3-D density kernel estimation for counting in microscopy image volumes using 3-D image filters and random decision trees

© Springer International Publishing Switzerland 2016. We describe a means through which cells can be accurately counted in 3-D microscopy image data, using only weakly annotated images as input training material. We update an existing 2-D density kernel estimation approach into 3-D and we introduce novel 3-D features which encapsulate the 3-D neighbourhood surrounding each voxel. The proposed 3-D density kernel estimation (DKE-3-D) method, which utilises an ensemble of random decision trees, is computationally efficient and achieves state-of-the-art performance. DKE-3-D avoids the problem of discrete object identification and segmentation, common to many existing 3-D counting techniques, and we show that it outperforms other methods when quantification of densely packed and heterogeneous objects is desired. In this article we successfully apply the technique to two simulated and to two experimentally derived datasets and show that DKE-3-D has great potential in the biomedical sciences and any field where volumetric datasets are used.