2.1 Definition and Properties

A nanotube is an element of 1D nanomaterial, category in which nanowires and nanofibers belong. Nanomaterials are classified as 3D, 2D, 1D and 0D; it means how many dimensions are above 100 nm (Fig. 2).

Fig. 2 Bulk material and nanomaterials. Classification based on the dimensions 

Nanotubes can be modified in many ways, associating a foreign element by physical and chemical techniques; resulting nanotubes are called meta-nanotubes. Five different types of association are listed below [¹⁵].

Doped nanotubes: nanotubes are associated with electron donor or acceptor elements.

Functionalized nanotubes: where various individual chemical functions are grafted.

Decorated (Coated) nanotubes: the foreign component is a genuine phase, from the point of view of chemistry and structure.

Filled nanotubes: the inner cavity is fully or partially filled with foreign atoms, molecules, or compounds.

Heterogeneous nanotubes: carbon nanotubes whose carbon atoms from the hexagonal graphene lattice are partially or even totally substituted with hetero-atoms.

2.2 Applications

The exceptional electrical, chemical, and mechanical properties made carbon nanotubes (CNT) used widely in the construction of chemical sensors and biosensors, especially in the field of supporting materials [²⁴]. Inorganic nanotubes (especially metal sulfides or oxides) are mostly fabricated to exploit other material-specific properties, and the focus of interest is on biomedical, photochemical, electrical and environmental applications [²¹,²⁵].

2.3 TiO₂ Nanotubes

In materials science, TiO₂ nanotubes are one of the most studied compounds because of their wide potential use in photocatalysis, dye-sensitized solar cells, and biomedical devices; reason why they were chosen for this work. These 1D nanoestructures provide highly stable unique electronic properties, such as high electron mobility or quantum confinememnt effects, a very high specific surface area, and even show a very high mechanical strength.

Self-organized oxide tube arrays or pore arrays can be obtained by an anodization process of a suitable metal. When metals are exposed to a sufficiently anodic voltage in an electrochemical configuration, an oxidation reaction will be initiated. The first self-organized anodic oxides on titanium were reported for anodization in chromic acid electrolytes containing hydrofluoric acid by [³³]. This work showed that organized nanotube layers (although the author called the structure porous) of up to about 500 nm in thickness. The tube structure was not highly organized and the tubes showed considerable sidewall in homogeneity [²²].

3.1 Working Principles

To be able to use a SEM, it is essential to recognize their features, as well as to understand the reasons for the contrast of SEM images. The scanning electron microscope is used for observation of specimen surfaces. When the specimen is irradiated with a fine electron beam (called an electron probe), secondary electrons are emitted from the specimen surface. Topography of the surfaces can be observed by two-dimensional scanning of the electron probe over the surface and acquisition of an image from the detected secondary electrons [¹²]. To form the electron probe, the SEM requires basically an electron gun, a condenser lens, and an objective lens. Other components are necessary to, but it could vary because of design, and applications.

3.2 Electron Matter Interactions

Since the interaction electron matter release different types of electrons and signals (see Fig. 3), there are different types of electron and signal detectors for image acquisition in materials science, some of the most commonly used in SEM are the SE (secondary electron), BSE (backscattered electron), in-beam SE, and the EDX detector.

Fig. 3 Scheme of emission. Various electrons and electromagnetic waves from the specimen [¹²] 

There are two main issues involved in image acquisition, the material composition and the information we want to obtain. For example, non-conductive materials limit the quality of image because of the material charging and the low signal, and the selected signal detector depends on the electron emitted from the sample, secondary electrons are sensitive to the morphology and give information near to the surface, while the back-scattered electrons comes deeper from the sample and give information of the atomic mass. Other photonic signals are emitted from the sample, for example, characteristic x-rays and continuum bremsstrahlung, the x-rays are used to know qualitative elemental composition of the sample.

3.3 Image Processing Mechanism

All the electronic or photonic signals resulting of the electron matter interaction can be used to produce an image according to the detector mechanisms, but the most common is the SE image. The called “raster image” begins in the scan of the specimen by means of a very thin electron beam (a few nanometers of diameter) controlled by electrostatic lens, the magnification depends on the scanned area and the screen resolution, smaller scanned area achieves larger magnification. Once the secondary electrons are emitted from the specimen, a grid whit a low positive voltage attract them, and then are accelerated to reaches the scintillator with enough energy to emit photons, a photomultiplier amplify the signal, the brightness of the image depends on how many electrons reaches the detector and the contrast can be modifying changing the photomultiplier voltage.

