In this strategy nuclear volume was first measured in 3-D to provide size information. As discussed in the introduction, this effectively allowed suppression of the sampling error posed by measurements from 2-D slices. As a result, a clear separation of adenocarcinoma from squamous cell carcinoma was observed. In contrast, the 2-D analysis showed much broader distributions for both cell types without clear separation of peak positions, potentially caused by the sampling noise. Second, the sampling error in 2-D also obscured identification of the nuclear size difference between examined cell types. It is worth mentioning that the peaks of the major axis lengths of adenocarcinoma and squamous cell carcinoma were about 6 and 5.5 μm [Fig. 5(f)], respectively. Although they were well separated in 3-D measurements, 2-D measurements of the same parameter did not show a clear difference. More importantly, both cell types showed the peak value of major axis length between 4 and 5 μmin 2-D [Fig. 5(b)], values that were substantially smaller than the resulting values in 3-D. These data strongly indicated that such 2-D measurements combined values associated with both sampling noise and real axis lengths. Specifically, if, in a given plane, we assume that all cell nuclei have the same axis length, then the measured axis length for a given nucleus can range from zero to its actual length, depending on the selection of the plane. This effect is true for every cell nucleus in that plane, resulting in a distribution of the measured value from zero to the actual length, especially when the spatial locations of individual nuclei are unrelated. As such, a sampling noise is created that lowers the peak position of the distribution curve away from the real value and also broadens the distribution curve if there are variations in the axis length among individual nuclei [Fig. 5(b)]. In contrast, 3-D measurement of the same parameter resulted in much narrower curves with clear separation of peak positions. The same observation was supported by minor axis lengths, as well [Figs. 5(c) and 5(g)]. Third, the relative orientation angle between neighbors showed a broad peak around 25 deg [Fig. 5(d)]. This peak was weakened in the 3-D results [Fig. 5(h)], where a more even distribution was observed across the spectrum of all angles, indicating a lack of orientation in such tumors. This distribution could be caused by the use of animal models, instead of human tumor samples, as it is well-known that adenocarcinomas tend to form glandular structures, while squamous cell carcinomas tend to form well-oriented cell sheets.45,46 Consequently, by showing more random cellular distribution patterns, the mouse tumor model could be more poorly differentiated compared to human tumors. Cell lines also tend to be relatively poorly differentiated, since these tumors tend toward immortalization. We therefore expect a much more prominent difference of their PDF curves in human tumors, especially when measured in 3-D. In another sense, this difference also supports the utility of the 3-D approach since this method even worked well on mouse models, which are harder to separate. However, the tremendous heterogeneity of human tumors, as compared with only two cell lines in this study, may pose challenges for classification that are difficult to capture in this model system. Finally, compared to the aforementioned features, a clear distinction between 2-D and 3-D approaches could not be found relative to measurements of distance-related features. This was expected because the sampling noise posed by 2-D does not affect the center position of cell nuclei, which are the major determinants of cell-cell distance.