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Identifying cells in microscopic images is a crucial step toward studying image-based cell biology research. Cell instance segmentation provides an opportunity to study the shape, structure, form, and size of cells. Deep learning approaches for cell instance segmentation rely on the instance segmentation mask for each cell, which is a labor-intensive and expensive task. An ample amount of unlabeled microscopic data is available in the cell biology domain, but due to the tedious and exorbitant nature of the annotations needed for the cell instance segmentation approaches, the full potential of the data is not explored. This paper presents a weakly supervised approach, which can perform cell instance segmentation by using only point and bounding box-based annotation. This enormously reduces the annotation efforts. The proposed approach is evaluated on a benchmark dataset i.e., LIVECell, whereby only using a bounding box and randomly generated points on each cell, it achieved the mean average precision score of 43.53% which is as good as the full supervised segmentation method trained with complete segmentation mask. In addition, it is 3.71 times faster to annotate with a bounding box and point in comparison to full mask annotation.