3.4 Nanotubes SEM Characterization

In nanotubes characterization, is necessary to define general properties as the chemical composition, random or aligned growth orientation. Specific features are obtained in individual nanotubes as the length, inner and external diameter, wall thickness, gap between nanotubes, and crystalline structure are the most commonly used fixtures to define the nanotubes (see Fig. 4) [¹¹,²⁸,³²].

Fig. 4 Nanotubes characterization. Features extraction of vertically aligned TIO₂ nanotubes sample 

Above mentioned features are normally obtained by means of several characterization technics; FESEM (field emission scanning electron microscopy), XRD (x-ray diffraction), TEM (transmission electron microscopy), EDX (energy dispersive x-ray spectroscopy), PL (photoluminescence), BET (Brunauer-Emmet-Teller) and XPS (x-ray photoelectron spectroscopy) are the most used [²⁷,²⁹].

In SEM, when a specimen is well known, extract sample features becomes easier. However, this rarely happens and the task begins to be tough. Each analyzed sample has its own image processing issues, but in general, get the optimum contrast and focus is critical to precisely define the edges. Edges are very important in feature measurements. In NT, it is all about edges, since a well-defined edge allows to measure distances, diameters, heights, etc.

In nanoscale, at very high magnification, SEM measurements are very susceptible to electromagnetic and mechanical noise, to avoid this, scan speed is increased and image quality is decreased, losing sharpness and getting inaccurate measurements. Also, acquirable statistics, as average diameter or density, may be a tedious, tired and very slow task, and are susceptible to the issues treated above.

However, depending on the tools at hand, strategies to separate by reduced areas, and manual counting could be used (see Fig. 5).

Fig. 5 Nanotubes density. Example of manual method to estimate the nanotubes density in a SEM image 

Actually, SEM’s software offers a wide variety of tools which could be useful in general applications areas, however, the mentioned tools have low performance in specific areas due to its not specialized development.

To overcome this problematic, it is necessary to buy an specialized expensive software or perform a post-processing image analysis procedure.

4.1 SEM Image Restoration

The main objective of restoration techniques is to recover a SEM image of VANT that has been degraded. To achieve this, it is necessary to know the degradation phenomenon that produced this result.

The principal sources of degradation in SEM images are generated during the acquisition process which is affected by a variety of factors such as: external influences, the fluctuation of temperature in the room and mechanical vibrations; equipment quality, defects and malfunctions of the sensing elements; and operation, the operator’s lack of experience and improper specimen preparation. The factors above listed are attributed to the followings types of image disturbances: noises, blurring, poor quality, low contrast, among others.

Practically, restoration techniques attempt to model the degradation and apply the inverse process, to recover an original SEM image of VANT with good quality. According to [³] this restoration process can be modeled as in Fig. 7, an input SEM image f(x, y) is modified by a degradation function H and additive noise η(x, y) to produce a degraded SEM image g(x, y). With some knowledge about the degradation function and the additive noise, a restoration filter is created and applied on the degraded SEM image to get an approximation f^(x,y), which is desired to be as close as possible to the original SEM image.

Fig. 7 Image restoration. Model of the SEM image restoration process 

There are exist two types of SEM image restoration techniques, some work in spatial domain and others in frequency domain.

The first operate directly on SEM image pixels and are applicable when degradation is additive noise produced by random processes in the microscope, and the others on the SEM image’s Fourier transform and are chosen to work with degradations such as SEM image blur due to lack of resolution. Below are some of these techniques as long as results generated on degraded SEM images of VANT. For spatial domain, statistic filters and adaptive filters are presented; and for frequency domain, inverse filtering and Wiener filtering.

