Osamu Watanabe

Hiroyuki Kobayashi, Osamu Watanabe, Hitoshi Kiya

We propose an efficient two-layer near-lossless coding method using an extended histogram packing technique with backward compatibility to the legacy JPEG standard. The JPEG XT, which is the international standard to compress HDR images, adopts a two-layer coding method for backward compatibility to the legacy JPEG standard. However, there are two problems with this two-layer coding method. One is that it does not exhibit better near-lossless performance than other methods for HDR image compression with single-layer structure. The other problem is that the determining the appropriate values of the coding parameters may be required for each input image to achieve good compression performance of near-lossless compression with the two-layer coding method of the JPEG XT. To solve these problems, we focus on a histogram-packing technique that takes into account the histogram sparseness of HDR images. We used zero-skip quantization, which is an extension of the histogram-packing technique proposed for lossless coding, for implementing the proposed near-lossless coding method. The experimental results indicate that the proposed method exhibits not only a better near-lossless compression performance than that of the two-layer coding method of the JPEG XT, but also there are no issue regarding the combination of parameter values without losing backward compatibility to the JPEG standard.

Osamu Watanabe, Hiroyuki Kobayashi, Hitoshi Kiya

An efficient two-layer coding method using the histogram packing technique with the backward compatibility to the legacy JPEG is proposed in this paper. The JPEG XT, which is the international standard to compress HDR images, adopts two-layer coding scheme for backward compatibility to the legacy JPEG. However, this two-layer coding structure does not give better lossless performance than the other existing methods for HDR image compression with single-layer structure. Moreover, the lossless compression of the JPEG XT has a problem on determination of the coding parameters; The lossless performance is affected by the input images and/or the parameter values. That is, finding appropriate combination of the values is necessary to achieve good lossless performance. It is firstly pointed out that the histogram packing technique considering the histogram sparseness of HDR images is able to improve the performance of lossless compression. Then, a novel two-layer coding with the histogram packing technique and an additional lossless encoder is proposed. The experimental results demonstrate that not only the proposed method has a better lossless compression performance than that of the JPEG XT, but also there is no need to determine image-dependent parameter values for good compression performance without losing the backward compatibility to the well known legacy JPEG standard.

Osamu Watanabe, Hiroyuki Kobayashi, Hitoshi Kiya

An efficient two-layer coding method using the histogram packing technique with the backward compatibility to the legacy JPEG is proposed in this paper. The JPEG XT, which is the international standard to compress HDR images, adopts two-layer coding scheme for backward compatibility to the legacy JPEG. However, this two-layer coding structure does not give better lossless performance than the other existing single-layer coding methods for HDR images. Moreover, the JPEG XT has problems on determination of the lossless coding parameters; Finding appropriate combination of the parameter values is necessary to achieve good lossless performance. The histogram sparseness of HDR images is discussed and it is pointed out that the histogram packing technique considering the sparseness is able to improve the performance of lossless compression for HDR images and a novel two-layer coding with the histogram packing technique is proposed. The experimental results demonstrate that not only the proposed method has a better lossless compression performance than that of the JPEG XT, but also there is no need to determine image-dependent parameter values for good compression performance in spite of having the backward compatibility to the well known legacy JPEG standard.

Linus Hermansson, Fredrik D. Johansson, Osamu Watanabe

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the generalized shortest path kernel outperforms the original shortest path kernel on a number of datasets. We give a theoretical analysis for explaining our experimental results. In particular, we estimate distributions of the expected feature vectors for the shortest path kernel and the generalized shortest path kernel, and we show some evidence explaining why our graph kernel outperforms the shortest path kernel for our graph classification problem.

Ryuhei Mori, Takeshi Koshiba, Osamu Watanabe et al.

Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear programming relaxation attack using local marginal polytope for randomly generated Goldreich's generators. We assume that $u(n)\in ω(1)\cap o(n)$ input variables are known. In that case, we show that when $r\ge 3$, there is an exact threshold $μ_\mathrm{c}(k,r):=\binom{k}{r}^{-1}\frac{(r-2)^{r-2}}{r(r-1)^{r-1}}$ such that for $m=μ\frac{n^{r-1}}{u(n)^{r-2}}$, the LP relaxation can determine linearly many input variables of Goldreich's generator if $μ>μ_\mathrm{c}(k,r)$, and that the LP relaxation cannot determine $\frac1{r-2} u(n)$ input variables of Goldreich's generator if $μ<μ_\mathrm{c}(k,r)$. This paper uses characterization of LP solutions by combinatorial structures called stopping sets on a bipartite graph, which is related to a simple algorithm called peeling algorithm.