1 Introduction
Microscopy plays a key role in addressing several issues in biology [1, 2], materials science [3, 4], geology [5], among other areas. Nowadays, image processing techniques are frequently used together with microscopy, helping scientists to analyze photomicrographs of different samples. For instance, image segmentation can be used to separate elements within a photomicrograph, conducting the scientist to obtain relevant information such as counting objects in a sample, or determining their area.
There are a considerable number of computational packages available for segmentation. One of the most known ones is the open source project Fiji [6], a tool based on ImageJ [7] and aimed primarily at life sciences. Also, there are several methods rising for segmentation of different photomicrographs, obtained by confocal [8], magnetic resonance [9], and transmission electron [10] microscopies.
Despite the satisfactory segmentation which general methods present on different images, more specific ones should be used with reservations as they can return poor results when analyzing objects different from their original specifications. In addition, incorrect segmentation can mislead when interpreting regions of interest (ROI), thus decreasing the success rate of additional computational procedures.
To address the issues on photomicrograph segmentation using general methods, the algorithms named MultiLevel Starlet Segmentation (MLSS) [11] and MultiLevel Starlet Optimal Segmentation (MLSOS) [12] were developed. These methods gave rise to the opensource software JansenMIDAS, available at [13]
, which a scientist can use to obtain a multilevel threshold segmentation of his/hers photomicrograph, besides using supervised learning based on the comparison between the photomicrograph ground truth and the Matthews correlation coefficient (MCC)
[14] to obtain the optimal segmentation between all levels. JansenMIDAS was used previously for separating elements of two different materials, gold nanoparticles reduced on natural rubber membranes [11] and fission tracks on the surface of epidote crystals [12], returning an accuracy higher than 89 % in these applications.This article is given as follows. Section 2 presents a brief introduction on starlet wavelet transform, MultiLevel Starlet Segmentation (MLSS) and MultiLevel Starlet Optimal Segmentation (MLSOS) algorithms, and Matthews correlation coefficient (MCC), the techniques implemented in JansenMIDAS. Next, the Section 3 describes the two versions (textbased and graphical user interface) of this software, and presents examples of their utilization. On Section 4, we discuss the use of JansenMIDAS on the previous applications. Finally, in the Section 5, we present our final considerations about this study.
2 Methods
JansenMIDAS allows the user to apply the MultiLevel Starlet Segmentation (MLSS), a multilevel segmentation method based on starlet wavelets, and aimed to separate elements in photomicrographs. Combining MLSS and the Matthews correlation coefficient (MCC), we developed the MultiLevel Starlet Optimal Segmentation (MLSOS), an optimal segmentation tool. These methods are described in this section.
2.1 The starlet wavelet
The starlet wavelet is an isotropic^{1}^{1}1An isotropic wavelet is insensitive to the orientation of features, as opposed to directional wavelets. and undecimated^{2}^{2}2An undecimated wavelet do not suffer decimation (the process of reducing the sampling rate of a signal) between its decomposition levels. transform, suited to the analysis of images which contains isotropic structures (e.g. astronomic [15] or biological ones [16]), and also for structure denoising (e.g. threedimensional electron tomographies [17]).
The twodimensional starlet wavelet is obtained from the scale and wavelet functions [18, 19]:
(1)  
(2) 
where is the onedimensional third order Bspline (spline), a smooth function capable of separating large structures within an image [20]. The wavelet function , in its turn, is obtained from the difference between two decomposition levels.
Similarly to Equations 1 and 2, the finite impulse response (FIR) filters related to the starlet wavelet are defined by [20]:
(3)  
(4) 
where , and is defined as and for all . One can obtain the detail wavelet coefficients from the difference between current and previous decomposition levels, as in Equations 2 and 4.
Using Equation 3, the twodimensional starlet application begins with a convolution between the input image and (Equation 5):
(5) 
This convolution returns a set of smooth coefficients corresponding to the first starlet decomposition level, . Then, the wavelet detail coefficients for this level, , are obtained from the difference , as discussed earlier.
Let be the last desired decomposition level. Therefore, one can calculate the decomposition levels by:
where and is the convolution operator (Figure 1).
For , has zeros between its elements [21]. These operations generate a set , which is the starlet decomposition of the input image .
2.2 MultiLevel Starlet Segmentation (MLSS)
The method used in JansenMIDAS for photomicrograph segmentation is denominated MultiLevel Starlet Segmentation (MLSS). It is based on the starlet wavelet, and provides the multilevel photomicrograph segmentation. There are two alternatives for applying MLSS: the original and derivative algorithms.
2.2.1 Original MLSS algorithm
The original MLSS algorithm is based on the addition of detail levels obtained from starlet application. After obtaining the sum of the detail levels, the input image is subtracted, in order to reduce background noise. This version is implemented as follows:

