mounted on the pumpas the main instrument to inspect the condition of thesystem. Typically a field operator is responsible forreading and recording the data from the gauge to eva-luate the performance of the pump. This is a timeconsuming and expensive process and it is prone tohuman errors. An alternative to the manual readingsis to record a video of the gauge and analyze the pres-sure variations using computer vision techniques.

Figure 1: Illustration of a circular pressure gauge with high-lighted features and their respective terms.

This paper presents such an approach, that auto-matically recognizes key parts of analogue circulargauges and identifies the transient behaviour of thepointer over the course of the video in order to cre-ate a digital time series. The terminology that will beused throughout the paper when describing gauges ispresented in Figure 1.

2 RELATED WORK

One of the early attempts to describe and break downthe problem of digitizing analogue dials was presen-ted by Sablatnig et al., who proposed a design stra-tegy for automatically reading dials of various shapesusing pattern recognition techniques (Sablatnig andKropatsch, 1994). Some years later Alegria et al. de-veloped a calibration system capable of reading di-als using thresholding, image thinning and the Houghline transform. However, this system was only ableto read dials where the pointer moves in a half circle(Alegria and Serra, 2000). The Hough line transformand its variations have since been a popular methodfor reading the pointer’s angle yielding feasible re-sults (Ye et al., 2013) (Jiannan Chi, 2015) (Jiale et al.,2011). Others have used least squares as an alterna-tive yielding more accurate results in general (Yang

Lauridsen, J., Grassmé, J., Pedersen, M., Jensen, D., Andersen, S. and Moeslund, T.Reading Circular Analogue Gauges using Digital Image Processing.DOI: 10.5220/0007386003730382In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 373-382ISBN: 978-989-758-354-4Copyright c© 2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

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et al., 2014) (Wang et al., 2013).M. Gellaboina uses a rotation of segmented ob-

jects and unwinding of the dial to read round pres-sure gauges (Gellaboina et al., 2013). The unwin-ding technique is also used by Zheng et al., who furt-hermore made the system more robust using colourcorrection and perspective transforms (Zheng et al.,2016). Yi et al. provide an algorithm robust to ax-ial noise changes by not assuming a perfect circularshape, finding the scale marks with the K-means clus-tering algorithm (Yi et al., 2017).

The aforementioned contributions exclude the as-sociation of unit related text on the dial to the scaleas a part of the automation. Sun et al. include this intheir contribution by recognizing the numbers in thedial and associating these to the dial scale (Sun et al.,2014).

A consistent flaw within the field is the lack ofpublic data, as it has not been possible to locate thesource code, videos, images or other relevant mate-rial from any of the state-of-the-art methods. Furt-hermore, several articles lack detailed descriptions ofcritical parts of the implementations, leading to a se-rious inadequacy within the field, as it is not possibleto make accurate comparisons and benchmark tests.

3 CONTRIBUTION

Based on the shortcomings of the current state-of-the-art methods, the following contributions will be pre-sented in the paper:

• Presentation of a new state-of-the-art method ba-sed on parametric classification of the pointer andscale marks.

• Application example: obtaining a digital time se-ries based on a recording of an analogue pressuregauge.

• Source code and video data are published for ben-chmarking.

4 APPROACH

We propose a system that takes a video of a circularanalogue gauge as input and translates the signal intoa digital time series.

The overall structure of the module based systemis illustrated in Figure 2 and every part will be descri-bed in the following sections. It should be noted thatthere has not been implemented a module for classi-fying the dial numbers as there exist excellent opensource solutions capable of handling this.

Preproccesing andsegmentation

Circle fitting

Scale mark and pointerrecognition

Pointer angleestimation

Time series

Figure 2: Algorithmic structure of automatic pressure rea-ding system.

4.1 Preprocessing and Segmentation

The need to separate and segment objects with mini-mal error is a traditional image processing problem.In the given case, the problem can be boiled down tohandling minor variations in light, contrast, and blurassuming that the camera is kept relatively steady infront of a well-lit gauge.

This problem has previously been handled usinglocal contrast normalization (Gellaboina et al., 2013),multi-scale retinex to reduce the influence of differentbrightness levels (Zheng et al., 2016), and a laplacianfilter to enhance the sharpness of the image (Selvathaiet al., 2017).

Our approach to handling irregularities and vari-ations in the input images is to use a bilateral filterfollowed by an adaptive threshold. An example of aninput image of a standard pressure gauge can be seenin Figure 3 (a).

