Gulzar Ali Khan

A variational model with hybrid images data fitting energies for segmentation of images with intensity inhomogeneity

Level set functions based variational image segmentation models provide reliable methods to capture boundaries of objects/regions in a given image, provided that the underlying intensity has homogeneity. The case of images with essentially piecewise constant intensities is satisfactorily dealt with in the well-known work of Chan-Vese (2001) and its many variants. However for images with intensity inhomogeneity or multiphases within the foreground of objects, such models become inadequate because the detected edges and even phases do not represent objects and are hence not meaningful. To deal with such problems, in this paper, we have proposed a new variational model with two fitting terms based on regions and edges enhanced quantities respectively from multiplicative and difference images. Tests and comparisons will show that our new model outperforms two previous models. Both synthetic and real life images are used to illustrate the reliability and advantages of our new model. Graphical abstractDisplay Omitted HighlightsWe model image segmentation problem using product and difference images.The convex formulation of the model is also presented.The proposed model takes care of the minute details and inhomogeneity in an image.This model is compared with LCV and FGM of the active contour model.The competing energies are qualitatively tested by using Jaccord Similarity Index.

Active contours textural and inhomogeneous object extraction

A new selective segmentation active contour model is proposed in this paper that embeds an enhanced image information. By utilizing the average image of channels (AIC), which handles texture and noise, our model is capable to selectively segment and capture objects with nonuniform features. Moreover, the AIC is fitted with linear functions which are updated regularly to accurately guide the level set function to handle nonconstant intensities. Furthermore, we employ prior information in terms of geometrical constraints which work in alliance with image information to capture objects with intensity inhomogeneity. Experiments show that the proposed method achieves better results than the latest selective segmentation models. In addition, our approach maintains the performance on some hard real and synthetic color images. HighlightsA new selective segmentation active contour model is proposed.The proposed model is based on the concept of average image of channels.The proposed model is capable to selectively segment noisy/textural objects of interest.

Conformal Killing Vectors in LRS Bianchi Type V Spacetimes

In this note, we investigate conformal Killing vectors (CKVs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Subject to some integrability conditions, CKVs up to implicit functions of (t,x) are obtained. Solving these integrability conditions in some particular cases, the CKVs are completely determined, obtaining a classification of LRS Bianchi type V spacetimes. The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.

Teleparallel conformal Killing vector fields of LRS Bianchi type V spacetimes in teleparallel gravity

The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity. The general solution of teleparallel conformal Killings equations is found in terms of some unknown functions of t and x , along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit proper teleparallel CKVF in only one case, while in remaining cases the teleparallel CKVFs reduce to teleparallel Killing vector fields (KVFs). Moreover, it is shown that the LRS Bianchi type V spacetimes do not admit any proper teleparallel homothetic vector field (HVF).

A note on teleparallel conformal Killing vector fields in plane symmetric non-static spacetimes

The aim of this paper is to investigate teleparallel conformal Killing vector fields (CKVFs) in plane symmetric non-static spacetimes. Ten teleparallel conformal Killing’s equations are obtained which are linear in the components of the teleparallel CKVF X. A general solution of these equations comprising the components of CKVF and conformal factor is presented, which subject to some integrability conditions. For seven particular choices of the metric functions, the integrability conditions are completely solved to get the final form of teleparallel CKVFs and conformal factor. In four different cases we get proper CKVFs, while in the remaining three cases it is shown that teleparallel CKVFs reduce to teleparallel homothetic or teleparallel Killing vector fields.

Proper conformal Killing vectors in static plane symmetric space–times

Conformal Killing vectors (CKVs) in static plane symmetric space–times were recently studied by Saifullah and Yazdan, who concluded by remarking that static plane symmetric space–times do not admit any proper CKV except in the case where these space–times are conformally flat. We present some non-conformally flat static plane symmetric space–time metrics admitting proper CKVs. For these space–times, we also investigate a special type of CKVs, known as inheriting CKVs.