The user chooses , the last desired decomposition level. The starlet transform is applied to the input image , resulting in wavelet detail decomposition levels: .

After obtaining the detail levels, the user chooses the initial detail level to be used in the sum, . Detail levels lower than () are ignored in this approach; this strategy can be useful for removing noise from the input image, which usually remains within the first decomposition levels.

Then, the detail levels to are summed, and is subtracted from the result:
where is the starletrelated segmentation for its decomposition level .
This algorithm results in }, a matrix with segmentation levels. Each level corresponds to the starlet detail level , and then the user can choose the best segmentation level for the input image.
2.2.2 Derivative MLSS algorithm
The derivative MLSS algorithm also uses the starlet detail decomposition levels, following the same basis of the original algorithm. However, there is no subtraction of the input image, in order to preserve possible small regions of interest (ROI). Its implementation follows:

The starlet transform is applied on the input image , generating detail levels: , where is the last decomposition level.

The user chooses the initial detail level, . Detail levels lower than () are ignored, and are summed:
where is the starletrelated segmentation for its decomposition level .
Similarly, the algorithm returns }. The segmentation level corresponds to the starlet detail level , and the user can choose the best segmentation level for the input image.
2.2.3 Matthews correlation coefficient (MCC)
Regions of interest (ROI) in an input image can be represented in a binary image denominated ground truth (GT). Generally, the GT is obtained by an expert, which indicates the ROI and the background on the input image. Then, the GT can be generated representing the ROI and the background using two different colors (usually, white and black).
One can compare the segmentation of an input image given by an algorithm with its GT, in order to estimate the success rate of this segmentation. From this comparison, we can define the resulting pixels as true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN), where:

TP: pixels correctly labeled as ROI by the algorithm.

FP: pixels incorrectly labeled as ROI by the algorithm.

FN: pixels incorrectly labeled as background by the algorithm.

TN: pixels correctly labeled as background by the algorithm.
From TP, TN, FP and FN, one can quantify the quality of the segmentation using the Matthews correlation coefficient (MCC) [14]:
(6) 
where .
Higher values indicate satisfactory segmentation: , zero and represent perfect, random and opposite segmentations, respectively [22].
2.2.4 MultiLevel Starlet Optimal Segmentation (MLSOS)
In this section we present the extension of MLSS. It employs the Matthews correlation coefficient (MCC, Equation 6) to obtain the optimal segmentation level. The refined method is named MultiLevel Starlet Optimal Segmentation (MLSOS), and is defined as follows [12, 23]:

MLSS is applied in a input image that has its GT for desired starlet decomposition levels, thus acquiring .

The segmentation results for each starlet level, , with , are compared with the GT of the input image, thereby obtaining TP, TN, FP and FN.