The output of running a bilateral filter on an imageof a gauge can be seen in Figure 3 (b). The bilateralfilter minimizes noise such as glass transition irregu-larities and trapped air pockets, which are common inpressure gauges.

A Gaussian mean adaptive threshold is used to bi-narize the filtered image as it is robust against variati-ons in lighting conditions. The thresholded image canbe seen in Figure 3 (c).

After the image has been binarized it is processedby the grassfire algorithm in order to label the objects.

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(a) (b) (c)Figure 3: (a) The input image of a standard pressure gauge.(b) The bilateral filtered image. (c) The filtered image afterbeing thresholded.

4.2 Circle Fitting

One of the most common methods to locate the gaugebezel is to use the Hough circle transform. However,this method has been found to perform poorly on gau-ges with chromed bezels, as they are highly reflective,which make the segmentation difficult and may resultin only a part of the bezel being binarized. Therefore,a more error tolerant method inspired by (Gellaboinaet al., 2013) is used as it has been found to providemore stable results on segmented circles.

4.2.1 The Circle Fitting Algorithm

In order to determine whether a given object in thebinarized image is circular, the center is first determi-ned by finding the centroid of the object via the imageMoment of the object contours. Then an overlap va-lue, V , is introduced as

V �

36n�0

C AND rot�Cr,10−n� (1)

where C is the original object and Cr is a copy of theobject, which is rotated 360 degrees around the centerof C in steps of 10 degrees.

It is assumed that the gauge bezel object is alwayscircular and among the largest objects, which meansthat it will stand out by accumulating the highest va-lue V .

After having identified the most likely gauge bezelobject, it is necessary to identify the circle describedby this object as this information is crucial for recog-nizing the scale marks and the pointer. This is done byfitting a circle to the object using least squares circlefitting (Crawford, 1983).

Given a set of N input points r�xi,yi�¶0 $ i & Nxeach coordinate �xi,yi� is translated into another coor-dinate set (αi,βi) by

αi � xi ◦ x βi � yi ◦ y (2)where the sample mean of the set of coordinates �x, y�is given by

x �1N

i

xi y �1N

i

yi (3)

The least square center (αc,βc) is found by solvingthe system

�Mαα Mαβ

Mαβ Mββ

��αcβc� � � 1

2�Mααα≡Mαββ�12�Mβββ≡Mααβ�� (4)

where Mαα �

iα2

i , Mαβ �

iαiβi and so forth.

The center point can then be transformed back intothe original coordinate system by letting �xc,yc� ��αc,βc�≡ �x, y� and the circle radius can be determi-ned by

R �

×α2

c≡β2c≡

Mαα≡Mββ

N(5)

With the gauge circle detected, characteristics of ob-jects inside of the circle can now be determined.

4.3 Recognition of Scale Marks andPointer

The idea of recognizing parts in the gauge dial origi-nates from (Yi et al., 2017), who recognizes the scalemarks on the dial using features of binary objects andthe clustering technique K-means. This idea can beexpanded by using parametric distributions to recog-nize both the scale marks and the pointer.

To describe the objects in the dial, five featuresare proposed, which will be outlined in this sectionalong with sample distribution graphs that illustratetheir capabilities to separate the objects.

The rotated bounding box ratio is a feature me-ant to capture the oblongness of an object. Each ob-ject is rotated to be aligned with the horizontal axisbefore the bounding box ratio is calculated.

The mass of an object is simply the number ofpixels it contains. To make sure that the mass doesnot reach unnecessarily large values, it is transformedwith the natural logarithm.

The compactness is the mass related to the areaof the bounding box.

The distance to gauge center is the Euclideandistance between the object’s bounding box centerand the center point of the gauge bezel. To ensurethat values are independent to the gauge size in theframe, the distance is normalized by the gauge radius.

The orientation inaccuracy is given by the Euc-lidean distance of the orthogonal vector between theorientation vector of a given object and the gauge cen-ter. The eigenvector of the largest eigenvalue foundusing PCA defines the orientation vector. The dis-tance is normalized by the gauge radius.

By describing objects according to these simplefeatures it becomes possible to differentiate betweenthem. As illustrated in Figure 4, the pairwise combi-nations of the proposed features reveal structures that

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Figure 4: Graphs showing all the feature-pairs and their ability to separate objects. The graphs on the left and right side of theempty diagonal shows the same feature-pairs but with a different focus. On the left, the red dots illustrate the scale marks andthe blue dots represent noise, which include the pointer objects. On the right, the green dots illustrate the pointer object andthe blue is noise, which include the scale marks.

are capable of separating the objects. All the graphsare based on manually classified objects in 49 imagesfrom each of three training videos of pressure gaugesthat are presented later.

