Compression of depth maps is important for "texture plus depth" format of multiview images, which enables synthesis of novel intermediate views via depth-image-based rendering (DIBR) at decoder. Previous depth map coding schemes exploit unique depth data characteristics to compactly and faithfully reproduce the original signal. In contrast, since depth map is only a means to the end of view synthesis and not itself viewed, in this paper we explicitly manipulate depth values, without causing severe synthesized view distortion, in order to maximize representation sparsity in the transform domain for compression gain-we call this process transform domain sparsification (TDS). Specifically, for each pixel in the depth map, we first define a quadratic penalty function, with minimum at ground truth depth value, based on synthesized view's distortion sensitivity to the pixel's depth value during DIBR. We then define an objective for a depth signal in a block as a weighted sum of: i) signal's sparsity in the transform domain, and ii) per-pixel synthesized view distortion penalties for the chosen signal. Given that sparsity (l0-norm) is non-convex and difficult to optimize, we replace the l0-norm in the objective with a computationally inexpensive weighted l2-norm; the optimization is then an unconstrained quadratic program, solvable via a set of linear equations. For the weighted l2-norm to promote sparsity, we solve the optimization iteratively, where at each iteration weights are readjusted to mimic sparsity-promoting lτ -norm, 0 ≤ τ ≤ 1. Using JPEG as an example transform codec, we show that our TDS approach gained up to 1.7dB in rate-distortion performance for the interpolated view over compression of unaltered depth maps.
Using cognitive ethnography as a guiding framework, we investigated US and Japanese fourth-grade teachers' domain knowledge of key fraction representations in individual interviews. The framework focused on revealing cultural trends in participants' organization of knowledge and their interpretations of that organization. Our analyses of the interviews, which included a representation sorting task, indicated three major differences that defined US and Japanese teachers' approaches to rational number representation: (1) Japanese teachers interpreted all rational number representations as conveying primarily mathematical information, whereas US teachers interpreted only some representations as conveying primarily mathematical information;(2) the US teachers focused more intently on part-whole relations than Japanese in their interpretations; and (3) Japanese teachers more easily linked rational number representations to more advanced upcoming content in the curriculum. A review of US textbooks used by the teachers reflected their consistency with US teachers' interpretations of the representations. These findings imply that strong cultural differences underlay the approaches that teachers in both nations take to rational number representation and that these differences may help explain established crossnational differences in student reasoning.It has been demonstrated that US teachers are less successful than their Asian counterparts in computing correct values as well as providing indepth explanations when given tasks that involve rational number relations (Ma, 1999). A logical extension of Ma's work is to examine the possibility that differences between US and Asian teachers may, in part, be due to the ways they conceive of the various meanings of rational number representations (e.g., part-whole and ratios). We believe that these differences are more accurately interpreted as representative of cultural approaches to rational numbers in the two nations than simply reflecting individual differences in teachers' cognitive capabilities. In this study we adopted a cognitive ethnography framework to study the knowledge that US and Japanese teachers access when working to organize representations for rational numbers.
Abstract-Depth map compression is important for compact "texture-plus-depth" representation of a 3D scene, where texture and depth maps captured from multiple camera viewpoints are coded into the same format. Having received such format, the decoder can synthesize any novel intermediate view using texture and depth maps of two neighboring captured views via depthimage-based rendering (DIBR). In this paper, we combine two previously proposed depth map compression techniques that promote sparsity in the transform domain for coding gain-graphbased transform (GBT) and transform domain sparsification (TDS)-together under one unified optimization framework. The key to combining GBT and TDS is to adaptively select the simplest transform per block that leads to a sparse representation. For blocks without detected prominent edges, the synthesized view's distortion sensitivity to depth map errors is low, and TDS can effectively identify a sparse depth signal in fixed DCT domain within a large search space of good signals with small synthesized view distortion. For blocks with detected prominent edges, the synthesized view's distortion sensitivity to depth map errors is high, and the search space of good depth signals for TDS to find sparse representations in DCT domain is small. In this case, GBT is first performed on a graph defining all detected edges, so that filtering across edges is avoided, resulting in a sparsity count ρ in GBT. We then incrementally add the most important edge to an initial no-edge graph, each time performing TDS in the resulting GBT domain, until the same sparsity count ρ is achieved. Experimentation on two sets of multiview images showed gain of up to 0.7dB in PSNR in synthesized view quality compared to previous techniques that employ either GBT or TDS alone.
This study examined the effects of a teaching strategy in which fifth‐grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems. The experimental and control group each consisted of thirty four elementary students in Japan who took the pre, post and retention tests. The experimental group showed a significantly better performance on the retention test although no significant differences were observed on the pre and post tests. This result suggests that the evaluation and improvement activity was important as a teaching strategy.
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