Based on these values, MCC is calculated for each .
Therefore, the optimal segmentation level obtained for the input photomicrograph is the one which returns the higher MCC value between segmentation levels obtained by MLSS.
Using MLSOS, one can establish the optimal segmentation level for the photomicrographs of a sample representing the set, thus estimating the optimal level for the entire photomicrograph set.
3 JansenMIDAS description and operating instructions
The software JansenMIDAS^{3}^{3}3The name JansenMIDAS is a tribute to the (possible) microscope inventors, Zacharias Jansen, and his father Hans, followed by an acronym: Microscopic Data Analysis Software. contains implementations for the MLSS and MLSOS methods. Using this software, scientists can apply these techniques on their own photomicrographs.
There are two versions of JansenMIDAS: one is based on text input, built for GNU Octave, and another has a graphical user interface (GUI), aimed to MATLAB users^{4}^{4}4MATLAB has a tool for creating graphical user interfaces, named GUIDE. Using it, the programmer can easily develop a GUI to integrate his/hers functions. Unfortunately, during the conception of this study, there was no equivalent tool on GNU Octave, difficulting the development of GUIs on that language.. They are distributed in the same package, in the folders TEXTMODE and GUIMODE, containing the textbased version and the GUI version respectively. On the next section, we describe both versions and how to use them.
3.1 Textbased version
Using JansenMIDAS’s textbased version is straightforward. After starting GNU Octave, it presents its GUI containing the Command Window and its prompt, represented by two “greater than or equal” symbols (>>). If Octave is running from the TEXTMODE folder, JansenMIDAS is started typing the following command in the Command Window:
>> jansenmidas();
Alternatively, the user can inform the variables which will store the processing results on Octave. This can be done using the following command, which starts JansenMIDAS and stores the processing results on the variables D, R, COMP and MCC:
>> [D,R,COMP,MCC] = jansenmidas();
These variables represent:

D: the starlet detail decomposition levels.

R: the MLSS segmentation levels.

COMP: a color comparison between the input photomicrograph and its GT, representing TP, FP, and FN pixels.

MCC: the Matthews correlation coefficient values for each segmentation level.
An example of applying the textbased version follows. First, the
software presents itself:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%% Welcome to JansenMIDAS %%%%%%%%%%%%%%%%
%%%%%%%%%% Microscopic Data Analysis Software %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The first step is to provide the first starlet detail level to be considered on the segmentation. If the user enters , for example, the starlet detail levels and will be disregarded from the segmentation. Remind that lower and higher detail levels present smaller and larger detail ROI, respectively.
Initial detail level to consider in segmentation:
In this example we suppose the user does not input a first detail level. When this happens, JansenMIDAS assumes this value as :
Assuming default value, initial level equals 1. Continue...
After that, the software asks the last desired segmentation level.
Last detail level to consider in segmentation:
Similarly to when choosing the first level, if the user does not input the last segmentation, the software assumes the default value, . In this example, we consider the last segmentation level equals to :
Last detail level to consider in segmentation: 3
Now JansenMIDAS asks the name of the photomicrograph to be processed. The TEXTMODE folder contains two test images, named test1.jpg and test2.jpg (Figure 2). These images are suitable to test the original and derivative MLSS algorithms, respectively.
Please type the original image name:
For this example, we chose the image test1.jpg^{5}^{5}5The optimal segmentation for this photomicrograph is obtained using and [11].. Then, the software performs the MLSS on it, asking before what processing algorithm to use (original or derivative).
Applying MLSS...
Type V for Variant or any to Original MLSS:
In order to use the derivative algorithm, the user will type v or V. However, the original algorithm is the suitable one for the photomicrograph test1.jpg. To apply it, simply press Enter.
After that, the software asks if it will apply MLSOS on the photomicrograph; if yes, it is sufficient to type y or Y. In order to do that, the user should have the GT image representing the ROI on the input photomicrograph, thus JansenMIDAS will estimate the MCC values for each segmentation and generate the comparison between input image and GT.
Do you want to apply MLSOS (uses GT image)?
Please type a GT image name:
The folder TEXTMODE contains also the GT images of the test photomicrographs. The file names are test1GT.jpg and test2GT.jpg (Figure 3). Since we chose test1.jpg, test1GT.jpg is the GT image to be used on the comparison.
When MLSOS application finishes, the values of MCC for each segmentation level are shown on a plot (Figure 4). Then the program asks if it should record the resulting images or only display them.
Type Y to save images or any to show them:
If the user enters y or Y, the images will be stored with the same name of the original image, and information about the results, in three groups:

