In this paper, we propose regularized tree partitioning approaches. We study normalized cut (NCut) and average cut (ACut) criteria over a tree, forming two approaches: normalized tree partitioning (NTP) and average tree partitioning (ATP). We give the properties that result in an efficient algorithm for NTP and ATP. Moreover, we present the relations between the solutions of NTP and ATP over the maximum weight spanning tree of a graph and NCut and ACut over this graph. To demonstrate the effectiveness of the proposed approaches, we show its application to image segmentation over the Berkeley image segmentation data set and present qualitative and quantitative comparisons with state-of-the-art methods.