A method for curvilinear object segmentation includes receiving at least one input image comprising curvilinear features. The at least one image is mapped, using a processor, to output segmentation maps using a deep network having a representation module and a task module. The mapping includes transforming the input image in the representation module using learnable filters trained to suppress noise in one or more of a domain and a task of the at least one input image. The segmentation maps are produced using the transformed input image in the task module.