Biomedical Examples (Biomedical Image Analysis)

In this topic, basic tools for a complete image analysis chain are introduced. These include, in order, image preprocessing (image enhancement or restoration, usually by filtering), image segmentation, some post segmentation enhancement, and finally, quantitative analysis. One very typical example was presented by de Reuille et al.,5 who acquired confocal sections of the shoot apical meristem in Arabidopsis thaliana. The meristem is plant tissue consisting of undifferentiated cells and is found in areas of the plant where growth takes place. Image contrast was gained by fluorescent labeling of the cell membranes. Confocal sections form z-stacks, two-dimensional images of thin sections that can be stacked to form a three-dimensional volume image. In this study, preprocessing consisted of Gaussian blurring to smooth images, in particular to reduce the impact of isolated bright or dark dots (it should be noted that isolated bright or dark dots can better be removed by median filtering). Subsequently, a threshold was applied to remove all the pixels with an image value of less than 10. This step was followed by linear histogram stretching. The segmentation step posed a challenge because the tissue area contained dark regions that were similar to the background outside the tissue region. To overcome this challenge, the segmentation process involved a combination of intensity-based thresholding followed by morphological closing (to fill the smaller dark regions inside the tissue region), which was then followed by watershed segmentation. With the fluorescently labeled cell walls now segmented, further analysis of cell geometry and topology (see topic 9) was possible, and plant development over time was quantitatively analyzed.

Related methods were used for image preprocessing and segmentation of electron microscopy images of collagen fibrils in the presence or absence of gold nanoparti-cles.9 The preprocessing steps were four iterations of the median filter followed by unsharp masking to remove background inhomogeneities. A binary mask was created by applying a threshold that was determined in an unsupervised manner by using Otsu’s method. Postprocessing of the mask was required to remove the nanoparticles, which was performed by identifying and removing connected regions with fewer than 150 pixels. Finally, morphological closing was applied to remove small interior holes or fissures. The steps that led to the final mask are shown in Figure 2.20. The resulting mask was now suitable for quantitative analysis using shape analysis methods (topic 9): namely, run-length analysis and topological analysis.

An example of an area in which image math becomes important is in the processing of microscope images to determine fluorescence anisotropy. In one example,8 fluorescent microscope images were used to map calmodulin binding over the projected cell area. A fluorescent calmodulin analog was imaged, and polarized microscope images were taken. Fluorescence anisotropy is based on the principle that some fluorescent molecules can be excited only in a specific polarization plane, and the fluorescent emission occurs in the same plane if the molecule is immobile. However, if the molecule can rotate during the excited lifetime, the fluorescence emission is randomized, and the degree of randomization is based on the rotational freedom. The degree of randomization can be determined from two images: one polarized parallel to the excitation polarization plane and one polarized perpendicular to it. Let those two images be designated Iy and I±, respectively. When the rotational freedom is low, most emission is still parallel to the original excitation plane, and Iy is high. Conversely, when the polarization is randomized with high rotational freedom, Iy and I± are about equally high. Polarization anisotropy can be defined through16

where R(x,y) is the spatially resolved anisotropy. When the rotational mobility is low, the ratio of Iy to I± assumes a very large value and R approaches unity. Conversely, when rotational mobility is high, the ratio Iy over I± is close to unity, and R is close to zero. When the fluorescent calmodulin interacts with myosin II light chain kinase,8 its rotational mobility is reduced and R is elevated. By computing R on a pixel-by-pixel basis using Equation (2.47) from microscope images of the cell, the locations of elevated calmodulin binding can be mapped.

FIGURE 2.20 Preprocessing and segmentation of collagen fibrils in the presence of gold nanoparticles. (A) is the original electron-microscope image. The fibrils are the long gray features, and the nanoparticles are the small black dots. After denoising (median filter) and background removal, (B) is obtained. The application of a hard threshold [Equation (2.45)] with Otsu’s method leads to image (C). A final mask (D) is created by removing all features that are smaller than 150 pixels.

