A computer- implemented method for curvilinear object segmentation, comprising: receiving at least one input image comprising curvilinear features; and mapping, using a processor, the at least one image to output segmentation maps using a deep network having a representation module and a task module, the mapping comprising: 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; and producing the segmentation maps using the transformed input image in the task module; wherein the learnable filters are trained to balance noise suppression with curvilinear segmentation error in training images, wherein the training comprises minimizing the output of a loss function, the loss function configured to balance noise suppression with minimizing curvilinear segmentation error in training images; wherein the loss function is given by E = L Y g, F f X Θ R, Θ T + L R 2 Θ R where f() represents the representation module having parameters Θ R, F() represents the task module having parameters Θ T, Y g is a ground truth segmentation map, L() represents network error on training samples, and L R2 () is the noise regularization term to suppress noise in the data given by where I j are a set of auxiliary training images comprising noise patterns and W ik are the weights of the learnable filters of scale k in Θ R. receiving at least one input image comprising curvilinear features; and mapping, using a processor, the at least one image to output segmentation maps using a deep network having a representation module and a task module, the mapping comprising: 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; and producing the segmentation maps using the transformed input image in the task module; wherein the learnable filters are trained to balance noise suppression with curvilinear segmentation error in training images, wherein the training comprises minimizing the output of a loss function, the loss function configured to balance noise suppression with minimizing curvilinear segmentation error in training images; wherein the loss function is given by E = L Y g, F f X Θ R, Θ T + L R 2 Θ R where f() represents the representation module having parameters Θ R, F() represents the task module having parameters Θ T, Y g is a ground truth segmentation map, L() represents network error on training samples, and L R2 () is the noise regularization term to suppress noise in the data given by where I j are a set of auxiliary training images comprising noise patterns and W ik are the weights of the learnable filters of scale k in Θ R. 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; and producing the segmentation maps using the transformed input image in the task module; wherein the learnable filters are trained to balance noise suppression with curvilinear segmentation error in training images, wherein the training comprises minimizing the output of a loss function, the loss function configured to balance noise suppression with minimizing curvilinear segmentation error in training images; wherein the loss function is given by E = L Y g, F f X Θ R, Θ T + L R 2 Θ R where f() represents the representation module having parameters Θ R, F() represents the task module having parameters Θ T, Y g is a ground truth segmentation map, L() represents network error on training samples, and L R2 () is the noise regularization term to suppress noise in the data given by where I j are a set of auxiliary training images comprising noise patterns and W ik are the weights of the learnable filters of scale k in Θ R.