Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) has been increasingly used for lesion detection in breast cancer diagnosis for its capability to provide spatial-temporal information. However, the massive and complex 4D spatial-temporal DCE-MRI data make the diagnosis process lengthy and error-prone. Moreover, normal fibroglandular tissue is occasionally enhanced through background parenchymal enhancement (BPE), which can degrade the performance of current algorithms. We propose a new method using a 3D Clifford analytic signal (CAS) approach for breast lesion segmentation of DCE-MRI data. A 2D temporal image is constructed from all the 2D DCE-MRI slices at different scanning time points on a given transverse plane, according to the CAS approach. Then, a 3D Clifford temporal image (CTI) is constructed by successively stacking temporal images. The proposed CTI can distinguish lesion regions both visually and quantitatively compared to the traditional DCE-MRI subtraction image. Finally, we employ a fully convolutional network (FCN) model for breast lesion segmentation using the CTI as one of the inputs. Experimental results on an independent public dataset (TCIA QIN breast DCE-MRI) and a private household breast DCE-MRI dataset (TBD) show that the proposed method can achieve superior performance over current methods, both qualitatively and quantitatively. INDEX TERMS Breast DCE-MRI, breast lesion segmentation, fully convolutional network, clifford analytic signal, clifford temporal image.