Fig 1.
Schematic of imaging system and principle of phase measurement.
(a) Schematic of reflection-type quantitative phase microscope. (b) Principle of phase measurement of the sample in QPM. (c) Configuration of custom-made slide chamber for cells in reflection-type QPM.
Fig 2.
Full-field of view of a QPM image of WBCs after the removal of curvature in phase.
White spots are QPM images of single WBCs, and the black region is background. Image size is 350×260 μm (1292×964 pixels). In the sample preparation, only WBCs were extracted from whole blood and then suspended in PBS.
Fig 3.
Representative segmented QPM images of single cells and their size distribution.
(a) QPM images of WBC of a healthy donor. (b) QPM images of five types of cancer cell lines, namely, SW480, DLD-1, HCT116, Panc-1, and HepG2. Images were captured immediately after trypsinization to imitate CTCs floating in circulation. Pseudo-color represents OPL in nanometers. (c) Size distributions of diameters of 250 WBCs (green bars) and 250 cell lines (red bars).
Fig 4.
Two-branch flowchart of preprocessing for size-invariant feature extraction for statistical- and HOG-based subcellular classification.
(a) Segmented image of a cell. (b) OPL normalizations by path length (PL) or diameter (D). Line profiles along the black lines in the pseudo color images of OPL/PL or OPL/D are shown for comparison of two normalizations. The details of subcellular structure are unclear in the profile of OPL/D because of spatial low frequency components (the hemisphere), whereas the details of intracellular structure are recognized in the flat region of the profile of OPL/PL. (c) Size normalization and gradient compensation. Function f represents the profile of OPL/D or OPL/PL. Red arrows represent the spatial gradients of f (i.e., f′). The gradients were divided by resize factor m for compensations.
Fig 5.
Representative QPM images and their visualized HOG features.
(a) QPM image of cell line. (b) QPM image of WBC. In (a) and (b), pseudo color represents OPL. OPL is not normalized by diameter or path length. (c) Visualized HOG feature of (a). (d) Visualized HOG feature of (b). In (c) and (d), angles and lengths of the yellow lines in each compartment respectively represent orientation and strength of spatial gradient in OPL of the image.
Table 1.
Ensemble mean values of statistical parameters of OPL/PL over all WBCs and CLs.
Table 2.
Ensemble mean values of statistical parameters of OPL/D over all WBCs and CLs.
Fig 6.
All QPM images (OPL) normalized by path-length or diameters.
(a) OPL/PL: QPM images normalized by path lengths of cell lines; (b) OPL/D: QPM images normalized by diameters of cell lines; (c) OPL/PL: QPM images normalized by path lengths of WBCs; and (d) OPL/D: QPM images normalized by diameters of WBCs.
Fig 7.
Statistical characteristics of two classes of training-data sets after two OPL normalizations.
(a) Histograms of mean OPL normalized by path length (OPL/PL) over all WBCs and CLs and (b) histograms of mean OPL normalized by diameter (OPL/D) over all WBCs and CLs.
Fig 8.
Weight vectors (w) of SMV classifiers visualized in five statistical parameters.
(a) Weight vector for statistical parameters of OPL/PL and (b) weight vector for statistical parameters of OPL/D.
Fig 9.
Histograms of decision values of training-data sets.
Positive decision values for each cell are classified as a WBC, whereas negative decision values are classified as a cell line. Most WBCs (green bars) are classified as a positive decision value, and most cell lines (red bars) are classified as a negative one. The training data set consists of (a) statistical features of OPL/PL, (b) statistical features of OPL/D, (c) HOG features of OPL/PL, and (d) HOG features of OPL/D.
Fig 10.
Detection-error trade-off (DET) curves for various training-data sets.
Values in parentheses in the legend represent AUCs of their ROC curves.
Fig 11.
Weight vectors of SVM classifier found by parameter search visualized in seven-by-seven compartments.
The angles and lengths of the yellow lines in each cell represent direction and strength of decline in an QPM image. (a) Weight vectors of QPM images (OPL) normalized by path length. Left side represents visualized weight vectors of HOG feature of cell lines. Right side represents vectors of WBCs. (b) Weight vectors of QPM images (OPL) normalized by diameter. In each panel, the left sides represent weight vectors of HOG feature of cell lines. The right sides represent the vectors of WBCs.
Fig 12.
Classifications of heterogeneous phantoms.
(a) Visualized HOG features superimposed on OPL/PL represented in pseudo color. The numbers above the figures are bump heights (%). (b) Cross sections of the phantoms. (c) Decision values of simulated phantoms with respect to bump heights are determined by the SVM classifier trained on HOG features of OPL/PL.
Table 3.
Performance of the classifications on the basis of various parameters.