To measure the water content (more precisely, the polarity of the environment) of a cell membrane, the fluorescent probe Laurdan is used. In a polar environment, the fluorescent emission of Laurdan experiences a red shift. Two fluorescent images can be taken, IB at the maximum emission of Laurdan in a nonpolar environment (440 nm) and IR at the maximum emission in a polar environment (490 nm). A ratiometric value of polarity, known as general polarization GP,18 can be computed by

Recently, the GP value was applied by Zhu et al.27 to examine the influence of reactive oxygen species on the cell membrane, a process hypothesized to be linked to cell damage and aging. To compute the GP map over the cell area, the two fluorescent images IB and IR were obtained. Equation (2.48) contains a division, which is a noise-sensitive operation. For this reason, both images first underwent Gaussian blurring; then the denominator was computed. Otsu’s threshold method was used to create a mask of the cell area. The final GP value was computed only within regions identified as cell regions, and the background was kept at zero. The individual steps are shown in Figure 2.21. The final map underwent histogram stretching to be printable, and negative values (dominant IR), which indicate regions of low polarity, are printed in dark shades and positive values (dominant IB, high polarity) are printed in lighter shades. The main advantage of ratiometric methods is the normalization. The GP value, for example, is independent of the overall exposure. For this reason, ratiometric methods are particularly well suited for quantitative image analysis.

FIGURE 2.21 Steps to compute the general polarization of Laurdan. One of the two unprocessed images (IR) is shown (A); after application of the smoothing operation, noise is reduced (inset in A, delimited by gray lines). After denoising and addition of IR and IB, a cell area mask (B) can be generated by thresholding with Otsu’s method. The final GP value [Equation (2.48)] is computed only inside the cell area, while the background is kept at zero. Since the GP image contains negative values, histogram stretching to the printable value range of 0 to 255 causes the zero-valued background to be gray, with negative values being darker and positive values being lighter (C).

The lung was used repeatedly as an example in this topic. In fact, an image analysis chain similar to the examples used in this topic was presented by Chen et al.4 CT slices of the lung were first filtered for noise removal, followed by a flood-filling process of the tissues surrounding the lung. Flood filling is functionally similar to region growing. The resulting mask was further enhanced by erosion. Results were similar to those shown in Figure 2.10.

Another example where the filtering techniques described in this topic play a key role is in the analysis of angiograms of the retina.25 The purpose is to detect aneurysms in the blood vessels of the retina, and contrast enhancement was performed with fluorescein. Fluorescein leads to a bright fluorescence of the blood vessels over the darker background of the surrounding tissue. Illumination inhomogeneities were first removed by dividing by a "flood image", that is, an image that reflects the illumination brightness. This operation was followed by unsharp masking to enhance the contrast of thin blood vessels. Bright pixels were then extracted using a top-hat filter,1 a morphological segmentation method that compares the brightest values in two concentric neighborhoods. If the brightest pixel in the smaller neighborhood is brighter by a threshold T than the brightest pixel in the larger neighborhood, the pixel is retained; otherwise, it is set to zero. In this formulation, the top-hat filter isolates local maxima. Those were eroded further to retain ultimate eroded points, which were used as seed points in the original fluorescent image for a region-growing process. In the final result, only small isolated and circular features, the suspected microaneurysms, were left in the image for visual inspection.

As a final example, a method is summarized to extract the steps of an aluminum step wedge from an x-ray image for the purpose of densitometry calibration.11 The purpose of using the step wedge was to eliminate fluctuations of film exposure and aging of film developer in quantitative x-ray images of mouse bones. A logarithmic curve fit of the film density over the aluminum thickness yielded the apparent x-ray attenuation coefficient for aluminum, which can then be compared with known attenuation coefficients. In addition, any density could be calibrated in equivalent units of aluminum thickness. A key element for the segmentation of the wedge steps was edge detection, because the edges from one step to the next could be used to delimit the flat areas of the step. Since the scanned x-ray image was very noisy, the edge detector (in this case, the Sobel operator) was preceded by a median filter and followed by a one-dimensional Gaussian smoothing filter that blurred the image in the horizontal direction only. The intensity average, computed line by line, made it possible to reliably identify a sufficient number of edges (Figure 2.22). The area between the edges was averaged and used to represent density under the corresponding step.

FIGURE 2.22 Segmentation of the steps of an aluminum step wedge in an x-ray projection image (A). The segmentation process makes use of the horizontal orientation of the steps. A median filter was used before the application of the Sobel operator for noise reduction, and the edge image was further filtered by convolving with a one-dimensional smoothing filter (B). Averaging of the intensity values line by line causes strong maxima at the edge locations (C), which can be used to detect edges. In this case, any maximum that exceeded the gray line (C) was recognized as an edge, and the algorithm allowed reliably to detect seven or eight steps.