One example is the feature space spanned by massand distance to gauge center, which clearly separa-

tes the pointer object from everything else. Anotherexample is the distance to gauge center and rotatedbounding box ratio, which separates scale marks andnoise.

The samples give rise to the assumption that ob-jects in the dial can be classified using multivariate

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Gaussian distributions. In most of the presented ex-amples a single Gaussian distribution should be ade-quate to describe the relevant object, whereas two dis-tributions seem to be needed in order to cover thenoise.

The Gaussian multivariate distributions are descri-bed by a mean vector, µk, and covariance matrix Σk,where the subscript, k, denotes the given distribution.A mixing coefficient αk is introduced to ensure thatthe probability density function integrates to 1 (Bis-hop and Nasrabadi, 2007). An object can then be des-cribed by its feature vector, x, and the likelihood ofthat object belonging to a class, i, can be expressedby

L�i¶x� � k"i

αkN �x¶µk,Σk� (6)

Parameters are fitted using unlabelled samples fromthe training videos, which are described later, and theunsupervised learning technique Expectation Maxi-mization (EM). The algorithm is run until conver-gence using initial mean vectors, and diagonal cova-riance matrices based on the manually classified ob-jects. Two feature-pairs are found to be able to dis-tinguish scale marks, the pointer and noise from eachother.

The feature-pair consisting of the distance togauge center and rotated bounding box ratio is usedto classify scale marks. A visualization of the distri-butions before and after EM can be seen in Figure 5.The classification of new objects is based on the like-lihood of the objects belonging to a given class.

The mass and distance to gauge center is used toclassify the pointer object and a presentation of thedistribution before and after EM is shown in Figure 5.When classifying the pointer, only one object needsto be found. Hence all objects are sorted by their Ma-halanobis distance to the pointer distribution and theclosest object is assumed to be the pointer.

4.4 Estimation of the Pointer Angle

The angle of the pointer is found using principal com-ponent analysis (PCA), which is defined as an ortho-gonal projection of the data set onto a subspace thatmaximizes the variance of the projected data.

The binary pixels of the pointer object can be in-terpreted as a set of two-dimensional points, x, and byprojecting x onto the one-dimensional subspace u1,that maximizes the variance of the set, the directionof the pointer can be determined.

The mean of the projected data can be describedas uT

1 x, where x is the mean of x. The variance of the

Figure 5: Visualization of distributions before and after es-timating parameters using the EM algorithm.

projected data can then be found by

uT1 Su1 �

1N

Nn�1

suT1 xn ◦uT

1 xy (7)

where N is the amount of points in x and the covari-ance matrix, S, is given by

S �1N

Nn�1

�xn ◦ x��xn ◦ x�T (8)

A practical solution to maximizing the projectedvariance, uT

1 Su1, is to set u1 equal to the eigenvectorof the largest eigenvalue found in the covariance ma-trix (Bishop and Nasrabadi, 2007).

However, the orientation of the object needs to bedetermined as the vector can point in two directionsseen from the object’s perspective. The pointy endof the pointer is assumed to always be longer thanthe blunt end relative to the center. Therefore, the di-rection vector formed from the center of the gauge tothe bounding box center of the pointer object is usedto determine the orientation.

With this known, the pointer vector with the lo-west angle to the direction vector can be determinedusing the angle between the vectors. To improve thedirection vector obtained by PCA, the object is crop-ped with a circle that has the same center as the gaugeand a radius of one fifth of the radius of the gaugebezel. This is done because the pointer occasionallypasses over the gauge numbers which produces noiseat the tip of the pointer.

The resulting method will extract the angle in eachframe of the video. This angle will have to be relatedto a reference location to obtain an absolute angle as

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seen in Figure 6, resulting in a time series expressingthe pointer’s angle as a function of time.

Figure 6: Visualization of how the rotation of the pointer isreferenced.

4.5 Data Time Series

As the angle of the pointer can be identified its tran-sient behaviour throughout a video can now be consi-dered. Without any filtering, the pressure time seriesbecomes noisy as seen in Figure 7. The noise is com-prised of misinterpreted pointer angles and scenarioswhere a direction could not be determined.

