Segmenting microvascular structures is an important requirement in understanding angioadaptation by which vascular networks remodel their morphological structures. Accurate segmentation for separating microvasculature structures is important in quantifying remodeling process. In this work, we utilize a deep convolutional neural network (CNN) framework for obtaining robust segmentations of microvasculature from epifluorescence microscopy imagery of mice dura mater. Due to the inhomogeneous staining of the microvasculature, different binding properties of vessels under fluorescence dye, uneven contrast and low texture content, traditional vessel segmentation approaches obtain sub-optimal accuracy. We consider a deep CNN for the purpose keeping small vessel segments and handle the challenges posed by epifluorescence microscopy imaging modality. Experimental results on ovariectomized - ovary removed (OVX) - mice dura mater epifluorescence microscopy images show that the proposed modified CNN framework obtains an highest accuracy of $99\%$ and better than other vessel segmentation methods.