Surface texture of an image plays an imperative role in understanding objects such as aggregates, woods, grains, soils, trees, and houses. Fractal dimension (FD) helps to characterise these objects by quantifying their complex texture patterns. Differential box counting (DBC) is one of the popularly used methods to measure FD of a gray-scale image. However, it suffers from several limitations. So, this study introduces three improved DBC methods using three box heights based on eigenvalue, kurtosis, and skewness of an image respectively. These methods also use a new xy-plane shifting mechanism and a modified formula for computing n(r). Moreover, weighted least squares (WLS) regression is adopted, where a trapezoidal membership function (TMF) based rule is proposed for assigning weights to each grid size. The image surface exhibits multifractal nature, hence two multifractal analysis methods are also analysed and included in the experiments. All the experiments are performed on three gray-scale image databases viz., the synthesized Fractal Brownian motion (FBM) images, natural texture images of Brodatz database, and images of Outex database that are captured at different rotations. Experimental results show that the proposed methods outperform some of the state-of-the-art methods. (C) 2020 Elsevier B.V. All rights reserved.