The accuracy of the algorithms depends on the technique used to label each crystal in the image. Second, another algorithm was developed that used convexity measures of the crystals based on area and perimeter to identify and reject overlapping and touching crystals.

The individual algorithms FB(b), UE(c) and DT(d) also underestimate the (FB+UE) area of the crystal. 46 4.5 The number of crystals segmented using UE+DT (dot) and manually. star) for each of the crystal images.

List of Abbreviations

## Introduction

### Justification

Research on agro-processing technology mainly controls product quality and thus improves the efficiency of the production process. In the sugar industry, the quality of the yield is highly dependent on the quality of the raw material supplied to the factory.

### Description of the Processes Involved in Sugar Production

*Sugar Cane Juice Extraction and Clarification**Crystallization Process**Fugal Stations*

The extraction process done by series of mills that crush the cane to separate the juice (which contains the sugar) from the fibrous part of the cane plant. This task is necessary to ensure the sufficient quality of the final product as defined by commercial specifications (i.e.

### Review of Crystal Size Measurement Tech- mques

The silicon detectors collected the laser light deflected by the solid suspensions in the solution. The main problem in the crystal image processing is the lack of an efficient algorithm to separate overlapping and touching crystals which compromises the accuracy of size measurements.

## Objectives

### Overview

The results presented in Chapter 7 demonstrate that it is possible to develop a computerized image-based system to characterize crystal size parameters that provides results comparable to the sieving technique. Finally, a summary of the entire study, including conclusions, recommendations and limitations, is provided in Chapter 8.

## Literature Review

*Introduction**Grain Size Analysis**Powers Method**Rens method**The RRSB Method**Butler Method**Comparison of Grain Size Methods usmg Artificial Data**Calculating MA and CV from Crystal Images**Summary of Size Distribution**Grain Size Analysis Using Sieve**Alternative Crystal Size Control Techniques**Image Based Techniques**Non-Image Based Techniques**MA and CV as Process Control*

For the normal probability distribution, MA is also equivalent to the mean size of the particles by mass. It was designed to provide the time history of the crystal content of the pans.

## Mathematical Morphology

*Introduction**Neighbouring Pixels**Connectivity of Connected Components**Structural Element (SE)**Basic Morphological Operators**E rosion**Dilation**Properties of Erosion and Dilation**Morphological Opening and Closing**Opening**Morphological Closing**Properties of Opening and Closing**Recursive Erosion**Ultimate Erosion**Distance Transformation**Watershed Segmentation**Summary*

As a result of this transformation, some foreground pixels in the original image become part of the background. Only the set foreground pixels that fit in the center of the texture element and all other pixels of the foreground texture element remain, i.e. In this way, depending on the size and shape of the SE, background pixels surrounding the foreground can be converted to foreground pixels.

The recursive erosion transformation of a binary image is based on the sequential morphological erosion of the image. The final erosion of a binary image is defined as a set of connected components corresponding to the union of the regional maxima of the transformed image using recursive erosion. In short, the eventual erosion of the object results in a region having an inner connected component.

## Algorithms for Crystal Size Measurements

*Introduction**Imaging Hardware and Acquisition**Applying Watershed Segmentation**Image Processing Algorithms**Foreground and Background Marker**Ultimate Erosion as a Marker**Distance Transform as a Marker**Combining Markers**Manual Clicking**Accuracy of the Segmentation Algorithm**Discussion and Conclusion*

The individual algorithms FB(b), UE(c) and DT(d) also underestimate the (FB+UE) area of the crystal. In most of the images, the number of crystals segmented by UE+DT is less than manually. The number of crystals segmented using UE+DT (puncture) and manually (star) for each of the crystal images.

To evaluate the performance of the UE+DT algorithm, the area of each crystal calculated using UE+DT is compared with the manually calculated area. Scatterplot of percent error in area calculated by UE+DT and manually for each of the crystals in Figure no. 23. Although the crystal area calculated by UE+DT and the manual click method showed a strong correlation (R plot slope was not 1:1.

## Use of Convexity to Remove Overlapping Crystals

### Introduction

This technique reduces erroneous data that can be introduced if overlapping crystals are included in the subsequent size measurements and determination of the crystal size distribution. The two general measures of convexity based on circumference and area are used to classify the sugar crystals as overlapping or non-overlapping. MA and CV were then calculated using this improved technique and were compared with the same parameters calculated using the manual method.

