# Drop Distribution Determination in a Liquid-Liquid  Dispersion by Image Processing

Authors: Luís M. R. Brás; Elsa F. Gomes; Margarida M. M. Ribeiro; M. M. L. Guimarães
Journal: International Journal of Chemical Engineering
 (2009)

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## Abstract

This paper presents the implementation of an algorithm for automatic identification of drops with different sizes in monochromatic digitized frames of a liquid-liquid chemical process. These image frames were obtained at our Laboratory, using a nonintrusive process, with a digital video camera, a microscope, and an illumination setup from a dispersion of toluene in water within a transparent mixing vessel. In this implementation, we propose a two-phase approach, using a Hough transform that automatically identifies drops in images of the chemical process. This work is a promising starting point for the possibility of performing an automatic drop classification with good results. Our algorithm for the analysis and interpretation of digitized images will be used for the calculation of particle size and shape distributions for modelling liquid-liquid systems.


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## Body

## 1. Introduction

Image
processing  is  a very relevant area of computer science with applications in
many domains. Quantitative analysis and interpretation of digitized images are currently
important tools in several scientific domains.The
acquisition and treatment of images of particulate phases become essential for
the calculation of particle size and shape distributions, namely in multiphase
systems modelling in chemical engineering. In particular, modelling and
validation of liquid-liquid systems, either for hydrodynamic or mass transfer phenomena,  can benefit from image  processing techniques.
This is of importance in simulation, interpretation, and performance
predictions of multiphase reactors. As reported in Ribeiro et al. [1], authors like Olney [2], Cruz-Pinto and Korchinsky [3] and Rod and Misek [4] have demonstrated that serious design and
performance prediction errors occur if drop size distribution is neglected.
According to Pacek et al. [5], any technique based on representative physical
sampling will drastically change the overall composition of the dispersion.In
Ribeiro et al. [1] and Ribeiro [6]
a video technique with nonintrusive probes was tested. Pictures of a small region
inside a transparent vessel near its wall were obtained, by lighting and
observing it from the outside. In that work, to obtain the drop size
distribution, images were analyzed by employing visual/manual techniques which
imply high costs, intensive labour, weariness buildup, and consequent high error
rates. A fully automated computational approach has a definite potential for
better performance.The
aim of the present work is to develop an algorithmic process capable of performing
shape discrimination and size classification for liquid drops in monochromatic
digitized frames of a liquid-liquid dispersion.In
order to automatically identify the contour of the drops, some known techniques
for edge detection in images have been tested. Preliminary results with the Sobel,
Marr-Hildreth, and Canny [7] methods were not satisfactory.Therefore,
we have developed a new approach which is described in this paper. After
preprocessing the images, we have used Hough transforms [8] for the detection of round drops.


## 2. Experimental Setup and Noninvasive Image Acquisition Technique

Image
frames were obtained at our SIPROM (Modelling and Simulation of Multiphase
Systems) Laboratory with a digital video camera  +  microscope  +  illumination
setup from a dispersion of toluene in water within a transparent mixing vessel
[1] as shown in Figure 1.Figure 1
Experimental
mixer-settler setup and image acquisition technique.The
mixer consists of a 6,28 L glass vessel (diameter  =  height) with flat bottom,
equipped with four flat vertical baffles. The agitation was provided by a
standard turbine with a 1/2 turbine/vessel diameter ratio and with turbine
diameter/disk diameter/paddle width/paddle height of 20/15/5/4. The mixer-settler
arrangement works in closed circuit with the mixer feeds being forced in by
peristaltic pumps.For
our experiments, the average residence time of the mixture in the mixer vessel
was between 1 and 10 minutes, the dispersed phase hold-ups between 1 and 10%,
and the agitation speed between 90 and 145 rpm.The
images were captured by a black and white SensiCam [9] camera, designed for weak lighting
and fast movement (exposure times from 1 millisecond to 1000 seconds, image
intervals between 0 and 1000 seconds).Due
to the high sensitivity of the camera, the lighting system had to respond to
strict requirements of target ability, no flicker, high light density, low heat
generation and simple and safe setup. So the light system was made up of four
cool halogen lamps (150 W, 12 V each) with mirror-concentrated beam and rear
cooling.Test
trials enabled the definition of the best placement of the microscope-camera
group, the best placement of the lighting array and the penetration depth (up
to 3 cm)
into the vessel. The amplification of the combined optical image system was
determined from images of a gauge made from calibrated wire immersed in the
vessel. In this routine work was used a minimum frame duration (1 millisecond)
in order to disable drop trails even at the highest agitation speeds. In this
way, many frames (up to 1000) may be obtained per second, which enables the
selection, in each frame, of only the best-defined drops without representative
sample size problems.


