Parameters, Experimental Setup & Evaluation

We evaluate our algorithm on two datasets: WarMiCe and MITOS datasets. The details about the datasets are provided in Section 1.6. This section provides details about the experimental settings of candidate detection and classification algorithms proposed in this chapter.

4.6.1 Candidate Detection

GGMM model is learned from a small set of training images randomly selected from the MITOS (Aperio) dataset. Since all the images were stain normalised, therefore model trained on the MITOS (Aperio) dataset was used without any change on the MITOS (Hama- matsu) and WarMiCe datasets. Algorithm 3 was run for500iterations with tolerance () set to0.01. The choice of these parameters was based on some preliminary experiments. We did not observe significant improvement in performance of the algorithm by further in- creasing the number of iterations or further reducing. Although EM provides estimates forρ1andρ2in (4.1), more accurate estimates (ρ1 = 0.0014andρ2 = 0.9986) were used

based on the ratio of mitotic and non-mitotic data used for model fitting.

4.6.2 Candidate Classification

As majority of mitotic cells in the two datasets fall in the range of30×30to60×60pixels, therefore in order to incorporate the surrounding context along with the candidate mitotic cells, we choose a patch size of81_×81(i.e. 10 pixels margin on each side of the image) as a trade-off between the amount of context and the computational burden. However, since we

Figure 4.7: Demonstration of candidate patch alignment on five patches from WarMiCe dataset using the procedure outlined in Section 4.6.2. (top) Five 81_×81 patches with mitotic cells in centre; (bottom) same five patches after cell alignment.

perform cell alignment, which involves rotation of candidate patches, an extra padding of 20 pixels is added on all sides of the image so as to compensate for this rotation. Therefore, patches of size 121_×121pixels around the centroids of the candidate mitotic cells are extracted, and after cell alignment, only the central81×81part is used in the subsequent steps. Figure 4.7 shows some of the candidate cells extracted from WarMiCe dataset and their alignment using the procedure outlined above.

Intensity features are neither translation-invariant nor rotation-invariant. As de- scribed in [236, 237, 238], the classical dictionary learning framework is sensitive to trans- lations and rotations inherent in the dataset. Without cell alignment, some atoms in the learned dictionary may just be simple translations of each other. Therefore, translation and rotation of patches is carried out to ensure that all the candidate mitotic cells are aligned at the centre. The candidate patch extraction step results in the patches having cell in the centre, but cells are not aligned. We perform cell alignment by performing PCA on the coordinates of cell pixels, yielding a rotation matrix in the form of principal component coefficients. Using the rotation matrix, each patch is rotated around its centre point in the counter-clockwise direction. Finally, each patch is cropped around its centre point to obtain a patch of size81_×81pixels.

We divide all the cell-aligned candidate patches into two sets: Strain which con-

total candidate patches. We further split candidate patches inStrainintoXtrain (70%) and

Xvalidate(30%), respectively.Xtrainis used in the training procedure of the proposed DDL

method, whileXvalidate is used to monitor the classification performance at each iteration

and to avoid over-fitting. We select the dictionary from the iteration that gives the highest classification performance onXvalidateand perform classification of patches fromStest.

In order to reduce the effect from random partition ofStrainintoXtrainandXtest,

we run each experiment for 10 repetitions. For each repetitioni, we generate the set of detections for Stest and count the number Ntp,i of TP (i.e. detections whose centroids

are closer than8µmfrom the GT centroid), FP (Nf p,i) and FN (Nf n,i). The total num-

bers of TP, FN, and FP are given by (Ntp = P10 i=1Ntp,i), (Nf n = P10 i=1Nf n,i), and (Nf p = P10

i=1Nf p,i), respectively. The following performance measures are calculated:

recall (Re = Ntp/(Ntp +Nf n)), precision (Pr = Ntp/(Ntp +Nf p)) and F1-score (F1 =

2Pr×Re/(Pr+Re)).

For CAPP, we use the LIBSVM implementation [239]. We use grid search to find optimal parameters for the soft margin and Gaussian kernel parameters of SVM. Moreover for SVM, a higher penalty for misclassification of mitotic class was used, since the data obtained as a result of candidate identification step (Section 4.3) was highly imbalanced (mitotic-20.1%, non-mitotic-79.9%).

For cell words, we use blue ratio (BR), that measures the spatial distribution of nu- clear content of an image, as input to the proposed DDL framework [209]. Using colour channels (R,G,B) would add a non-trivial computational burden on the dictionary learn- ing algorithms, therefore BR was used as it incorporates information from all three colour channels. BR= 100 B 1 +R+G 256 1 +R+G+B . (4.13)

whereR, G andB refer to the red, green and blue channels of a coloured RGB image. To make the input data consistent with the dictionary optimisation procedure that does not constrain coefficients of atoms to be non-negative, all the data are linearly transformed to

have zero median. A stopping criterion for the algorithm is that the relative difference on the cost of the objective function for the consecutive iterations is less than10−6_{. We}

manually select regularisation parametersλfor training, andτ for classification such that a certain level of average sparseness (0.8) is attained when the algorithm converges. Similarly, number of atoms were fixed to [40, 40], i.e. 40 atoms for mitotic class and 40 atoms for non- mitotic class. The choice of parameters was empirically found to produce highly accurate results. For details on various experiments related to the choice of these parameters, refer to [38].