4.1.1 Linear Filtering

These filters transform a pixel value of noisy SEM image given some neighboring pixels values. This transformation is carry out by statistical operations such as mean, median and mode filtering. In the case of mean filtering, the technique is applied directly in spatial domain that given a noisy SEM image g(x, y) obtains a filtered SEM image f^(x,y) whose values for each pixel are calculated by averaging pixel values from neighborhoods of the noisy image. The operation can be represented with the following equation:

f^(x,y)=1mn∑(s,t)∈Sxyg(s,t), (1)

where S_xy is the set of coordinates in a neighborhood of size mxn, centered at point (x, y). For others filters, the pixel values of filtered SEM image are calculated by obtaining the median and mode of noisy image neighborhoods. The following example serves to explain this concept. It has a SEM image region with pixel values 1 and 2, and there is a noise pixel 8 (see Fig. 8). When applying a mode filtering, the noise pixel is transformed to a more representative value of its neighborhood, in this case is 1 because it is more frequently. In [³¹] an example of the use of median filtering to remove SEM image noise is presented.

Fig. 8 Mode filtering. Example of mode filtering on a matrix 

In plain words, statistic filters are actually a SEM image smoothing to mitigate or eliminate pixels with very different values in image’s homogeneous regions such as noise and borders. In the case of noise, the desired effect is the elimination of this in the SEM image; and in the case of borders, the result is an attenuation of them [¹⁹].

4.1.2 Adaptive Filters

While statistic filters work on SEM images regardless of the change of characteristics and noise from one region to another, adaptive filters modify their operation according to statistical information of the filtering region (neighborhood). For this reason adaptive filters have better performance than statistic filters, greater computational cost and complexity [¹⁷]. It is important to remember that these are applied only when the SEM image degradation is additive noise.

Adaptive filters are based on two simple parameters of the SEM image, mean and variance. These measures have a strong relationship with the SEM image appearance, on the one hand the mean represents the average pixel value or intensity in a determined SEM image region, and on the other hand the variance a measure of contrast in that region.

Desired operation of the adaptive filters is to transform a noisy SEM image g(x, y) into a filtered SEM image f^(x,y) close to the original SEM image whose pixel values are computed as follows: If a pixel g(x, y) is located in a relatively uniform neighborhood, that is, with little noise, the filtering result for this pixel is a close value to its neighborhood. If noise is present, it is expected that the filter output is a weighted average of the pixels in the neighborhood. Finally, if the pixel belongs to the SEM image edges, its value should be preserved to avoid blurring in the resulting SEM image. According to literature, the operation described above can be expressed as:

f^(x,y)=g(x,y)−ση2σL2[g(x,y)−mL], (2)

where ση2 is the variance of the noise that has corrupted the original SEM image. σL2 and m_L are the local variance and mean of the neighborhood pixels, respectively.

A comparison between a statistic filter and an adaptive filter is seen in Fig. 9. Filters were applied to a SEM image of vertically aligned TiO₂ nanotubes with simulated noise. Results (Fig. 9c and Fig. 9d) clearly show that the adaptive filter has a better performance to reduce noise and improve the edges of nanotubes, and therefore it gets a good approximation of the original SEM image.

Fig. 9 Spatial domain filters. (a) Original image of vertically aligned TiO₂ nanotubes, (b) degraded image by salt-and-pepper noise, (c) result of 9x9 median filtering and (d) result of adaptive median filtering with maximum neighborhood size of 9x9 

4.1.4 Wiener Filtering

Unlike inverse filtering, Wiener filtering takes into account both the degradation function and statistical information of the noise when trying to restore a degraded SEM image. It reduces the additive noise and inverts the blurring simultaneously. The main idea of the filter is to find a filtered SEM image f^ from the degraded SEM image such that the mean square error e² between it and the original SEM image f is minimized. This measure is given by:

c2=E{(f−f^)2}. (5)

In addition to the above minimum error criterion, it is assumed that the degradation function and noise are uncorrelated and that the filtered SEM image has a linear relationship with the degraded SEM image. According to these assumptions and others, it can be found the following expression for Wiener filtering in the frequency domain:

F^(u,v)=[1H(u,v)|H(u,v)|2|H(u,v)|2+Sη(u,v)Sf(u,v)]G(u,v), (6)

where F^(u,v) is the filtered SEM image, H(u, v) the degradation function, G(u, v) the degraded SEM image, S_η(u, v) and S_f(u, v) are the power spectrum of the noise and of the original SEM image, respectively. There are two important observations about this expression: first, no filtering errors occurs if the degradation function has zero values; and secondly, if the noise is not present its power spectrum is discarded and Wiener filtering is reduced to an inverse filtering [¹³].