Pressure time series recorded manually with digi-tal pressure sensors from waste water pumping stati-ons were obtained by consulting [an anonymous en-gineering company], which specializes in waste watersystems. An FFT of the received time series showedthat the important frequency components were below1Hz. Therefore, based on the Nyquist–Shannon sam-pling theorem the frequency resolution should be sa-tisfactory at a minimum of 2 Hz.

To remove outliers, the 30 Hz recorded signal isfiltered by a tenth-order low pass FIR filter, which hasa cutoff frequency of 2 Hz. An example of a recordedtime series before and after being filtered is presentedin Figure 7.

0 5 10 15 20

Time [s]

-3/2

-

-1/2

Poin

ter

angle

[ra

d]

Time series

Unfiltered

Filtered

Annotated

Figure 7: Graph illustrating a raw and noisy signal in blueand its low pass filtered counterpart in red.

5 DATA SET

Figure 8: Images from the train1, train2 and train3 recor-dings, seen from left to right, respectively.

The data set that has been used consists of 3 trainingvideos and 7 testing videos of running analog pres-sure gauges used in the waste water industry. The re-cordings have been edited to mainly contain the gaugebezel and scaled to a size of 512⊆512 pixels. Howe-ver, the raw videos and additional recorded videos arealso provided in the published data set.

The 3 training videos are recorded under a vari-ety of conditions to diversify the training set. train1is stationary with bright lighting, train2 is stationarywith ambient lighting and train3 is hand held withambient lighting. Images from the three recordingscan be seen in Figure 8.

The 7 testing videos are edited to match the for-mat of the training videos and are provided alongwith their corresponding annotations. They are na-med test1, test2, ..., test7 and are all recorded witha stationary camera under ambient lighting but eachhas a unique combination of characteristics, such asshaking, erratic pointer, angle, water level, bezel re-flection and light glare that make them relevant to testagainst. Images from the seven recordings can be seenin Figure 9.

6 RESULTS

Figure 12 shows the results of running the algorithmon test1. The grey dashed lines in the figure corre-sponds to a recognized mark in the first frame of thevideo. The algorithm recognizes scale marks in allframes, but for visual purposes, only scale marks fromthe first frame are used. Comparing each measure-ment of the pointer’s angle to the annotated truth, anerror is assigned.

The histogram plot presented in Figure 10 illustra-tes the absolute error between the annotated and me-asured signal in radians. The error is normally distri-buted with a mean and standard deviation of 0.02 and0.02 radians, respectively. This low error correspondsto the pointer being approximately 1 degree offset ac-cording to the annotated data and in a few cases 2-3degrees off. The observable negative tail in the nega-tive area may by caused by periods in test1 where the

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Figure 9: Images from the test1, test2, ..., test7 recordings, seen from left to right, respectively.

Recording: Test1

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Error [rad]

0

500

1000

1500

Fre

qu

ecy [

]

Figure 10: Histogram of the absolute error between the an-notated and measured signal of the captured time series oftest1.

pointer is covered or by a periodically present shadowfrom the pointer.

In some frames, the implementation of the algo-rithm fails to produce a meaningful angle of the poin-ter, at which it gives up and stores NAN as the result.This is illustrated in Figure 13 that shows the compu-ted signal from test2 with almost no detected pointerangles in the last part of the signal.

Figure 14 shows the results of running the propo-sed algorithm on test3. Here it should be noticed howthe computed angle fluctuates heavily. By inspectionof the annotated data, it can be seen that the pointerdoes not change as much as predicted during the giventime periods.

However, as emphasized by Figure 11 a signifi-cant error occurs at almost exactly ◦π, which is ana-logue for a half circle rotation. By inspection of therecorded video it can be seen that the pointer is erratic,and in some frames the pointy end is nearly invisibledue to heavy motion blur. In those frames the algo-rithm misjudges the direction of the pointer to be theblunt end resulting in an error of ◦π radians.

Table 2 shows the number of hits and misses aswell as the mean and standard deviation of the pointerangle error in radians for the seven test videos. Hitsdescribe the number of frames where the gauge bezel,pointer and marks are found such that the angle of thepointer can be estimated. Misses describe the oppo-site, where the system is not capable of determiningan angle of the pointer relative to the bezel.

Inspection of test2 and test6 shows that the low hitrate is due to varying lighting conditions, which is es-

Recording: Test3

- -0.3 0 0.3

Error [rad]

0

200

400

600

800

1000

1200

Fre

qu

ecy [

]

Figure 11: Histogram of the absolute error between the an-notated and measured signal. Notice how there is a signifi-cant accumulation of erroneous measurements around ◦π.

pecially apparent in the chrome gauge bezels makingthem undetectable for the system in large parts of therecordings.

