Cell Segmentation in Microscopy Imagery Using a Bag of Local Bayesian Classifiers Zhaozheng Yin RI/CMU, Fall 2009

Motivation Accurate segmentation is challenging Segmentation using a single threshold yields poor results: Segmentation using a singe global Bayesian classifier also generates bad results:

Our Solution A bag of local Bayesian classifiers: Local Bayesian classifiers (experts) are learned from clustered training image patches. Any new pixel to be classified is assigned a posterior probability about how likely it is a cell or background pixel based on the mixture- of-experts model.

System Overview A new input pixel is classified by Maximum a Posteriori (MAP): is the feature around pixel x, for example, intensity, gradient etc. is the weight dependent on the input (different from boosting) Using the Bayes’ rule on each local Bayesian classifier, we have : where: Train and combine a bag of local Bayesian classifiers: represents pixel class (Cell or Background )

Training (get ) 1.Spectral clustering on local histograms (a) Compute local histograms around N sample pixels (b) Compute a pair-wise similarity matrix among the N histograms. (c) Group the N histograms into K clusters.

Training (get ) 2. Train local Bayesian classifiers (d) Achieve local histogram clusters from the spectral clustering (e) Obtain corresponding clustered image patches (f) Train local Bayesian classifiers from the clustered image patches

Classification First, we calculate a local histogram around, and then compute the similarity between and every histogram cluster,, where represents the histogram of cluster. The weighting function on classifier is defined as We combine the local Bayesian classifiers as Pixel is classified by

h=5 h=10 h=15 Classifier 1 Classifier 2Classifier 3 win size

Results

Cyan square: miss detection Yellow circle: false alarm Red: our detection Green contour: ground truth

Cyan square: miss detection Yellow circle: false alarm Red: our detection Green contour: ground truth

Cyan square: miss detection Yellow circle: false alarm Red: our detection Green contour: ground truth

Cyan square: miss detection Yellow circle: false alarm Red: our detection Green contour: ground truth

Cyan square: miss detection Yellow circle: false alarm Red: our detection Green contour: ground truth

Input: Cell posterior probability: Ground truth labeling:

Bayesian Classifiers on DIC Images We use intensity and gradient features on DIC images 10 bin Ix (intensity) 10 bin Gx (gradient magnitude)

k=1k=2k=3 h = 5 h = 10 h = 20 Cluster Win sz

Conclusion We propose a bag of local Bayesian classifier approach for cell segmentation in microscopy imagery. Our approach is validated on four types of cells of different appearances captured by different imaging modalities and device settings with 92.5% average accuracy.