D, representing the starlet detail decomposition levels;

R, representing the MLSS segmentation levels;

COMP, representing the comparison between the input photomicrograph and its GT, when the last is provided.
For first and last levels equal to and , the information presented on the screen is:
Saving detail image... Level: 1
Saving detail image... Level: 2
Saving detail image... Level: 3
Saving segmentation image... Level: 1
Saving segmentation image... Level: 2
Saving segmentation image... Level: 3
Saving comparison image... Level: 1
Saving comparison image... Level: 2
Saving comparison image... Level: 3
When the user chooses to not store the images, the results are presented directly on the screen (Figure 5). For first and last starlet detail levels equal to and , the presented information follows:
Showing detail image... Level: 1
Showing detail image... Level: 2
Showing detail image... Level: 3
Showing segmentation image... Level: 1
Showing segmentation image... Level: 2
Showing segmentation image... Level: 3
Showing comparison image... Level: 1
Showing comparison image... Level: 2
Showing comparison image... Level: 3
Finally, JansenMIDAS processing ends with the following final message:
End of processing. Thanks!
3.2 Graphical user interface version
JansenMIDAS’s graphical version is also easy to use, although it is not straightforward as the textbased version. This version has interactive elements such as buttons, check and text boxes.
As in GNU Octave, the MATLAB environment has several areas. Its prompt is also available on the Command Window and represented by >>. Inside the folder GUIMODE, JansenMIDAS starts when typing the following command in MATLAB:
>> JansenMIDAS
Then the initial screen is presented (Figure 6). The first elements presented are:

The state button MLSOS (with GT). When pressed, the software will apply MLSOS besides MLSS.

The text boxes First dec level and Last dec level, where the user can inform to JansenMIDAS what are the first and the last segmentation levels to use.

The check box Variation algorithm. When checked, the software applies the derivative MLSS algorithm.

The check boxes Show D and Show R. When checked, JansenMIDAS will present the starlet detail levels and segmentation results instead of storing them on the disk.

The welcome text Welcome to JansenMIDAS, which presents information on the processing as the software performs its tasks.

The button Open image…, which asks the input image, to the user, thus starting the processing.
One example of JansenMIDAS’s application using the GUI version is given below. The processing starts when the user clicks on the button Open image…. Then, a window asks the input photomicrograph. The GUIMODE folder also contains the test images test1.jpg and test2.jpg, which can be used to simulate the software usage (Figure 2).
In this example we suppose the chosen photomicrograph is test2.jpg^{6}^{6}6The optimal segmentation for this photomicrograph is obtained using and [12].. The welcome text indicates the performing action, being changed to Opening image…. Then, the software shows the input image and the button Open image… becomes Process… (Figure 7).
At this point the user can choose other options:

If MLSOS will be used, pressing the button MLSOS (with GT).

The first and last segmentation levels, on the text boxes First dec level and Last dec level. As in JansenMIDAS’s text version, the default first and last segmentation levels, assumed when these boxes do not receive values, are and respectively.

