We present a novel depth-map codec aimed at free-viewpoint 3D-TV. The proposed codec relies on a shape-adaptive wavelet transform and an explicit representation of the locations of major depth edges. Unlike classical wavelet transforms, the shape-adaptive transform generates small wavelet coefficients along depth edges, which greatly reduces the data entropy. The wavelet transform is implemented by shape-adaptive lifting, which enables fast computations and perfect reconstruction. We also develop a novel rate-constrained edge detection algorithm, which integrates the idea of significance bitplanes into the Canny edge detector. Along with a simple chain code, it provides an efficient way to extract and encode edges. Experimental results on synthetic and real data confirm the effectiveness of the proposed algorithm, with PSNR gains of 5dB and more over the Middlebury dataset.