HeLa Cells

Figs. 4.6(a) and (b) separately show the projection images of two HeLa cells. The first HeLa cell, named HeLa1, contained 84 identified projected feature points. Six reliable feature points were selected from the identified projected feature points. Fig. 4.7(a) shows the loci of the selected points in the x-θ coordinate system. Fig. 4.7(b) shows the sine waves that fit the loci most effectively. The projection images of HeLa1 are aligned according to the fitted sine waves, and Fig. 4.7(c) shows the loci of the projected feature points after alignment. In the second HeLa cell, HeLa2, four reliable features were selected from 89 identified projected feature points, and Fig. 4.7(d) shows the loci. Fig. 4.7(e) shows the sine waves that fit the loci. Fig. 4.7(f) shows the loci of the projected feature points after alignment. To compare the different alignment methods, SPIDER and Xradia were also applied to align the projection images of HeLa1 and HeLa2. The same FBP algorithm was then applied to reconstruct the volumes from the aligned images.

Slices in the reconstructed volumes of HeLa1 and HeLa2 are shown in Figs. 4.8(a), (b), and (c) and Figs. 4.8(d), (e), and (f) respectively. Figs. 4.8 (a) and (d) were obtained using the proposed method, Figs. 4.8 (b) and (e) were obtained using SPIDER, and Fig. 4.8 (c, f) were obtained using Xradia. As shown in Fig. 4.8, the results of the proposed method were more favorable than those of SPIDER and Xradia. Comparing the results of the SPIDER and Xradia, the proposed method exhibits most well-defined membrane structures with least amount of artifacts, which is evident from 4.8(a) and (d).

The texture-based volume rendering algorithm [5] was used to produce a 3D image of the volume data. Figs. 4.9 (a), (b), and (c) show the volume-rendering results of HeLa1, and Figs. 4.9 (d), (e), and (f) show the volume-rendering results of HeLa2. Figs. 4.9 (a) and

(d) show the results of the proposed method, Figs. 4.9 (b) and (e) show the results of SPIDER, and Figs. 4.9 (c) and (f) show the results of Xradia. The gold nanoparticles in Figs. 4.9 (a) and (d) are clearly shown, thereby enabling the evaluation of the location, the size, and the amount of the particles. The cell membranes can also be visualized in the rendered image, helping the user identify the geometry of the cells.

The proposed algorithm was applied to process 10 other X-ray image sets of HeLa cells.

Among these 10 image sets, eight were successfully reconstructed (A1-A8, Figs. 4.10 and 4.11) except the other two (B1 and B2, Fig. 4.12 and 4.13). SPIDER and Xradia were also applied to the same sets of image data. Neither SPIDER nor Xradia could align the images in B1 and B2 for reconstruction. Specifically, SPIDER was effective for A3, A5, and A6;

Xradia was effective for A1, A2, A5, A7, and A8. Although the reconstructions could be completed, comparing to our results, the artifacts produced due to the misalignment are more apparent.

Table 4.1 lists the experiments conducted in this study including the phantom, HeLa1, HeLa2, and the other 10 HeLa cells, as well as the computing time required. This table shows that the main factors affecting computational time are the image size, number of images, and number of identified projected features. The experiments in this study show that when the input data contains 180 images of 1024 × 1024 pixels, the alignment can be performed in 10 min.

Fig. 4.12 and 4.13 show 16 frames of unsuccessful cases respectively. The main reason for the unsuccessful cases is the insufficient number of projected feature points in the X-ray images. In B1, most projected features exist in the image series less than 10 frames.

Although the membrane of cell appears in each frame, the low contrast and large size cause the membrane cannot be a feature. The occluded projected features also exist in B1 and cause the feature matching failed. The same problem is in B2. No any reliable projected feature can be found in B2.

The most crucial factor affecting the performance of the proposed method is the num-ber of reliable projected feature points. If there are enough reliable projected feature points, even if the projected feature points are not in the field of view in some

projec-tions, the method still works well because it also considers the set of partial loci. The proposed method performs most favorably if the features that produce the projected fea-ture points are close to the rotational axis. Carefully adjusting the rotation axis before images acquisition can improve the quality of the reconstruction.