A drawback of this filter is the prior knowledge of the original SEM image power spectrum which in practice isn’t available. Moreover, its main advantage is perform well in the noise presence. In [¹⁴] a study about carbon nanotubes characterization is presented which uses the Wiener filtering to reduce noise in images and improve their quality.

Fig. 10 shows the results of applying the inverse and Wiener filtering on a simulated blur image of vertically aligned TiO₂ nanotubes with Pt protective layer. Remember that this disturbance can be originated by lack of resolution and misconfiguration of the SEM. As can be seen, Wiener filtering (Fig. 10d) obtained a better result than inverse filtering (Fig. 10c) in the image restoration because it reduced noise and clearly defined edges.

Fig. 10 Frequency domain filters. (a) Original image of vertically aligned TiO₂ nanotubes with Pt protective layer, (b) degraded image by motion blur, (c) result of inverse filtering and (d) result of Wiener filtering 

4.2 Nanotubes Segmentation

Once the SEM image of VANT is restored, the next step in image analysis is nanotubes segmentation, which aims to divide the SEM image into its interest objects (nanotubes) and background. This is the most difficult and important step because an effective feature extraction method is required. For example, in the characterization of VANT images it’s very common to perform counts and measure diameters and lengths, these features can be extracted easily if the nanotubes segmentation is accurate, otherwise this data may be false. In other words, the correct VANT characterization is strictly dependent on the accuracy of SEM image segmentation.

There are several nanotubes segmentation methods but most are based on two SEM image properties: similarity and discontinuity. The former divides the SEM image into similar regions according to the pixel intensity values; and the later searches for abrupt changes in SEM image intensity (image edges) and uses these discontinuities to assess different regions [¹⁸]. This section focuses on the similarity based methods because in the image analysis area applied to VANT characterization are the most used, some of these methods are: thresholding, region growing, region splitting and merging and k-means clustering.

4.2.5 Experimental Results of Segmentation Methods

The different segmentation methods were tested on an image of a cross section of TiO₂ nanotubes, see Fig. 11. A comparison of these against the ground truth (Fig. 11b) show that k-means clustering achieved the best segmentation result because it has well defined objects (nanotubes are not merged) and a low rate of false positives (background’s pixels labeled as object’s pixels).

Fig. 11 Segmentation methods. (a) Original image of an exposed intermediate cross section of TiO₂ nanotubes, (b) ground truth segmentation, (c) segmentation results by thresholding, (d) region growing, (e) region splitting and merging and (f) k-means clustering 

4.3 Feature Extraction

At this stage, the features of the detected objects in the previous segmentation are extracted. In our case the objects are nanotubes, thus the features of interest could be: counts, areas, diameters, lengths, density, among others.

Counting nanotubes and their geometric features are simple features extracted directly from the pixels labeling; others such as density (nanotubes number per square unit) and diameter are derived features because are calculated from simple features. Finally there are also higher level features like type of nanotube that require further processing. Some of the methods proposed in literature for calculating these features are presented.

4.3.1 Nanotubes Counting

In order to extract this feature it is necessary the connected components labeling in the binary image of segmentation. The labeling groups the object pixels in components based on pixel connectivity (similar intensity). So all the pixels that belong to the same connected component have equal label, while the pixels that belong to others components get different labels. Generally the labels used are integer numbers, being zero the label for background pixels.

For more information, see [²⁶] for a complete description of the algorithm. Fig. 12 shows experimental results of this method.

Fig. 12 Connected components labeling. (a) Binary image with three objects and (b) result of the labeling algorithm 

As described above, counting nanotubes can be performed as follows: select an original image of nanotubes as that of Fig. 11a, execute some segmentation method to obtain a binary image as shown in Fig. 11b, apply a labeling algorithm to this binary image and get the number of labels corresponding to the total number of nanotubes, which in this example would be 30. Performing automatic counts on images with hundreds or thousands of nanotubes is an advantage of image analysis compared to manual methods because reduce effort and time.

4.4 Validation

After the nanotube’s features have been extracted, the next and last step in image analysis is to validate that these are correct. To perform this, it is necessary to have an images dataset whose correct features are well known and compare them against the results obtained by the image analysis methods. In literature, the images dataset is known as ground truth and it is assambled mainly in two ways, by manual inspection of samples under microscope or by computer and using simulated images [¹⁸].