## 3. Definition of the Problem

The
experimental conditions (mainly phase ratio and agitation speed) led to frames
of deeply focused fields with partially overlapping drops and high background
noise, as we can see in Figure2. In this figure we show two images, Figure 2(a) is what we
consider a better quality image whereas Figure 2(b) is very difficult to process. Since
noninvasive image acquisition and lighting were our uncompromising starting
option, no significant improvements were obtained although all available image
acquisition and cleaning techniques were used within this fundamental
constraint. Thus, partial images and ill-defined drop boundaries led to all low
cost, market-available image processing software packages requiring a high
number of frames in order to secure statistically significant drop samples
which, again, made for greatly time-consuming, unreliable procedures.Examples of
images, (a) is a very good image, and (b) is an image with low photographic
quality.
(a)(b)This led us to develop our own software for which a
preliminary test and calibration stage was performed on archive images previously
obtained with a semiautomated procedure [1]. We have developed a promising approach, implemented
in MATLAB [10], which, given one of these photographic images of a
dispersion, automatically identifies the contour of existing drops and
classifies them according to their diameter.


## 4. Description of the Method

Given one of the photographic images
of the dispersion, our approach, implemented in MATLAB, automatically identifies the contour of existing drops
and classifies them according to their diameter.In
our proposed approach, the process for the detection of the drops in an image has
two distinct steps. In the first step, we detect the edges of the drops in the
original image by monitoring the values of the gradient and the descending
thickness and by creating an output image with those contours. In the second
phase, we detect the drops in this contour image, using the Hough Transform [8, 11]. This transform is widely used in image processing
to detect lines and also to detect circles.


### 4.1. Edges Detection

In Figure3, we show the step of the detection process of the
drops. Thus, starting from the original image (Figure 3(a)), we detect the edges (Figure 3(b))
and in the next step, we detect the contours of the drops using the Hough
transform (Figure 3(c)).Original
image, the edge detection and the detection of the drop using the Hough
transform.
(a)(b)(c)In our images, of relatively poor
quality, the drops have, in majority, dark edges.To reduce the noise, and consequently
reduce the probability of false edges detection, the original image (Figure5(a)) is smoothed using a Gaussian filter. This
eliminates some false contours and reduces the detection of false drops.Using the typical
profile of the signal, edge detection is made by evaluating the relation
between the gradient’s descent (Gd) and its respective thickness (Ed), shown in
Figure4.The signal profile typically presents two steep
ascents and two steep descents. The algorithm uses the gradient’s descent (Gd)
and its respective thickness (Ed) to identify the contour of the drops.
(a)(b)(a) Original
image; (b) the resulting contour image; (c) representation of the drop contour
as an irregular object.
(a)(b)(c)The filtered image (If) is derived, with kernels of
convolution, as indicated below, originating two matrices, Ix and Iy (see (1)) corresponding to the partial
derivatives  dz/dx and dz/dy: (1)Ix=If∗[1−1],Iy=If∗[1−1]. From the images Ix and Iy we obtain the
average and the standard deviation of the descending gradient (μg,σg)
and the average and the standard deviation of the descending thickness (μe,σe).
The edge detection threshold is defined by the combination of Gd and Ed
(computed from the Ix and Iy images), where Gd takes negative
values and Ed positive.In the processing of each descent
(negative derivative) from its origin to inflexion point, ifEd>μe−σe/2
and Gd<μg+σg/2, then the pixel of this point is considered an edge pixel.
From the matrix Ix we obtain the partial
contour matrix Ia, and from Iy the matrix Ib.Since there may be very high values ofe and very low values of g, the detection of the edge pixels could be negatively
affected. To reduce that possible effect we have introduced the terms −σe/2 and σg/2. By moving the edge detection thresholds in this way, we
intend to obtain the maximally useful information without increasing
significantly the risk of obtaining unnecessary information.The sum ofIa and Ib yields the
contour image Ic, shown in Figure 4.  Currently, we
only consider the vertical and horizontal derivatives. Taking other directions
into account (such as 45 degrees derivatives) could saturate the contour
detection and degrade the results. Moreover, this would increase significantly
the computational effort of the method.Preliminary
experiments with other known methods for contour detection such as Sobel, Canny,
and Marr Hildreth showed that these degrade the results of the Hough Transform in
the detection of the drops. They introduce additional information that causes
the detection of false drops.


