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Segmentation-Based Morphological Interpolation of Partition Sequences

Authors:
Roland Brémond at Gustave Eiffel University
Roland Brémond
Ferran Marqués at Polytechnic University of Catalonia
Ferran Marqués
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Abstract and Figures

A new algorithm for partition sequence interpolation is proposed. In a coding context, such a tool is necessary to reach high compression rates. Our scheme relies on a region-by-region approach. We propose a region ordering, based on an error criterion. Before ordering, some regions are merged according to a motion criterion. The shape of each region changes continuously, and the intermediate images are built from the new shaped regions with a dead leave model.
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Region
Parametrization
Region
Partition
Ordering
Creation
Interpolated Partitions
Region
Interpolation
Initial Partitions
L2
L1
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... This approach estimates the evolution of the partition by computing a geodesic distance [18], [27] between the regions in the known partitions. Therefore, as pointed out in [4] and [18], this approach is only feasible when regions slightly vary their position between the two known partitions. If this is not the case, the evolution of each region has to be separately analyzed. ...
... If this is not the case, the evolution of each region has to be separately analyzed. A second approach is to analyze the partition in a regionby-region basis [4]. The evolution of each region is predicted independently. ...
... This approach does not make any a priori assumption on the movement of the regions. However, in the work presented in [4], the procedure to predict the region evolution is based on the definition of a geodesic distance. This procedure does not allow causal prediction, since geodesic distances are only defined between the regions from the two known partitions. ...
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This paper presents a prediction technique for partition sequences. It uses a region-by-region approach that consists of four steps: region parameterization, region prediction, region ordering, and partition creation. The time evolution of each region is divided into two types: regular motion and shape deformation. Both types of evolution are parameterized by means of the Fourier descriptors and they are separately predicted in the Fourier domain. The final predicted partition is built from the ordered combination of the predicted regions, using morphological tools. With this prediction technique, two different applications are addressed in the context of segmentation-based coding approaches. Noncausal partition prediction is applied to partition interpolation, and examples using complete partitions are presented. In turn, causal partition prediction is applied to partition extrapolation for coding purposes, and examples using complete partitions as well as sequences of binary images--shape information in video object planes (VOPs)--are presented.
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... Two other approaches based on the above have also been presented in [4, 5]. Another kind of the morphological interpolation, presented in [3, 10] can be called a morphological 'intra-frame' interpolation. It deals with a single incomplete image and reconstructs its surface starting from given image fragments. ...
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... There are other papers dealing with geometrical and morphological processing of label images, but which do not use our label morphology. In [8], motion interpolation between two images in a sequence (that is, estimating the frames at time t þ aD, 0 < a < 1, from the two frames at times t and t þ D) was solved by segmenting both images, establishing a correspondence between objects in both images, labelling these objects, and finally interpolating the two resulting label images with geometrical and morphological operations. In [27], the ''average" of a set of label images is obtained by associating to each pixel the label minimizing the average of the pixel's signed distance transforms among the images (if several proper labels minimize it, the pixel is classified ''ambiguous", which corresponds to label >). ...
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The time necessary to follow a path defined on a grey scale image is defined as the sum of the image values along the path. The geodesic time associated with two points of the image is nothing but the smallest amount of time necessary to link these two points. Starting from this notion, we define a new geodesic metric on the image plane: the generalized geodesic distance. The generalized geodesic distance betweeen two points is the length of the shortest path(s) linking these points in a minimum amount of time. This distance is used for defining a propagation function. Applications to shape description and interpolation from contour data are provided.
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  • Oct 1988
  • Proceedings of SPIE
A hierarchical blockmatching algorithm for the estimation of displacement vector fields in digital television sequences is presented. Known blockmatching techniques fail frequently as a result of using a fixed measurement window size. Using distinct sizes of measurement windows at different levels of a hierarchy, the presented blockmatching technique yields reliable and homogeneous displacement vector - fields, which are close to the true displacements, rather than only a match in the sense of a minimum mean absolute luminance difference. In the environment of a low bit rate hybrid coder for image sequences, the hierarchical blockmatching algorithm is well suited for both, motion compensating prediction, and motion compensating interpolation. Compared to other high sophisticated displacement estimation techniques, the computational effort is decreased drastically. Due to the regularity and the very small number of necessary operations, the presented hierarchical blockmatching algorithm can be implemented in hardware very easily.
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Hierarchical Morphological Segmentation for Image Sequence Coding
Article
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This paper deals with a hierarchical morphological segmentation algorithm for image sequence coding. Mathematical morphology is very attractive for this purpose because it efficiently deals with geometrical features such as size, shape, contrast, or connectivity that can be considered as segmentation-oriented features. The algorithm follows a top-down procedure. It first takes into account the global information and produces a coarse segmentation, that is, with a small number of regions. Then, the segmentation quality is improved by introducing regions corresponding to more local information. The algorithm, considering sequences as being functions on a 3-D space, directly segments 3-D regions. A 3-D approach is used to get a segmentation that is stable in time and to directly solve the region correspondence problem. Each segmentation stage relies on four basic steps: simplification, marker extraction, decision, and quality estimation. The simplification removes information from the sequence to make it easier to segment. Morphological filters based on partial reconstruction are proven to be very efficient for this purpose, especially in the case of sequences. The marker extraction identifies the presence of homogeneous 3-D regions. It is based on constrained flat region labeling and morphological contrast extraction. The goal of the decision is to precisely locate the contours of regions detected by the marker extraction. This decision is performed by a modified watershed algorithm. Finally, the quality estimation concentrates on the coding residue, all the information about the 3-D regions that have not been properly segmented and therefore coded. The procedure allows the introduction of the texture and contour coding schemes within the segmentation algorithm. The coding residue is transmitted to the next segmentation stage to improve the segmentation and coding quality. Finally, segmentation and coding examples are presented to show the validity and interest of the coding approach.
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Conference Paper
  • Nov 1995
This paper presents an interpolation/extrapolation technique for sequence partitions. It consists of four steps: region parametrization, region interpolation, region ordering and partition creation. The evolution of each region is divided into two types: regular motion and random deformations. Both types of evolution are parametrized by means of the Fourier descriptors of the regions and they are separately interpolated in the Fourier domain. The final interpolated partition is built from the ordered combination of the interpolated regions, using morphological tools
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