Similarity maps and hierarchical clustering for annotating FT-IR spectral images

Abstract

Background: Unsupervised segmentation of multi-spectral images plays an important role in annotating infrared microscopic images and is an essential step in label-free spectral histopathology. In this context, diverse clustering approaches have been utilized and evaluated in order to achieve segmentations of Fourier Transform Infrared (FT-IR) microscopic images that agree with histopathological characterization.

Results: We introduce so-called interactive similarity maps as an alternative annotation strategy for annotating infrared microscopic images. We demonstrate that segmentations obtained from interactive similarity maps lead to similarly accurate segmentations as segmentations obtained from conventionally used hierarchical clustering approaches. In order to perform this comparison on quantitative grounds, we provide a scheme that allows to identify non-horizontal cuts in dendrograms. This yields a validation scheme for hierarchical clustering approaches commonly used in infrared microscopy.

Conclusions: We demonstrate that interactive similarity maps may identify more accurate segmentations than hierarchical clustering based approaches, and thus are a viable and due to their interactive nature attractive alternative to hierarchical clustering. Our validation scheme furthermore shows that performance of hierarchical two-means is comparable to the traditionally used Ward's clustering. As the former is much more efficient in time and memory, our results suggest another less resource demanding alternative for annotating large spectral images.

Figure 1

Principle of FT-IR microscopy. (A) At each pixel (indicated by circles), the infrared absorbance spectrum is measured, reflecting the biochemical status of the sample at the corresponding position. (B) Average spectra for different tissue components from a well established training dataset [3] exhibit relatively subtle differences on an absolute scale. (C) Mean spectra of crypts and tumor regions, with shaded areas around the mean spectra indicating standard deviation. Spectral variability within each class is small even in relation to the subtle differences between average spectra, so that differences between classes (here exemplified by crypts vs. tumor) remain distinguishable by classifiers.

Figure 2

Schematic overview of the cross-validation scheme for hierarchical clustering. (A) Composition of training data set, indicating an index color and proportion of spectra per class. (B) Dendrogram of the training data set and result of an optimal class assignment under a horizontal cut (indicated by dashed line in the left dendrogram) and an optimal tree assignment (right dendrogram) where each class is identified with the subtree colored according to its associated index color. Tree-assignment based segmentation not only achieves a much higher accuracy, but exhibits substantial differences in the assignment of several classes. The classes of crypts and submucosa are even identified as disjoint sets of spectra in both approaches, while substantial differences exist in the classes of tumour, inflammatory tissue, follicles, and support cells. The two segmentations indicate that even on well-curated training data, non-horizontal cuts in the dendrogram represent tissue classes much more reliably than horizontal cuts.

Figure 3

Indexed spectral images and confusion matrices of image 120514 . (A): Random-forest classified reference image. (B-D): Segmentations and confusion matrices obtained by different annotation approaches. In the confusion matrices, the numbers beside the tissue names indicate class sizes, and the tissues are sorted by size in descending order. Ward’s clustering in combination with the power metric achieves an Rand index of 0.83 and accuracy of 53.35% (data not shown).

Figure 4

Comparison of tree assignments, k -means and horizontal cut. Clustering the training dataset into 14 classes using k-means (left) or Ward’s clustering using a horizontal cut (middle) leads to partitionings with a Rand index of around.9 with relatively high standard deviation. A partitioning obtained from Ward’s clustering using tree-assignments leads to a significantly higher Rand index (right). Note that the Rand index approaches 1 for datasets with many classes. Yet, the difference after Monte-Carlo type validation is clearly significant.

Figure 5

Comparison of different hierarchical clustering approaches under varying the depth of segmentation Q . Three hierarchical clustering schemes are evaluated in terms of Rand index and accuracy on both the training dataset (A-B) and image 120514 (C-D). 10-fold Monte-Carlo cross validation is performed on the training dataset (the error bar indicates standard deviation).