from the background. There are about 40 different global thresholding algorithms
[2]. Classically, an algorithm involving thresholding includes the following stages:
• Preprocessing steps, which decrease the spatial variation of the image
• Thresholding, which produces one or more binary masks
• Masking or region of interest (ROI) selection
• Post-processing steps, for example, including second thresholding or
watershed
The watershed is based on a topographical interpretation of the grayscale image
as terrain of mountains and valleys; the algorithm interpolates boundaries between
objects based on the continuity in intensity peaks.
Various image filtering techniques can be introduced as preprocessing steps.
These transformations are representations of mathematical operators. These operators have formal properties, which make them suitable for certain types of signals.
For example, the convolution-based linear operators assume continuity of the sampled signal, while morphological operations do not. The notion of scale comes as the
support of the sampled kernel, so multiscale analysis provides rules how the supports of different operators change with scale. It is also important to consider the
sampling of the operators in the digital domain.
There are various geometry-based segmentation approaches, for example, using
edges, distances, or texture statistics. In addition, there is a vast array of pre- and
post-processing techniques, such as smoothing, mathematical morphology operations (i.e., watershed), partial differential equation methods, and shape methods.
This manuscript will focus on the geometry-based methods with a particular
emphasis on the edge detection techniques. Geometry-based approaches are invariant to changes of illumination, which is an issue in natural images and some microscopic techniques. In contrast, geometry-based approaches are susceptible to
structural or texture “noise” so extra care must be taken to address such issues.
3. Mathematical morphology
The mathematical morphology (MM) theory is a way of analyzing objects’
shapes by way of interaction with shape primitives called structuring elements (SE)
or kernels. A structuring element can be thought of as a small window that scans the
image and alters the central pixel within its frame. The mathematical morphology
theory was developed by Matheron and Serra [3].
MM operators are useful for the analysis of both binary and grayscale images.
Their common usages include edge detection, noise removal, image enhancement,
and image segmentation. MM approaches employ topological transformations and
hence do not depend, on the particular noise model. Therefore, they can be used
also in situations, where the noise is non-Gaussian.
The main building blocks of MM are the erosion ⊖ and dilation ⊕ operators (see
Appendix A.1). Erosion and dilation are best understood by their action on blackand-white images. If the white pixels represent the objects of interest, then after an
erosion with a SE, the white objects are contracted as the SE is inscribed inside every
white object. After a dilation with a SE, the white pixels are expanded as the SE is
circumscribed outside every white object. The action on grayscale images is similar
but must be understood in terms of ranking operations—that is, taking maxima and
49
Multiscale Segmentation of Microscopic Images
DOI: http://dx.doi.org/10.5772/intechopen.89003
[2]. Classically, an algorithm involving thresholding includes the following stages:
• Preprocessing steps, which decrease the spatial variation of the image
• Thresholding, which produces one or more binary masks
• Masking or region of interest (ROI) selection
• Post-processing steps, for example, including second thresholding or
watershed
The watershed is based on a topographical interpretation of the grayscale image
as terrain of mountains and valleys; the algorithm interpolates boundaries between
objects based on the continuity in intensity peaks.
Various image filtering techniques can be introduced as preprocessing steps.
These transformations are representations of mathematical operators. These operators have formal properties, which make them suitable for certain types of signals.
For example, the convolution-based linear operators assume continuity of the sampled signal, while morphological operations do not. The notion of scale comes as the
support of the sampled kernel, so multiscale analysis provides rules how the supports of different operators change with scale. It is also important to consider the
sampling of the operators in the digital domain.
There are various geometry-based segmentation approaches, for example, using
edges, distances, or texture statistics. In addition, there is a vast array of pre- and
post-processing techniques, such as smoothing, mathematical morphology operations (i.e., watershed), partial differential equation methods, and shape methods.
This manuscript will focus on the geometry-based methods with a particular
emphasis on the edge detection techniques. Geometry-based approaches are invariant to changes of illumination, which is an issue in natural images and some microscopic techniques. In contrast, geometry-based approaches are susceptible to
structural or texture “noise” so extra care must be taken to address such issues.
3. Mathematical morphology
The mathematical morphology (MM) theory is a way of analyzing objects’
shapes by way of interaction with shape primitives called structuring elements (SE)
or kernels. A structuring element can be thought of as a small window that scans the
image and alters the central pixel within its frame. The mathematical morphology
theory was developed by Matheron and Serra [3].
MM operators are useful for the analysis of both binary and grayscale images.
Their common usages include edge detection, noise removal, image enhancement,
and image segmentation. MM approaches employ topological transformations and
hence do not depend, on the particular noise model. Therefore, they can be used
also in situations, where the noise is non-Gaussian.
The main building blocks of MM are the erosion ⊖ and dilation ⊕ operators (see
Appendix A.1). Erosion and dilation are best understood by their action on blackand-white images. If the white pixels represent the objects of interest, then after an
erosion with a SE, the white objects are contracted as the SE is inscribed inside every
white object. After a dilation with a SE, the white pixels are expanded as the SE is
circumscribed outside every white object. The action on grayscale images is similar
but must be understood in terms of ranking operations—that is, taking maxima and
49
Multiscale Segmentation of Microscopic Images
DOI: http://dx.doi.org/10.5772/intechopen.89003