## 1 Introduction  
During tumour progression, cancer cells interconvert between epithelial and mesenchymal states with a high degree of plasticity based upon environmental signals [1]. These bidirectional transitions are known as epithelial to mesenchymal transitions (EMT) and mesenchymal to epithelial transitions (MET). Both transitions are required for the complex series of processes that result in metastatic dissemination [2; 3; 4; 5; 6]. For example, EMT is involved in both tumour cell migration and the transformation of cancer cells into a cancer stem cell (CSC) phenotype, each of which promotes growth of new tumours at distant locations [7; 8]. However, the repression of EMT and induction of MET is also essential for metastatic colonization [3; 4]. Since metastases cause most cancer-related deaths [9] it is of vital importance to understand the EMT/MET processes. Efforts to identify candidate therapeutics that interfere with the process are underway [10; 11]. However, dependent on the stage and identity of each cancer cell within a tumour or a patient, inhibition of either EMT or MET could be beneficial or harmful. Given the complexity of the transitions and their relationship to metastatic dissemination, more comprehensive characterization of the effect of candidate therapeutics on EMT and MET are needed. Characterization of EMT and MET is challenging due to several types of substantial heterogeneity. First, the processes of EMT/MET do not describe a binary toggling between two discrete states, but rather transitions along an \"epithelial-mesenchymal phenotypic (EMP) spectrum\" from more epithelial-like states to more mesenchymal-like states [1; 5]. Second, cells are heterogenous in the ease with which they can transverse this spectrum, often referred to as plasticity. Each cell line and individual cells within a cell line population can occupy distinct locations along the EMP spectrum and possess varying degrees of plasticity dependent on contextual signals. Third, the intracellular gene circuits and morphological changes that define the EMP spectrum differ from cell line to cell line [8; 9]. Finally, the EMP spectrum is only one of many transcriptional programs that define a cell. Some cancers, such as melanoma, are not derived from epithelial cells but, nevertheless, undergo an \"EMT-like\" transition during metastasis [10; 11]. Thus, simply defining the EMP spectrum for any specific cellular context is non-trivial and it cannot be assumed that parameters that accurately define EMP in one cell line apply to another. To further develop the candidate therapeutics for clinical application, it is first essential to develop assays capable of capturing and quantifying the degree, kinetics, heterogeneity and cell-line specificities of transitions along the EMP axis. Defined changes in morphology, specifically the acquisition of a spindle-like shape, constitute one hallmark of EMT that could serve as an informative feature. EMT has been monitored in real time by fluorescence imaging of vimentin by [PERSON] et al [12]. Both EMT and MET have been monitored by time-lapse imaging [13; 14] giving insights into the ongoing process. Digital holographic cytometry (DHC) has emerged as a complementary technique to obtain time-lapsed imaging for label free long-term cell analysis [15; 16]. The quantitative 3D images acquired can be used to follow morphological changes or changes in cell movement induced by therapeutic treatment [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. It has also been presented as a technique suitable for classifying distinct cell phenotypes [17; 23]. We have previously suggested that DHC can be used as a tool for identifying and monitoring EMT or MET [24] by characterizing the change in cell movements. Recently, it has been suggested that the application of machine learning techniques to DHC-derived features can detect epithelial and mesenchymal characteristics in cell lines of unknown EMP status [25].