Quadtree-like pyramids have the advantage of re-suiting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L(2)) and the discrete (l(2)) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.

A spatially scalable video coding scheme for low bit rates is proposed. The codec is especially well suited for communications applications because it is based on motion-compensated predictive coding which provides the necessary low-delay property. The frames to be coded are decomposed into a Gaussian pyramid. Motion estimation and compensation are performed between corresponding pyramid levels of successive frames. We show that, to fulfill specific needs of spatial scalability, the motion compensation on each level must result in compatible prediction errors (displaced frame differences, DFD). Compatibility of the prediction errors means that the pyramid formed by independently obtained DFD's (the DFD pyramid) is close to a Gaussian pyramid decomposition of the DFD of the highest resolution level. From the DFD pyramid, a least squares Laplacian pyramid is derived, which is quantized and coded. The DFD encoder outputs an embedded bit stream. Thus, the coder control may truncate the bit stream at any point, and can keep a fixed rate. The motion vector fields obtained at the different resolution levels are also encoded by employing a pyramid approach. Simulation results show that the proposed coder achieves a coding gain compared to simulcast coding.

The approach described in this paper improves block-based motion estimation and compensation by introduction of a block segmentation dividing each block into two parts. For each block a segmentation pattern is derived from the motion vectors, which circumvents the transmission of the segmentation as side information. Motion vectors are estimated for both parts of a block. Although the number of motion vectors increases, the coding overhead can be kept sufficiently low by incorporating a Gibbs-criterion into the motion estimation criterion to trade off coding rate versus prediction error.

A method for still image coding is proposed which allows for progressive transmission, because low detailed versions of the image can be reconstructed from a truncated bit stream. The proposed method is in its main aspects close to the classical pyramid approach of Burt and Adelson (1983). While retaining the main idea of using a Laplacian pyramid type decomposition, the new proposal differs in the filters employed for pyramid decomposition and in the bit allocation and quantization. The image is decomposed into an improved Laplacian pyramid. The pyramid is quantized and coded following a layered quantization approach together with a layered coding method based on conditional arithmetic coding. The encoder outputs an embedded bit stream. Thus the decoder may truncate the bit stream at any point, which results in a more or less detailed image. Besides this rate-distortion scalability the coder has a multiresolution property, due to the pyramid decomposition. An extension to hybrid video coding is also discussed.

Image sequences are mostly coded by motion compensated predictive coding. The motion vector field to be transmitted as side information is typically predictive coded. In this paper a new approach is presented for coding of motion vector fields at low bit rates (<64 kbit/s) more efficiently by applying a pyramid decomposition, which is encoded using zero-trees. The embedded coding of the pyramid allows for progressive transmission of the motion vectors and is well suited for source adaptive channel coding.

A new method for coding of displaced frame differences (DFD) is proposed. DFD coding is a necessary task in hybrid video coding. In particular a Laplacian pyramid is employed which decomposes the DFD into several layers with differing spatial resolution. The pyramid is encoded in an embedded fashion using zero-trees. Simulation results show promising rate-distortion performance for low bit rate video coding.

For hybrid video coding, knowledge about the prediction error statistics is needed for both, application of source coding theory and efficient motion estimation. A statistical model for the joint probability density function (pdf) of the prediction error signal in a hybrid coding environment is proposed. The model claims segmentwise stationarity of the prediction error. It is based on spherically invariant random processes (SIRPs) and allows modeling of correlations inside the segments as well as varying univariate distributions for the different segments. Computer experiments show a good fit of the proposed model to actual statistics of prediction error signals which were obtained by motion compensation under idealized conditions.>