### 4.2. Detection of Drops in the Contour Image

In the second step of the work, we
applied the Hough transform to the contour imageIc (Figure 5(b)) to detect the contour of the drops for different values
of the radius.We consider, as we can see in Figure5(c), that the contour of each drop can be
represented as one object with irregular form, centred in a point and with a radius
that varies from r1 to r2.The Hough transform is widely used to
detect lines and also to detect circles. To find circles using a Hough
transform, each edge element votes for all the pointsx,y which are centres of
the circles with radius r that it
could lie on. This transform allows determining the centre of the drop through
the identification of the most voted zone. It has the inconvenience of, for
each useful vote, generating 2×π×r−1 noise votes. For this reason, in an image with
many drops, this could cause the detection of inexistent drops.As referred above, in
this step of the process we applied the Hough transform to the contour imageIc taking into account the relative
deformation k=(r2−r1)/r2 of the drops. The value of k is a parameter of the algorithm. For a
maximum deformation of radius r2 the
minimum deformation will be r1=r2×(1−k). Votes will be generated from the successive application of the
Hough Transform to the range r1:r2.This procedure is repeated for all the radii considered
as maximum deformation (r2), in order
to process all the contours, of all dimensions, of the drops (see Figure 5(c)).The voting window (centre of Figure6) has a dimension of 3×3pixels for radii above 15 and
dimension of 1×1 otherwise. To reduce the number of noise points we considered
half of the voting amplitude (two quadrants). For that we analyze the signal of
the partial derivatives according to the partial contour matrix, Ia or Ib, related to the edge pixel.Figure 6
Voting
window and voting amplitude.Figure7 illustrates the detection quadrant voting procedure
for an edge pixel related to matrix Ia.
If the
drop was a regular solid, it would be possible to determine the correct
quadrant, by analyzing the gradient’s angle variation, β. In our case, it is only possible to determine a pair of possible
voting quadrants (A, C or B, D), by analysing the partial derivative’s signal.
The similar process is used for the edge pixels related to matrix Ib.Detection of the quadrant voting across theX axis.
(a)(b)The detection process starts with the
set of drops with radii between 17 and 48 pixels (0.17 and 0.48 millimeter,
resp.) because these are the most frequent. Then, we treat the drops
with at least 48 pixels of radius. Finally, we process the drops with radius
between 8 and 16 pixels (0.08 and 0.16 millimeter, resp.).Processing the drops with higher
radius first reduces the probability of detecting false drops with a lower
radius, caused by agglomerates of pixels in the contour of the drops. However,
the detection is not efficient for radii below 8 pixels (0.08 millimeter).This detection process is enhanced with the erosion of
the contour images of detected drops. This is not a common process of
morphologic erosion [11]. In this process, after finding a centre, we
eliminate the pixels that have contributed to find this centre so that they do
not interfere in the subsequent process [12, 13].In Figure8, we
can see the results obtained on two images for a radius ranging from 5 pixels
(0.05 millimeter) to 46 pixels (0.46 millimeter).The drops
detected by our program. Each detected drop is marked with a white circle on
top of the original image.
(a)(b)