Considering the shape of the projected feature points, aside from particle objects, the proposed method can manage any shape of object if it contains a sufficient number of distinct projected features. For examples, the corners of a square, the two tips of a rod, and the branch points of a tree-structured object can be used as feature points as long as the features do not deform during image acquisition. If the images satisfy these requirements, then the proposed method can successfully align the images.

A graphical user interface software system for the Windows system and Mac OS X 10.8 has been developed. The software system can be downloaded from the following URL: http://www.cs.nctu.edu.tw/∼chengchc/SCTA or http://goo.gl/s4AMx.

Figure 4.3: The simulated X-ray image of the phantom data. 180 emulated X-ray images were generated. The size of each image is 512 × 512 pixels, the rotation angle between two consecutive images is 1^◦, and the ranges of the vertical and horizontal errors are ±20 pixels.

Figure 4.4: Feature loci of the phantom data: (a) loci of 16 projected feature points before horizontal alignment; (b) best-fit sine waves; and (c) the aligned loci.

Figure 4.5: One slice in the phantom data: (a) original image; (b) result of proposed method; and (c) the result of SPIDER.

Figure 4.6: X-ray projection images of HeLa cells. 140 synchrotron X-ray projection images of 1024 × 1024 pixels were acquired for HeLa1 (a) and HeLa2 (b). The rotation angle between two projection images is 1^◦.

Figure 4.7: The loci of the reliable projected feature points of HeLa1 and HeLa2. (a) There were six reliable feature loci found in the acquired images of HeLa1.

(b) Most suitable sine waves of HeLa1, and (c) aligned loci of HeLa1. (d) There were four reliable feature loci identified in the acquired images of HeLa2. (e) Best-fit sine waves of HeLa2, and (f) aligned loci of HeLa2.

Figure 4.8: One slice in the reconstructed tomographic images of HeLa1 and HeLa2. (a), (b), and (c) are the same slice in the tomographic images of HeLa1: (a) result of proposed method; (b) result of SPIDER, and (c) result of Xradia. (d), (e), and (f) are the same slice in the tomographic images of HeLa2: (a) result of proposed method;

(b) result of SPIDER, and (c) result of Xradia.

Figure 4.9: The 3D volume rendering of the reconstructed volume (a), (b), and (c) are HeLa1; (d), (e), and (f) are HeLa2: (a) and (d) Results of proposed method; (b) and (e) results of SPIDER, and (c) and (f) results of Xradia.

Figure 4.10: Eight examples of successful alignment (1).

Figure 4.11: Eight examples of successful alignment (2).

Figure 4.12: The first example of unsuccessful alignment, B1. No one projected feature exists in the image series over 10 frames. The membrane of cell cannot be a feature because the low contrast and large size.

Figure 4.13: The second example of unsuccessful alignment, B2. No any reliable projected feature can be found in B2.

Table 4.1: The test results.

Number of

Size Number of identified Number of Time

Name (pixel) images projected features reliable features (sec.)

Phantom 512 × 512 180 16 16 102

HeLa1 1024 × 1024 140 84 6 364

HeLa2 1024 × 1024 140 89 4 397.5

A1 1024 × 1024 300 86 3 886

A2 1024 × 1024 150 85 4 393

A3 1024 × 1024 140 104 72 518

A4 1024 × 1024 320 64 8 712

A5 1024 × 1024 140 121 4 454.5

A6 1024 × 1024 280 80 8 784.5

A7 1024 × 1024 140 103 4 406

A8 1024 × 1024 280 26 3 590

B1 1024 × 1024 270 0 0 477

B2 1024 × 1024 300 0 0 490

The run time statistics were obtained by using a MacBook Pro, Intel i7 2.2GHz, 8GB main memory, and running Mac OS X 10.8.

Chapter 5

High-Resolution Large Volume