An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having smaller blocks at the ends of histogram plot of each horizontal, vertical and diagonal components, while for the approximation component it provides for finer block size around the mean, and larger blocks at the ends of histogram plot coefficients. It is found that the proposed algorithm has significantly less time complexity, achieves superior PSNR and Structural Similarity Measurement Index as compared to similar space domain algorithms[1]. In the process it highlights finer image structures not perceptible in the original image. It is worth emphasizing that after the segmentation only 16 (at threshold level 3) wavelet coefficients captures the significant variation of image.
Deep Dive into A Fast Statistical Method for Multilevel Thresholding in Wavelet Domain.
An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having smaller blocks at the ends of histogram plot of each horizontal, vertical and diagonal components, while for the approximation component it provides for finer block size around the mean, and larger blocks at the ends of histogram plot coefficients. It is found that the proposed algorithm has significantly less time complexity, achieves superior PSNR and Structural Similarity Measurement Index as compared to similar space domain algorithms[1]. In the process it highlights finer image structures not perceptible in the original image. It is worth emphasizing that after the segmentation only 16 (at threshold level 3) wavelet coefficients captures the significant variation of image.
Image segmentation is the process of separating the processed or unprocessed data into segments so that members of each segment share some common characteristics and macroscopically segments are different from each other. It is instrumental in reducing the size of the image keeping its quality maintained since most of the images contain redundant informations, which can be effectively unglued from the image. The purpose of segmentation is to distinguish a range of pixels having nearby values. This can be exploited to reduce the storage space, increase the processing speed and simplify the manipulation. Segmentation can also be used for object separation. It may be useful in extracting information from images, which are imperceptible to human eye [2].
Thresholding is the key process for image segmentation. As thresholded images have many advantages over the normal ones, it has gained popularity amongst researchers. Thresholding can be of two types -Bi-level and Multi-level. In Bi-level thresholding, two values are assigned -one below the threshold level and the other above it. Sezgin and Sankur [3] categorized various thresholding techniques, based on histogram shape, clustering, entropy and object attributes.
Otsu’s method [4] maximizes the values of class variances to get optimal threshold. Sahoo et al. [5] tested Otsu’s method on real images and concluded that the structural similarity and smoothness of reconstructed image is better than other methods. Processing time of the algorithm in Otsu’s method was reduced after modification by Liao et al. [6]. In Abutaleb’s method [7], threshold was calculated by using 2D entropy. Niblack’s [8] method makes use of mean and standard deviation to follow a local approach. Hemachander et al. [9] proposed binarization scheme which maintains image continuity.
In Multilevel thresholding, different values are assigned between different ranges of threshold levels. Reddi et al. [10] implemented Otsu’s method recursively to get multilevel thresholds. Ridler and Calward algorithm [11] defines one threshold by taking mean or any other parameter of complete image. This process is recursively used for the values below the threshold value and above it separately.
Chang [12] obtained same number of classes as the number of peaks in the histogram by filtered the image histogram. Huang et al. [13] used Lorentz information measure to create an adaptive window based thresholding technique for uneven lightning of gray images. Boukharouba et al. [14] used the distribution function of the image to get multi-threshold values by specifying the zeros of a curvature function. For multi-threshold selection, Kittler and Illingworth [15] proposed a minimum error thresholding method. Papamarkos and Gatos [16] used hill clustering technique to get multi-threshold values which estimate the histogram segments by taking the global minima of rational functions.
Comparison of various meta-heuristic techniques such as genetic algorithm, particle swarm optimization and differential evolution for multilevel thresholding is done by Hammouche et al. [17].
Wavelet transform has become a significant tool in the field of image processing in recent years [18] [19]. Wavelet transform of an image gives four components of the image -Approximation, Horizontal, Vertical and Diagonal [20]. To match the matrix dimension of the original image, the coefficients of image is down sampled by two in both horizontal and vertical directions. To decompose image further, wavelet transform of approximation component is taken. This can continue till there is only one coefficient left in approximation part [21]. In image processing, Discrete Wavelet Transform (DWT) is widely used in compression, segmentation and multi-resolution of image [22].
In this paper a hybrid multilevel color image segmentation algorithm has been proposed, using mean and standard deviation in the wavelet domain. The method takes into account that majority of wavelet coefficients lie near to zero and coefficients representing large differences are a few in number lying at the extreme ends of histogram. Hence, the procedure provides for variable size segmentation, with bigger block size around the weighted mean, and having smaller blocks at the ends of histogram plot of each horizontal, vertical and diagonal components. For the approximation coefficients, values around weighted mean of histogram carry more information while end values of histogram are less significant. Hence, in approximation components segmentation is done with finer block size around weight mean and larger block size at the end of the histogram [1]. The algorithm is based on the fact that a number of distributions tends toward a delta function in the limit of vanishing variance. In section 2, illustration of approach for new hybrid algorithm is provided followed by algorithm in section 3. Section 4 consists of the observations seen and results obtained in terms of SSIM, PSNR and Tim
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