## 4.1. Edges Detection

In Figure3, we show the step of the detection process of the
drops. Thus, starting from the original image (Figure 3(a)), we detect the edges (Figure 3(b))
and in the next step, we detect the contours of the drops using the Hough
transform (Figure 3(c)).Original
image, the edge detection and the detection of the drop using the Hough
transform.
(a)(b)(c)In our images, of relatively poor
quality, the drops have, in majority, dark edges.To reduce the noise, and consequently
reduce the probability of false edges detection, the original image (Figure5(a)) is smoothed using a Gaussian filter. This
eliminates some false contours and reduces the detection of false drops.Using the typical
profile of the signal, edge detection is made by evaluating the relation
between the gradient’s descent (Gd) and its respective thickness (Ed), shown in
Figure4.The signal profile typically presents two steep
ascents and two steep descents. The algorithm uses the gradient’s descent (Gd)
and its respective thickness (Ed) to identify the contour of the drops.
(a)(b)(a) Original
image; (b) the resulting contour image; (c) representation of the drop contour
as an irregular object.
(a)(b)(c)The filtered image (If) is derived, with kernels of
convolution, as indicated below, originating two matrices, Ix and Iy (see (1)) corresponding to the partial
derivatives  dz/dx and dz/dy: (1)Ix=If∗[1−1],Iy=If∗[1−1]. From the images Ix and Iy we obtain the
average and the standard deviation of the descending gradient (μg,σg)
and the average and the standard deviation of the descending thickness (μe,σe).
The edge detection threshold is defined by the combination of Gd and Ed
(computed from the Ix and Iy images), where Gd takes negative
values and Ed positive.In the processing of each descent
(negative derivative) from its origin to inflexion point, ifEd>μe−σe/2
and Gd<μg+σg/2, then the pixel of this point is considered an edge pixel.
From the matrix Ix we obtain the partial
contour matrix Ia, and from Iy the matrix Ib.Since there may be very high values ofe and very low values of g, the detection of the edge pixels could be negatively
affected. To reduce that possible effect we have introduced the terms −σe/2 and σg/2. By moving the edge detection thresholds in this way, we
intend to obtain the maximally useful information without increasing
significantly the risk of obtaining unnecessary information.The sum ofIa and Ib yields the
contour image Ic, shown in Figure 4.  Currently, we
only consider the vertical and horizontal derivatives. Taking other directions
into account (such as 45 degrees derivatives) could saturate the contour
detection and degrade the results. Moreover, this would increase significantly
the computational effort of the method.Preliminary
experiments with other known methods for contour detection such as Sobel, Canny,
and Marr Hildreth showed that these degrade the results of the Hough Transform in
the detection of the drops. They introduce additional information that causes
the detection of false drops.


## 4.2. Detection of Drops in the Contour Image

In the second step of the work, we
applied the Hough transform to the contour imageIc (Figure 5(b)) to detect the contour of the drops for different values
of the radius.We consider, as we can see in Figure5(c), that the contour of each drop can be
represented as one object with irregular form, centred in a point and with a radius
that varies from r1 to r2.The Hough transform is widely used to
detect lines and also to detect circles. To find circles using a Hough
transform, each edge element votes for all the pointsx,y which are centres of
the circles with radius r that it
could lie on. This transform allows determining the centre of the drop through
the identification of the most voted zone. It has the inconvenience of, for
each useful vote, generating 2×π×r−1 noise votes. For this reason, in an image with
many drops, this could cause the detection of inexistent drops.As referred above, in
this step of the process we applied the Hough transform to the contour imageIc taking into account the relative
deformation k=(r2−r1)/r2 of the drops. The value of k is a parameter of the algorithm. For a
maximum deformation of radius r2 the
minimum deformation will be r1=r2×(1−k). Votes will be generated from the successive application of the
Hough Transform to the range r1:r2.This procedure is repeated for all the radii considered
as maximum deformation (r2), in order
to process all the contours, of all dimensions, of the drops (see Figure 5(c)).The voting window (centre of Figure6) has a dimension of 3×3pixels for radii above 15 and
dimension of 1×1 otherwise. To reduce the number of noise points we considered
half of the voting amplitude (two quadrants). For that we analyze the signal of
the partial derivatives according to the partial contour matrix, Ia or Ib, related to the edge pixel.Figure 6
Voting
window and voting amplitude.Figure7 illustrates the detection quadrant voting procedure
for an edge pixel related to matrix Ia.
If the
drop was a regular solid, it would be possible to determine the correct
quadrant, by analyzing the gradient’s angle variation, β. In our case, it is only possible to determine a pair of possible
voting quadrants (A, C or B, D), by analysing the partial derivative’s signal.
The similar process is used for the edge pixels related to matrix Ib.Detection of the quadrant voting across theX axis.
(a)(b)The detection process starts with the
set of drops with radii between 17 and 48 pixels (0.17 and 0.48 millimeter,
resp.) because these are the most frequent. Then, we treat the drops
with at least 48 pixels of radius. Finally, we process the drops with radius
between 8 and 16 pixels (0.08 and 0.16 millimeter, resp.).Processing the drops with higher
radius first reduces the probability of detecting false drops with a lower
radius, caused by agglomerates of pixels in the contour of the drops. However,
the detection is not efficient for radii below 8 pixels (0.08 millimeter).This detection process is enhanced with the erosion of
the contour images of detected drops. This is not a common process of
morphologic erosion [11]. In this process, after finding a centre, we
eliminate the pixels that have contributed to find this centre so that they do
not interfere in the subsequent process [12, 13].In Figure8, we
can see the results obtained on two images for a radius ranging from 5 pixels
(0.05 millimeter) to 46 pixels (0.46 millimeter).The drops
detected by our program. Each detected drop is marked with a white circle on
top of the original image.
(a)(b)


