Optical microscopy imaging techniques have enabled a wide spectrum of biomedical applications. Among visualization, a quantitative analysis of tumour cell growth in lungs is of great importance. The main challenges inherently linked with such data analysis are: local contrast changes related to tissue depth, lack of clear object boundaries due to the presence of noise, and cluttering with motion artefacts due to translational shift of the specimen and non-linear lung tissue collapse. This paper aims to address these problems by introducing a novel image registration framework specifically designed to correct for motion artefacts from optical microscopy of lung tumour cells imaging. For this purpose, a previously developed modality independent neighbourhood descriptor (MIND) was adapted to cope with multiple image channels for optical microscopy data. Two versions of this novel multichannel MIND (mMIND) are here presented. The proposed registration technique estimates both rigid transformations and non-linear deformations both common in the optical microscopy volumes and time-sequences acquisition. The performance of our registration technique based on a novel multichannel image representation is demonstrated using two distinctive optical imaging data sets of lung cells: 3D volumes with translation motion artefacts only, and time-sequences with both rigid and non-linear motion artefacts. Visual inspection of the registration outcomes and reported results of the qualitative evaluation show a promising improvement compared to images without correction.