BlockGraphTransforms

Edge-adaptive transforms for efficient depth map coding

In this work a new set of edge-adaptive transforms (EATs) is presented as an alternative to the standard DCTs used in image and video coding applications. These transforms avoid ?ltering across edges in each image block, thus, they avoid creating large high frequency coef?cients. These transforms are then combined with the DCT in H.264/AVC and a transform mode selection algorithm is used to choose between DCT and EAT in an RD-optimized manner. These transforms are applied to coding depth maps used for view synthesis in a multi-view video coding system, and provides up to 29% bit rate reduction for a ?xed quality in the synthesized views.

Edge adaptive transform (EAT) design

The EAT design process consists of three steps, i.e., (i) edge detection is applied on the residual block to find edge locations, (ii) a graph is constructed based on the edge map, then (iii) an EAT is constructed and EAT coefficients are computed. The EAT coefficients are then quantized using a uniform scalar quantizer and the same run-length coding used for DCT coefficients is applied. The 2 × 2 sample block in Fig. 1 is used to illustrate the main ideas. We describe the encoder operation when applied to blocks of prediction residuals, though the same ideas can be easily applied to original pixel values.

[[1]Figure 1]

EAT construction

First edge detection is applied on the residual block to ?nd edge locations and a binary edge map is generated that indicates the locations of edges. If no edges are found in a residual block, then a DCT is used and no further EAT processing is performed. Otherwise, the encoder computes an EAT. A graph is generated from this edge map, where each pixel in the residual block is connected to each of its immediate neighbors (e.g., 4-connected neighbors) only if there is no edge between them. From this graph, we derive the adjacency matrix, diagonal degree matrix, and the Laplacian matrix. Projecting the signal of a graph G onto the eigenvectors of the Laplacian matrix yields a spectral decomposition of the signal, i.e., it provides a “frequency domain” interpretation of the signal on the graph. EAT coef?cients are computed as the projection of the one-dimensionalized image-signal onto the eigenvectors of the Laplacian matrix.