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In this paper a novel approach to the compression of sparse histogram images is proposed. First, we define a sparsity index which gives hints on the relationship between the mathematical concept of matrix sparsity and the visual information of pixel distribution. We use this index to better understand the scope of our approach and its preferred fie...
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In the past three or four decades, scientists working in computer science, physics and mathematics have had significant research studies on origami. Currently, most of the articles and books that can be reached by designers or architects describe and deal with the subject through mathematical expressions. It does not seem possible for a reader who...
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... Some studies on image coding report that coding efficiency can be improved by considering amplitude sparseness. Lossless coding algorithms [14], [15] and a near-lossless coding algorithm [16] improve coding efficiency by utilizing fewer pixel values for images with amplitude sparseness. ...
We formulate the design of an optimal quantizer as an optimization problem that finds the quantization indices that minimize quantization error. As a solution of the optimization problem, an approach based on dynamic programming, which is called DP quantization, is proposed. It is observed that quantized signals do not always contain all kinds of signal values which can be represented with given bit-depth. This property is called amplitude sparseness. Because quantization is the amplitude discretization of signal value, amplitude sparseness is closely related to quantizer design. Signal values with zero frequency do not impact quantization error, so there is the potential to reduce the complexity of the optimal quantizer by not computing signal values that have zero frequency. However, conventional methods for DP quantization were not designed to consider amplitude sparseness, and so fail to reduce complexity. The proposed algorithm offers a reduced complexity optimal quantizer that minimizes quantization error while addressing amplitude sparseness. Experimental results show that the proposed algorithm can achieve complexity reduction over conventional DP quantization by 82.9 to 84.2% on average.
... In Refs. [11,12,[22][23][24][25][26][27][28][29][30], the sparseness of a histogram of an image is used for efficient compression. 'Sparse' histogram means that not all the bins in a histogram are utilized. ...
... For image signals having such sparseness, it is well known that the histogram packing technique improves lossless compression performance [24][25][26][27][28][29]. In Refs. ...
... In Refs. [24][25][26][27][28][29], the sparseness α was increased and the range D(x) became narrower by using histogram packing. It was also reported that the lossless image compression performance improved for histogram packed images. ...
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.
... It means that not all the pixel value bins are used in an image. Therefore the dynamic range can be reduced with the histogram packing for lossless coding [12][13][14]. It was extended to lossy coding under the L infinity constraint [15,16]. ...
... Especially for HDR images, its histogram tends to be 'sparse' as they have longer bit depth than normal LDR images. Therefore this histogram sparseness can be utilized to reduce the dynamic range with the 'histogram packing' as illustrated in Fig.3 [12][13][14]. Table II summarizes some approaches for dynamic range reduction. Method (a) truncates lower bit planes of pixel values of the original H planes remaining upper L planes for integers H and L. As a result, its dynamic range is reduced from 2 H to 2 L . ...
This paper proposes a new range reduction method
with the minimum amount of quantization error in the L2 norm
under the L infinity norm constraint. It is necessary to reduce
dynamic range of pixel values of high dynamic range (HDR)
images to have backward compatibility with low dynamic range
image processing systems. The simplest approach is to truncate
lower bit planes in binary representation of pixel values.
However it does not have fine granularity of the reduced range,
and also it does not utilize the histogram sparseness.
Furthermore, it generates significant amount of quantization
errors. In this paper, we propose a new range reduction method
which can 1) utilize the histogram sparseness, and also 2)
minimize variance of the error 3) under a specified maximum
absolute value of the error.
... It means that not all the pixel value bins are used in an image. Therefore the dynamic range can be reduced with the histogram packing for lossless coding [12][13][14]. It was extended to lossy coding under the L infinity constraint [15,16]. ...
... Especially for HDR images, its histogram tends to be 'sparse' as they have longer bit depth than normal LDR images. Therefore this histogram sparseness can be utilized to reduce the dynamic range with the 'histogram packing' as illustrated in Fig.3 [12][13][14]. Table II summarizes some approaches for dynamic range reduction. Method (a) truncates lower bit planes of pixel values of the original H planes remaining upper L planes for integers H and L. As a result, its dynamic range is reduced from 2 H to 2 L . ...
This letter proposes an efficient lossless compression method for high dynamic range (HDR) images in OpenEXR format. The proposed method transforms an HDR image to an indexed image and packs the histogram of the indexed image. Finally the packed image is losslessly compressed by using any existing lossless compression algorithm such as JPEG 2000. Experimental results show that the proposed method reduces the bit rate of compressed OpenEXR images compared with equipped lossless compression methods of OpenEXR format.
... They exploit the fact that the input symbols are binary, and so dynamic programming can be used to find the globally optimal CQ. This approach is interesting and some other research groups have followed [17] or intend to follow [18] it. ...
... Equation (18) gives as a quantitative evaluation of the effectiveness of a classification function. We evaluated this quantity for the classes defined in the previous section and we find an excellent agreement with experimental data of tables 14 to 17. Moreover this equation allows to derive an algorithm to improve a given classification function. ...
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.
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.
