Several morphological transformations to detect noise are introduced. The initial method is a modification of a procedure presented previously in the current literature. The proposals given in the study allow to detect noise in two ways: (i) using a contrast measure and (ii) applying different proximity criteria into several proposed toggle mappings. In the end, two of the proposals given in this study yield a better performance with respect to methods in which this research is based. However, although the methodology to identify noise works adequately, the results are limited due to the use of the structuring element. In Section 4, an image with two types of noise is cleaned. Such image is contaminated with zero mean Gaussian noise with 0.01 variance and 5% of salt and pepper noise. From this experiment, the proposal giving the best performance is selected; subsequently, this is compared with other recent operators as PDEs, wavelets, morphological connected rank max opening and amoebas.

Colour vector angle has been widely used in edge detection and image retrieval, but its investigation in image hashing is still limited. In this study, the authors investigate the use of colour vector angle in image hashing and propose a robust hashing algorithm combining colour vector angles with discrete wavelet transform (DWT). Specifically, the input image is firstly resized to a normalised size by bi-cubic interpolation and blurred by a Gaussian low-pass filter. Colour vector angles are then calculated and divided into non-overlapping blocks. Next, block means of colour vector angles are extracted to form a feature matrix, which is further compressed by DWT. Image hash is finally formed by those DWT coefficients in the LL sub-band. Experiments show that the proposed hashing is robust against normal digital operations, such as JPEG compression, watermarking embedding and rotation within 5°. Receiver operating characteristics curve comparisons are conducted and the results show that the proposed hashing is better than some well-known algorithms.

Fuzzy c-means (FCM) clustering algorithm has been widely used in image segmentation. In this study, a modified FCM algorithm is presented by utilising local contextual information and structure information. The authors first establish a novel similarity measure model based on image patches and local statistics, and then define the neighbourhood-weighted distance to replace the Euclidean distance in the objective function of FCM. Validation studies are performed on synthetic and real-world images with different noises, as well as magnetic resonance brain images. Experimental results show that the proposed method is very robust to noise and other image artefacts.

In this study, a robust image watermarking method based on geometric modelling is presented. Eight samples of wavelet approximation coefficients on each image block are utilised to construct two line segments in the two-dimensional space. The authors change the angle formed between these line segments for data embedding. Geometrical tools are used to solve the tradeoff between the transparency and robustness of the watermark data. They analytically determine the probability density function of the embedding angle for Gaussian samples. Maximum-likelihood decoder is implemented in the receiver side. Owing to embedding in the angle between two line segments, the proposed scheme has high robustness against the gain attacks. In addition, using the low frequency components of the image blocks for data embedding, high robustness against noise and compression attacks has been achieved. Experimental results confirm the validity of the theoretical analyses given in this study and show the superiority of the proposed method against common attacks, such as Gaussian filtering, median filtering and scaling attacks.

Recently, a lossless vector quantisation (VQ) index compression algorithm, called the coding tree assignment scheme with improved search-order coding (CTAS-ISOC) algorithm, has been proposed to enhance the coding efficiency of the original SOC by exploiting the correlations of the neighbouring blocks using the left-pair and upper-pair patterns in the index domain. This study proposes a modified coding tree assignment scheme (MCTAS) to further improve the coding performance of CTAS-ISOC by the dynamic index table coding (DITC). The DITC technique exploits the correlation of neighbouring index pairs not in the original vector-quantised index map, but in the temporarily constructed index table that has been classified and updated for each current index. The searching matched index in a previously qualified index table results in low-time complexity. In addition, the identical index table can be regenerated in the reconstruction process of the index map at the decoder end. Experimental results show the time complexity of MCTAS is more efficient than that of CTAS-ISOC. Moreover, the proposed MCTAS apparently reduces the bit rate in comparison with conventional VQ and some popular lossless index coding schemes, such as index searching algorithm with index associated list, adaptive index coding scheme, SOC and so on.

For pixel-level image fusion, the edges of the source images should be as much as possible integrated into the fused image because the human visual system is sensitive to them. In this study, the authors utilise the multiscale edge-preserving decomposition (MSEPD) based on the weighted least squares filter to fuse the source images. In the authors’ method, first, the source images are decomposed by the MSEPD into a base image and a series of detail images, respectively. Then, the detail images of same scale are combined via the different fusion rules designed for different kinds of source images; the base images are combined via the average-value rule. Finally, the fused image is constructed by adding the fused base image and detail images together. The proposed fusion method is verified on several kinds of images and compared with some methods based on multiscale decomposition. The experimental results indicate that the proposed method can provide better fused images, meanwhile manifesting a good edge-preserving performance.