We propose a method for local spectral component decomposition based on the line feature of local distribution. Our aim is to reduce noise on multi-channel images by exploiting the linear correlation in the spectral domain of a local region. We first calculate a linear feature over the spectral components of an M -channel image, which we call the spectral line, and then, using the line, we decompose the image into three components: a single M -channel image and two gray-scale images. By virtue of the decomposition, the noise is concentrated on the two images, and thus our algorithm needs to denoise only the two gray-scale images, regardless of the number of the channels. As a result, image deterioration due to the imbalance of the spectral component correlation can be avoided. The experiment shows that our method improves image quality with less deterioration while preserving vivid contrast. Our method is especially effective for hyperspectral images. The experimental results demonstrate that our proposed method can compete with the other state-of-the-art denoising methods.

In this paper, we propose a learning-based supervised discrete hashing (SDH) method. Binary hashing is widely used for large-scale image retrieval as well as video and document searches, because the compact binary code representation is essential for data storage and reasonable for query searches using bit operations. The recently proposed SDH method efficiently solves mixed-integer programming problems by alternating optimization and the discrete cyclic coordinate descent (DCC) method. Based on some preliminary experiments, we show that the SDH method can be simplified without performance degradation. We analyze the simplified model and provide a mathematically exact solution thereof; we reveal that the exact binary code is provided by a “Hadamard matrix.” Therefore, we named our method Hadamard coded-SDH (HC-SDH). In contrast to the SDH, our model does not require an alternating optimization algorithm and does not depend on initial values. The HC-SDH is also easier to implement than the iterative quantization. Experimental results involving a large-scale database show that the Hadamard coding outperforms the conventional SDH in terms of precision, recall, and computational time. On the large data sets SUN-397 and ImageNet, the HC-SDH provides a superior mean average of precision (mAP) and top-accuracy compared with the conventional SDH methods with the same code length and FastHash. The training time of the HC-SDH is 170 times faster than the conventional SDH and the testing time including the encoding time is seven times faster than the FastHash which encodes using a binary-tree.

Depth-from-focus methods can estimate the depth from a set of images taken with different focus settings. We recently proposed a method that uses the relationship of the ratio between the luminance value of a target pixel and the mean value of the neighboring pixels. This relationship has a Poisson distribution. Despite its good performance, the method requires a large amount of memory and computation time because it needs to store focus measurement values for each depth and each window radius on a pixel-wise basis, and filtering to compute the mean value, which is performed twice, makes the relationship among neighboring pixels too strong to parallelize the pixel-wise processing. In this paper, we propose an approximate calculation method that can give almost the same results with a single time filtering operation and enables pixel-wise parallelization. This pixel-wise processing does not require the aforementioned focus measure values to be stored, which reduces the amount of memory. Additionally, utilizing the pixel-wise processing, we propose a method of determining the process window size that can improve noise tolerance and in depth estimation in texture-less regions. Through experiments, we show that our new method can better estimate depth values in a much shorter time.

This study primarily presents efficient tools for optimization-based image processing using a bilateral filter (BF). Generally, for image restoration, e.g., deblurring, a forward operation and its adjoint operation pair are required to solve inverse problems via iterative approaches such as the gradient method. Image data comprise millions of variables; thus, the operations should be performed as image filters rather than matrix products because of the considerable matrix size. This approach is known as a matrix-free approach, i.e., filter form, because it is executed without explicitly generating an enormous matrix. When BF is incorporated into optimization, its matrix-free adjoint BF is required to solve the optimization problem. This study discusses the matrix-free adjoint BF and its constant-time algorithm to solve optimization problems in a practical time frame. The experimental results demonstrate that the proposed method yields sufficient filtering accuracy for solving inverse problems. Furthermore, BF-based optimization improves accuracy by adjusting the image quality of resultant images.

We present a new image integration technique for a flash and long-exposure image pair to capture a dark scene without incurring blurring or noisy artifacts. Most existing methods require well-aligned images for the integration, which is often a burdensome restriction in practical use. We address this issue by locally transferring the colors of the flash images using a small fraction of the corresponding pixels in the long-exposure images. We formulate the image integration as a convex optimization problem with the local linear model. The proposed method makes it possible to integrate the color of the long-exposure image with the detail of the flash image without causing any harmful effects to its contrast, where we do not need perfect alignment between the images by virtue of our new integration principle. We show that our method successfully outperforms the state of the art in the image integration and reference-based color transfer for challenging misaligned data sets.

In color image processing based on mathematical optimization, a color-line image feature has been considered and many methods that give good results have been proposed. A color-line is a linear color distribution (correlation line) observed in a local image region, and is numerically represented by the sparsity of a data matrix generated from the neighboring pixel values. However, the calculation requires a lot of processing time because each data matrix is processed by inverse calculation or singular value decomposition (SVD) with some operations on the decomposed singular values. In this paper, in order to address this problem, we propose a method that can effectively compute SVD for each data matrix. Using the experimental knowledge that matrices obtained from neighboring regions (each centered at an adjacent pixel) are similar to each other, we intentionally design the SVD by using an iterative method (Arnoldi iteration), and propagate the converged singular vectors at a pixel to the next pixel as the initial vectors of the iteration. This propagation can drastically reduce the number of iterations required for convergence. Additionally, the singular values and vectors are obtained in descending order, which is advantageous when a matrix is reconstructed after reducing small singular values, so we can truncate the calculation when a singular value becomes lower than a threshold value. To show the effectiveness, we apply the proposed method to a denoising method, arranged structure-tensor total variation (ASTV), and show that the processing time is shortened by 95% compared to the naive method without losing numerical accuracy.