In the first way, a group of experts select a set of samples (e.g., nanotubes) and characterizes them either directly under microscope or by using semiautomatic computer programs on their digital images. It is recommended to repeat this manual characterization several times for reducing effects such as the subjectivity of experts on the results [³⁰]. In the second way, the ground truth is obtained by simulation software that generates images based on parameters specified. For example, it could simulate an image whose number of nanotubes and areas are known. Here there is not subjectivity problem because the images are always created with the same algorithms; however, these may not be sufficiently similar to real experimental images.

After obtaining the ground truth data, the following is to use its images as input of the image analysis system and to compare the correct characteristics with those obtained by the feature extraction procedures. If there is similarity between both characterizations, it is said that implementations of the methods perform satisfactory; on the contrary, the methods that provided incorrect measurements of the features must be implemented again, and this is based on an error tolerance defined by experts. Finally, it is recommended to test the system with real images which could represent cases that will be found later and with important challenges such as noise, blurring and lighting changes.

This effectively to ensure robustness and good performance of the system.

4.5 Characterization of VANT

Next it is presented an example of automatic characterization of VANT by image analysis. Two images of vertically aligned TiO₂ nanotubes were used and the following methodology was applied to these: for the image restoration stage an adaptive median filtering was performed, the segmentation was carried out by the k-means clustering algorithm, and finally the feature extraction was made with the formulas mentioned above.

Fig. 13 shows the segmentation results over the two images to visualize the nanotubes detected and Table 1 presents the characterization results of the two images with the applied methodology. The extracted features were: number of nanotubes (count), average diameter and area, gap between nanotubes (GBN) and density. The results obtained are presented in the column approximation while the correct results in the column ground truth.

Fig. 13 Nanotubes detection. Segmentation results over two images to visualize the nanotubes detected 

As can be seen in Table 1, the approximation obtained for the image in Fig. 13a was acceptable compared against the ground truth. This result is due to the good quality of the image, the small noise and high contrast allowed a good image segmentation (see Fig. 13b) that was crucial for the posterior feature extraction. In the case of the image in Fig. 13d which has a poor quality, it was not achieved a good approximation of features. Here, the nanotubes detection (61 NTs of 69 NTs) and the diameter measurement (90.70 nm against 115.91 nm) were affected by the lack of contrast and noise.

This example shows that the methodology applied produces acceptable characterization results on good quality images, but not in the opposite case. Some recommendations to improve these results are include image contrast techniques and morphological operations for a better detection of nanotubes.

A similar example is found in [²⁰], where an image analysis system for properties assessment of VANT is presented. It is provided a novel way of a surface bioactivation in titanium dental implants. The system is based on advanced image processing and includes restoration, segmentation and classification methods. It works with images of vertically aligned TiO₂ nanotubes obtained with SEM and extracts the following essential parameters for the nanomaterial characterization: inner tube area, tube wall thickness and residual space between tubes.

Fig. 14 shows the detection results of the parameters mentioned above with the presented system. Because of the image quality, the system does not detect all nanotubes, but a representative set is obtained to evaluate mean values of the parameters as shown in Table 2.

Fig. 14 Parameters detection. (a) the original image, (b) tube walls detection, (c) non-tube objects detection and (d) all objects detected. Source: [²⁰] 

These results are considered significant in the samples assessment but in the paper there is no comparison against the ground truth (correct measurement of parameters). Finally, the system could be applied in nanomaterial quality assessment.

Currently, there are tools for image processing and analysis that can be used to characterize VANT, e.g., ImageJ. The main usage of this software is to calculate particle features as average size, spacing, wall thickness and nearest neighbors; in this case the particles could be tubules or pores located randomly in a sample. A use case of ImageJ is shown in [⁴], where the measurement of tubule diameter and their spacing in tubular scaffolds is performed. Fig. 15 shows the segmentation and feature extraction results for a SEM image of a tubular scaffold in that paper. As can be seen, this tool provides an automatic way to characterize tubular structures which can be applied easily to vertically aligned nanotubes.

Fig. 15 Tool for image analysis. (a) SEM image of a tubular scaffold, (b) its segmentation after using ImageJ and (c) results table listing some extracted features. Source: [⁴]