This study addresses computer-aided breast cancer diagnosis through a hybrid framework for breast tumor segmentation in ultrasound images. The core of the three-stage method is based on the autoencoder convolutional neural network. In the first stage, we prepare a hybrid pseudo-color image through multiple instances of fuzzy connectedness analysis with a novel distance-adapted fuzzy affinity. We produce different weight combinations to determine connectivity maps driven by particular image specifics. After the hybrid image is processed by the deep network, we adjust the segmentation outcome with the Chan-Vese active contour model. We find the idea of incorporating fuzzy connectedness into the input data preparation for deep-learning image analysis our main contribution to the study. The method is trained and validated using a combined dataset of 993 breast ultrasound images from three public collections frequently used in recent studies on breast tumor segmentation. The experiments address essential settings and hyperparameters of the method, e.g., the network architecture, input image size, and active contour setup. The tumor segmentation reaches a median Dice index of 0.86 (mean at 0.79) over the combined database. We refer our results to the most recent state-of-the-art from 2022–2023 using the same datasets, finding our model comparable in segmentation performance.