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Emerging video technologies like 3DTV and Free Viewpoint Video require to transmit more information than just 2D color data. To allow rendering of arbitrary viewpoints of a video scene a new data format including 2D color and an accompanying depth map has been proposed. Consequently this new technique requires an efficient coding method not only for color information, but also for depth data. Depth maps are characterized by segments describable by piecewise linear functions bounded by sharp edges. Preserving these depth discontinuities is a crucial requirement for high quality view synthesis. To adapt to these characteristics we propose a novel algorithm for depth map compression explicitly signaling the location of discontinuities. Experimental results show that the proposed method yields up to 9dB PSNR gain compared to a JPEG-2000 encoder in high- bitrate scenarios. Subjective quality assessment of synthesized views using compressed depth maps can prove the superior visual quality originating from less geometric distortions.