## 5. Results

To  evaluate our approach more
objectively we have chosen two images with different levels of photographic
quality, and compared the sets of drops obtained automatically with the drops
manually identified by us. Each image contains more than 100 drops with varying
conditions (radii, overlapping, border quality, etc.). In Table1, we show the results obtained with two of the images,
the images shown in Figure 8, in terms of recall and precision values. We have
calculated those values as defined in (2) where TP is the true positives (number of drops correctly identified by
the program), FN the false negatives
(actual drops not identified by the program) and FP the false positives (drops incorrectly identified by the
program). In other words, recall measures the proportion of existing drops that
the program was able to identify correctly, whereas precision is the proportion
of drops identified by the program that are truly correct:(2)recall=TPTP+FN,precision=TPTP+FP.  In the case of the first image, we
have obtained the following results. For a radius below 7 pixels the program
cannot find any drop. For the radius 10 (0.1 millimeter), not in the table
because recall=0 and precision not defined, we have TP=0, FP=0, and FN=3. For
the radius 12 (0.12 millimeter), also not in the table, because recall=0 and
precision are not defined, we have a TP=0, FP=0 and FN=1. For the other values of the radius not represented in the
table, we have TP=0, FP=0, and FN=0. As final results, taking into account all the values of
radius, we have for this image a recall of 0.71 and a precision of 0.89.Table 1
Precision and recall for different radii on two images: one pixel
corresponds to 0.01 millimeter.
First imageSecond imageRadius (pixels)RecallPrecisionRadius (pixels)RecallPrecisionRadius (pixels)RecallPrecisionRadius (pixels)RecallPrecision70.251.0017–191.000.9070.440.80160.571.0080.501.00200.751.0080.501.00170.771.0090.571.00210.600.6090.401.00180.571.00111.000.67220.601.00110.251.00190.501.00130.671.00230.671.00120.251.00200.500.60140.801.00240.331.00130.250.50220.250.33150.671.0025-261.000.75140.570.57230.751.00160.750.7528–441.001.00150.571.0024–441.001.00For the second image, which has a lower photographic
quality, we have worse results, having a total 0.55 for recall and 0.87 for
precision. Nevertheless we have, for many values of radius in the image,
maximum recall and precision. For several values of radius from 7 to 23 and for
radius equal to 35, 40, and 45, recall and precision are not shown in the
table, for the same reasons as in the previous image. We believe the cause for
these worse results with respect to the previous image is the lower quality of
this second image.


## 6. Conclusions and Future Work

In this paper, we have presented a
method for the automatic identification of drops in images taken from agitated
liquid-liquid dispersion. The results obtained with two images with more than
200 drops with diverse conditions (radii, overlapping, border quality, etc.)
lead to the conclusion that our program is able to detect a good percentage of
the drops. In the case of a better quality image, the program recognized 71% of
the drops. For the other image, with lower quality, only 55% were detected. We
have also observed that the approach is less efficient for smaller values of
the radius, since very small drops can be easily mistaken by noise.This work is a promising starting
point for the possibility of performing an automatic drop classification with
good results. However, given the limited number of images used in these
experiments, these results must be further validated. Currently, we are
manually identifying drops in our large library of images. Having a larger
number of annotated images, we can proceed with experimental validation and further
improve our results.This can be done by fine tuning the
parameters of the process, and learning the appropriate parameters given the
image conditions (quality, lighting, etc.). Another line of research we are
pursuing implies employing neural networks for strengthening drop recognition.



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*Source: 746439-2009-03-04.xml*