6.1 Comparison with State-of-the-Art

Over the last couple of decades, many articles havebeen published on how to digitise analogue dialsusing computer vision and a comparison between thestate-of-the-art methods would, therefore, be appro-priate. However, even though the meticulousness ofthe publications vary, they share the same bad traitswhich makes such a comparison difficult to realise.

As presented in the first row of Table 1, the datathat have been used for testing the methods generallyconsists of images of a single dial, with the excep-tion of (Jiannan Chi, 2015) and (Yang et al., 2014).Furthermore, the results are in many cases based ononly a few images taken from the same angle and lightcondition (Ye et al., 2013)(Yi et al., 2017)(Sun et al.,2014)(Jiale et al., 2011)(Wang et al., 2013). This me-ans that, even though the results may be good, thereis a high possibility that the methods have been over-fitted to their respective setups. Lastly, none of theauthors has published their source code or test data,so it is not possible to replicate their findings.

In order to create a foundation for future bench-marking tests and comparisons, the entire source codeused for the presented work is published along withthe raw and edited test and training videos.

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Figure 12: Time series captured by processing test1 using the proposed method. Notice how the measured pointer angle isclosely related to the annotated angle throughout the recording.

Figure 13: Results from performing the algorithm on test2. The system fails to produce any meaningful angle of the pointerin a significant amount of frames.

0 5 10 15

Time [s]

-3/2

-

-1/2

0

1/2

Poin

ter

angle

[ra

d]

Recording: Test3

Unfiltered

Filtered

Annotated

Figure 14: Results from performing the algorithm on test3. The measured signal jumps incorrectly from ◦π to 0 often. Thisis due to motion blur of the pointer in test3.

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Table 1: Overview of state-of-the-art methods with regards to accessibility and the number of dials involved in the work.

J. Chi X. Ye C. Zheng M. Yi B. Sun H. Jiale B. Yang Q. Wang ProposedNo. of Dials 2 1 1 1 1 1 8 1 10Open Source No No No No No No No No YesPublic Data No No No No No No No No Yes

Table 2: Classification and error rate of the proposed met-hod when processing the seven test videos.

Hit Miss µ [rad] σ [rad]test1 11811 0 0.02 0.02test2 967 1253 -0.47 1.28test3 1801 0 -0.42 0.39test4 1111 0 0.08 0.32test5 451 0 -0.12 0.39test6 347 704 -6.07 0.56test7 571 2 -0.13 0.61

7 CONCLUSION

A method to automatically digitize analog circulargauges using computer vision is presented with an ap-plication example of a video recording of a pressuregauge translated into a digital time series.

The method is based on segmenting objects ineach frame using Gaussian adaptive mean threshol-ding and subsequently classifying the objects usingprobability distributions estimated with the unsuper-vised learning method Expectation Maximization.The output of the algorithm is an estimated angle ofthe pointer object, which is determined using PCA.

Recordings of seven pressure gauges, mounted onwaste water pumping stations, have been processedby the algorithm. The mean and standard deviation ofthe angle error are calculated for each of the videoswith the best case of µ � 0.02 radians and σ � 0.02radians.

However, in three of the recordings, significant er-rors are present. In test2 and test6 the bezel is madefrom a reflective material, which makes it difficult tosegment objects properly with the proposed methoddue to reflections. In another case, a problem is iden-tified where the angle of the pointer is miscalculatedby ◦π radians due to motion blur.

The shortcomings that have been uncovered in thetests are related to specific scenarios, which should betaken into consideration during the next iteration ofthe project. Generally, the results are very promisingand there is a great potential in the proposed parame-tric classification method.

The source code is published at (Lauridsen andGrassmé, 2018a) and the test and training data is pu-blished at (Lauridsen and Grassmé, 2018b).

8 FUTURE WORK

The current system only processes a single frame ata time, neglecting the benefits that might arise fromutilizing data from neighbouring frames. As an ex-ample, to achieve better estimates for the circle, cen-ter or for more accurate scale creation the temporalneighboring data could be utilized. This could also beused to reduce the errors introduced by motion blur,where the angle is incorrectly determined by the bluntend of the pointer.

Exploring other features, higher feature spaces orother compositions could possibly increase the accu-racy and make the proposed solution more robust.The training data could also be more diverse in orderto better generalize to different types of dials. Lastly,the level of automation can be improved by recogni-zing the dial numbers and associating those numbersto the scale marks.

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