Novel biomedical imaging techniques have enabled the acquisition of quantitative information from cells, tissues, and organs with unprecedented accuracy and specificity. Combined with the availability of vast computational resources, quantitative biomedical imaging pipelines have the potential to accelerate scientific discovery and improve clinical practice. An important engineering problem in this area relates to extracting quantitative information related to the form (shape and texture) of cells, tissues, and organs. I will describe our recent efforts toward the development of a general purpose segmentation method and present preliminary evidence that a tool capable of high-enough accuracy for quantitative imaging pipelines may one day be available. In addition, recent efforts in developing geometric data analysis tools for mining morphological information from biomedical image data will be described. In particular, I will describe the application of deformation and transportation related metrics, in combination with discriminant analysis techniques, towards understanding the distribution of cellular patterns in cancerous and normal tissues.