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Lena image quantized to 16, 8, 4 and 2 bits/pixel and distortion measure d(x, y) = | log(x) − log(y)|.

Lena image quantized to 16, 8, 4 and 2 bits/pixel and distortion measure d(x, y) = | log(x) − log(y)|.

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We study the perceptual problem related to image quantization from an optimization point of view, using different metrics on the color space. A consequence of the results presented is that quantization using histogram equalization provides optimal perceptual results. This fact is well known and widely used but, to our knowledge, a proof has never a...

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Citations

... Object detection and tracking task are performed by utilizing color-based segmentation. To improve the quality of the detection process color quantization (Mota, 2001) is used. To detect object positions, simple color labels are used. ...
... The color image quantization however, is ancillary but still remains very important in image clustering. It is a process to reduce the color distortion quantitatively in the image [6,7,9]. There have been conventional image clustering algorithms in literature and out of these numerous methods, K-means clustering happens to be the simplest and widely used method. ...
... In the paper [6][7][8][16][17][18], the need for color quantization has been discussed to achieve lesser time consumption and the resultant images can be further used for better optimization in results. As in [7][8][9], there is a need to remove redundant pixels that can improve the quantization process in color space. ...
... In the paper [6][7][8][16][17][18], the need for color quantization has been discussed to achieve lesser time consumption and the resultant images can be further used for better optimization in results. As in [7][8][9], there is a need to remove redundant pixels that can improve the quantization process in color space. The PDE method has been used with K-means for quantization [17]. ...
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... p k refers to the channel's kth level and M to the total channel level. The detection (color thresholding) process is shown in Fig. 2. Color quantization is a type of clustering method that groups similar colors into a threshold value (Mota et al. 2001). Quantization was used to reduce the negative effects of light changes. ...
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... The detection process is illustrated in Fig. 4 and scheme is given in Fig. 5. Illumination in the working environment is a problematic issue that causes false segmentation. To overcome this problem, we utilize additional color quantization method [37]. It assumes that masks for thresholding give better results. ...
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... Las imágenes de Lena que se presentan han sido cuantificadas utilizando el algoritmo Median Cut empleando 16, 8, 4 y 2 bits / píxel [Mota et al., 2001]. (Ver Gráfica 6). ...
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... 6) Other quantizers: Other quantizers proposed in the literature seek to minimize objective functions specific to their individual problem spaces, utilising additional application specific knowledge. Examples include: perceptual distance quantizers which leverage labelled binary data to symbolize in order to maximise a binary discrimination task [18] and quantizers focusing on maximising quantities such as temporal stability [19] or human perception [20]. Being application specific, unlike the other quantizers detailed, these are not directly applicable to the generalized outlier detection problem considered here. ...
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... Assuming additional, application specific knowledge, these approaches are not applicable to the general class of time-series comparison problems we consider. Other proposed quantizers have included perceptual distance quantizers, which seek to quantize such that as much perceptual information is retained [17], and the Persist algorithm [18] which aims to quantize such that the symbols are persistent temporally with a focus on the human interpretability of the states. While approaching their specific problems from a similar angle to ourselves, the end use, the problems addressed, and the subsequent developments of a custom quantizer, are very different to that presented here. ...
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The abundance and value of mining large time series data sets has long been acknowledged. Ubiquitous in fields ranging from astronomy, biology and web science the size and number of these datasets continues to increase, a situation exacerbated by the exponential growth of our digital footprints. The prevalence and potential utility of this data has led to a vast number of time-series data mining techniques, many of which require symbolization of the raw time series as a pre-processing step for which a number of well used, pre-existing approaches from the literature are typically employed. In this work we note that these standard approaches are sub-optimal in (at least) the broad application area of time series comparison leading to unnecessary data corruption and potential performance loss before any real data mining takes place. Addressing this we present a novel quantizer based upon optimization of comparison fidelity and a computationally tractable algorithm for its implementation on big datasets. We demonstrate empirically that our new approach provides a statistically significant reduction in the amount of error introduced by the symbolization process compared to current state-of-the-art. The approach therefore provides a more accurate input for the vast number of data mining techniques in the literature, providing the potential of increased real world performance across a wide range of existing data mining algorithms and applications.
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