Median based approaches for noise suppression and interest point detection.
Date of Issue2013
School of Electrical and Electronic Engineering
Mean and median are two basic operations in signal/image processing. They are widely used for their easy implementation and soundly mathematical analysis tools. The mean filter achieves the best performance in attenuating Gaussian noise. However, it cannot effectively suppress the long-tailed noise and it blurs image structures. On the contrary, the median filter has the advantages in suppressing the long-tailed noise and preserving image structures. These advantages motivate us to develop the median based approaches in both noise suppression and interest point detection. Noise suppression is a fundamental and important research topic in signal/image processing. The recently proposed iterative truncated arithmetic mean (ITM) filter provided an effective way to suppress the long- and short-tailed noise. By iteratively truncating the extreme samples, the ITM filter's output starts from the mean and approaches the median. The termination condition enables the ITM filter owning merits of these two operations. The filter's output can be used as an approximation of the sample median without using the time consuming data sorting algorithm. The merits of the ITM filter inspire part of the work in this thesis. We firstly analyze the ITM filter and verify that the ITM filter is more effective than the median filter in suppressing both Gaussian and Laplacian noise. Furthermore, we propose a fast implementation named fast ITM (FITM) filter. Mathematical analysis of the computational complexity is given. The ITM and FITM filters are of order O(n√n) and O(n log(n)). respectively. It is seen that the FITM filter has a lower computational complexity than the ITM filter. As band- and high-pass characteristics are expected in many applications, we propose a rich class of filters named weighted ITM (WITM) filters in this thesis. By iteratively truncating the extreme samples, the output of the WITM filter moves from the weighted mean towards the weighted median. Proper stopping criterion makes the WITM filters own some merits of both the weighted median and mean filters and, therefore, outperform the both in some applications. Three structures are designed to enable the WITM filters being low-, band- and high-pass filters. Properties of these filters are presented and analyzed in this work. A more practical noise model for real images is a mixed-type noise which contains the additive and exclusive noise. Although the ITM filter can effectively deal with the additive noise, its result is not optimal in case the exclusive noise exists. As samples corrupted by the exclusive noise do not contain the information of the signal, the best way is to remove (trim) such samples from the filter inputs. This inspires the proposed iteratively trimmed and truncated mean (ITTM) filter. The proposed ITTM filter outperforms the mean, median and ITM filters in many cases. It has a linear computational complexity with order of O(n) which is smaller than that of the ITM filter. Another important research topic in image processing is the interest point detection. The interest points refer to the image patterns which are different from their immediate neighborhoods. As such image patterns can be used to represent the image robustly and sparsely, the interest point detection has drawn great attentions and been widely used in computer vision in the last two decades. However, designing a robust interest point detector to deal with the complex image structures and various variations is still a challenging task. Many leading detectors, such as SIFT and SURF detectors, employ the linear LoG filter to detect the blob structures from images. The inherent shortcoming of the linear filter that cannot effectively deal with abrupt variations limits the performance of the corresponding detectors. Such detectors cannot stably extract the interest points in case impulsive noise or abrupt variations exist. The merit of the median filter that can effectively deal with such kind of variations inspires the proposed detectors in this thesis. A rank order filter named rank order Laplacian of Gaussian (ROLG) filter is designed in this work. A novel interest point detector is designed based on this filter to detect the image local structures where a significant majority of pixels are brighter or darker than a significant majority of pixels in their corresponding surroundings. Compared to the linear filter based detectors, e.g. SIFT detector, the proposed ROLG detector is more robust to abrupt variations of images. Another issue of the linear filter based detectors is that their responses are proportional to the local image contrast. This makes such detectors prefer the local structures with high contrast. Low contrast structures will not be easily detected even if they are stable under different variations. The ROLG detector uses the rank order filter instead of the linear filter to reduce the influence of noise and the nearby structures. However, it still prefers the structures which have high contrast. In this thesis, a vote of confidence (VC) based detector is proposed to detect bright and dark regions from images. Whether a local region is bright or dark is voted by all the pixels in this region. The proposed VC detector is robust to illumination changes and effective to cluttered structures. In general, our work is based on the median operation but not restricted on it. The proposed FITM, WITM, and ITTM filters own some merits of both the median and mean operations. These filters have better performance in suppressing noise and preserving structures. The median based interest point detectors inherit the merits of the median filter which is insensitive to the abrupt structures. Therefore, the proposed ROLG and VC detectors can effectively deal with the abrupt variations caused by illumination and geometric changes. The contributions of this thesis are summarized as follows: 1) Studied the properties of the ITM filter and proposed a fast realization named FITM filter. Compared to the median filter, the FITM filter has a better performance in suppressing both Gaussian and Laplacian noise with a faster speed. 2) Proposed a rich class of weighted ITM (WITM) filter. By assigning the proper weights, the WITM filter can be designed as low-, band- and high-pass filters. 3) Proposed the ITTM filter. By iteratively trimming and truncating the extreme samples, the ITTM filter outperforms the median and ITM filters in some cases, and has a lower computational complexity. 4) Proposed the ROLG filter for interest point detection and designed the ROLG detector. The ROLG detector is more robust to the abrupt variation than the linear filter based detector. 5) Proposed a vote of confidence based filter for interest point detection and designed the VC detector. Compared to the leading interest point detectors, the VC detector is more robust to illumination changes.
DRNTU::Engineering::Electrical and electronic engineering::Electronic systems::Signal processing