If the software will present the starlet detail levels and segmentation results on the screen, using the check boxes Show D and Show R.
The derivative MLSS algorithm is suited to segment test2.jpg. Thus, if the user would want to apply MLSOS, with first and last segmentation levels equal to and , derivative MLSS algorithm and showing starlet details (D) and segmentation results (R), the options on the software interface would be filled as in Figure 8
After choosing the desired options, the processing starts when the button Process… is pressed. In this example the user pressed the state button MLSOS (with GT); therefore, JansenMIDAS asks the GT image corresponding to the input photomicrograph. The folder GUIMODE also contains the GT images of the test photomicrographs, test1GT.jpg and test2GT.jpg (Figure 3). The GT image test2GT.jpg is used to apply MLSOS on test2.jpg.
When the user inputs the GT image, the software presents it and the segmentation starts. Then JansenMIDAS shows a window containing MCC values for each segmentation (Figure 9) and the windows presenting D, R and COMP, according to the user’s choices (Figure 10).
In this example, the check boxes Show D and Show R were checked. Therefore, JansenMIDAS returns the image sets of starlet detail levels (D) and MLSS results (R). When MLSOS is applied, the images referring to the comparison between MLSS results and the GT corresponding to the input photomicrograph (COMP) is presented automatically. These results can be stored using the Save menu or button on each window. When the software ends its processing, the welcome text changes its information to Done.
4 Discussion
Most of the segmentation methods demand human intervention at some point of their execution. For example, the user of [24]
needs to select between 60 and 70 % of wellbinarized cells, and then the method continues the processing. Also,
[25] uses texturebased features for providing a coarse segmentation of dendritic structures from C. elegans, which is improved after by postprocessing.Automatic segmentation methods benefit their users, which employ less effort on image processing. Besides, multilevel segmentation methods based on isotropic undecimated wavelets may enhance the segmentation process by offering a set of detail coefficients for each wavelet decomposition level. Based on these ideas, the algorithms implemented in JansenMIDAS were used previously on the study of two different materials:
Gold nanoparticles reduced on natural rubber membranes. The original MLSS algorithm implemented in JansenMIDAS was used for separating gold nanoparticles in scanning electron microscopy (SEM) photomicrographs reduced on natural rubber membranes [11], thus being able to estimate the amount of synthesized gold nanoparticles contained on the surface of these samples [23]. The amount of nanoparticles within a sample can be estimated combining Mie’s theory and ultravioletvisible spectroscopy [26], a laborious approach. Moreover, it is difficult to define the stoichiometry and necessary parameters to estimate the density, i.e. the concentration/distribution of synthesized nanoparticles over a substrate, of organic substances developed using green chemistry.
Fission tracks on the surface of epidote crystals. The derivative MLSS algorithm implemented in JansenMIDAS was used for separating fission tracks in photomicrographs obtained from the surface of epidote crystals [12], which contain small ROI. Usually these tracks are counted manually on an optical microscope. There are commercial systems which perform this operation; for example, [27] describes an automatic method for counting fission tracks, based in two photomicrographs obtained from transmitted and reflected lights. These images are binarized and their intersection generates a coincidence mapping, which is used for the track analysis. A commercial system based on this method is available; however, the results acquired using this system often needs to be manually adjusted by the operator, being more time consuming than the usual measure [28]. JansenMIDAS’s application on the surface of epidote crystals had an accuracy higher than 89 %, and our approach can be extended to be an open alternative to these systems.
5 Conclusion
In this article we presented JansenMIDAS, a software developed to provide MultiLevel Starlet Segmentation (MLSS) and MultiLevel Starlet Optimal Segmentation (MLSOS) techniques. These methods are based on the starlet transform, an isotropic undecimated wavelet, in order to determine the location of objects in photomicrographs.
MLSS uses the addition of detail levels obtained from applying the starlet transform. There are two possible algorithms for MLSS: the input image may be subtracted (original algorithm) or not (derivative algorithm) from the sum of the detail coefficients. MLSOS, in its turn, chooses the optimal segmentation level from MLSS based on the Matthews correlation coefficient (MCC), which establishes the comparison between the set of training images and their ground truths.
JansenMIDAS is an opensource software released under the GNU General Public License. Its previous versions were used in the study of two different materials, returning an accuracy higher than 89 % in both applications. JansenMIDAS is presented in two versions: a textbased version, available for GNU Octave, and a graphical user interface (GUI) version, compatible with MathWorks MATLAB, which can be employed on the segmentation of several types of images, becoming a reliable alternative to the scientist.
Acknowledgements
The authors would like to acknowledge the São Paulo Research Foundation (FAPESP), grants # 2007/049525, 2009/049626, 2010/032829, 2010/204962, and 2011/094383.
References
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