Contour Tracing

## The Boundary Tracing Algorithm

### Convex Hull

The convex hull is the smallest area containing the object, so that any two points of the area can be connected by a straight line, all points of which belong to the area. If you imagine a thin rubber band being pulled around the object, the shape of the rubber band creates the convex hull of the object (Sonka et al., 1998). A sample area (shaded in gray) together with its convex hull (area bounded by a dotted line) that would be formed by a rubber band if it were placed around the area. Starting at a point PI on the boundary, and moving counterclockwise to the next point on the convex hull, Pqi is found when the angle formed by the vector or PI Pq is minimum.

## Algo rithm to construct th e convex hull of a region

*Convexity Measure**Evaluation of the Two Class Classifiers Using the ROC Curve**AUe as a Performance Measure**Segmentation and Calculating Convexity**Segmentation of Crystals**Calculation of Convexity Measures**Classification and Choice of Thresholds**Classifier Accuracy using AUC**Calculation of MA and CV**Discussion and Conclusion*

Two common parameters that have been used to characterize the convexity of a shape are based on the object's area and perimeter. The value of the area under the curve (AUC) is then used to categorize a classifier as either random or non-random (Fawcett, 2006). 5.3) N = Gn +Gp = Rn +Rp • The actual non-overlapping rate (also called hit rate and recall) of a classifier is estimated as.

Often, however, the area under the operating characteristic curve is used to measure the performance of the two-class classifier. Once the perimeter and area of the regions and their corresponding convex hull were calculated, the convexity measures, CA and Cp, could be obtained. ROC curve for a classification of crystals into overlapping and non-overlapping classes using different threshold values of CA and Cp convexity measures according to their convexity measure.

Application of ANNs and SVMs to Classify Crystals as Overlapping and

## Non-overlapping

*Introduction**Artificial Neural Networks**Multilayer Perceptrons (MLPs)**Supervised Classification Results using N eu- ral Network**Support Vector Machine**Supervised Classification Results using Sup- port Vector Machines**Conclusions*

60% of the dataset was used for training and the remaining unseen 40% was used to test the network. It was seen that the majority (94.28%) of non-overlapping and (95.5%) overlapping crystals were correctly classified. The hyperplanes for the two classes become Yi(w.x+b) ~ l-~i' The optimal hyperplane (i.e., f(x) = 0) is located where the difference between the two classes of interest is maximized and the error is minimized.

The solution to the optimization problem in the equation above is obtained in terms of the Lagrange multipliers, ai. According to the Karush-Kuhn-Tucker optimality condition, some of the multipliers will be zero. It is seen that most (98.76%) of the non-overlapping and (85.21%) overlapping crystals were correctly identified.

## Comparison of Crystal Sizing Algorithms and Sieving Technique

*Introduction**Crystal Size Distribution Analysis using Me- chanical Sieve**Using Digital Image Processing**DIP and Mechanical Sieving Methods**Comparing with UE+DT Algorithm**Comparing with Convexity Based Algorithm**Discussion*

The size of the crystals passing through a particular mesh is not always smaller than the size of the sieve. The crystals passing through a sieve may actually have one dimension larger than the size of the sieve opening. The result of the siphon analysis can be used to estimate the crystal size parameters (MA and CV) using either a look-up table based on the mass fraction retained or by empirical equations (such as the Rens method) based on the cumulative percentage by mass.

The shift factor value was calculated by finding the value of S that gave the best correlation between the cumulative percentage by mass curves calculated by seeding and the UE+DT algorithm. A summary of the MA and CV values calculated from the shift of the cumulative percentage relative to the mass curve for a shift factor of S = 0.61 is shown in Table 7.3. As shown in Figures 7.2 and 7.3, the size of the crystals passed through the sieve can be larger than the size of the sieve.

## Summary and Conclusions

*Summary**Limitations and Recommendations**Conclusions**Future Work*

As described in Chapter 5, two convexity measures based on the area and perimeter of the object were used. The convexity of the crystals based on their area and perimeter were used as input features. This in turn will affect the accuracy of the measurement of the crystal size parameters.

This problem could be alleviated by using an adaptive structural element, which would change its size and shape according to the size and shape of the crystals in the sample. These algorithms were compared to each other and to the manual click method (used as ground truth) that directly traced the boundary of the individual crystals using the computer mouse. The accuracy of the segmentation algorithms depended on the technique used to mark the crystal in the image.

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