CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

We study diffusiophoretic exclusion zone (EZ) formation in rectangular channel flow, driven by CO2 dissolution from one side wall. By using a similarity transform and considering the flow structure, we obtain the relation between EZ and the wall shear rate.

Variation of paramets method for squeezed flow of a Casson fluid

The implementation of the variation of parameters method has been demonstrated for the flow of a Casson fluid through squeezed parallel plates. Governing PDE has been reduced, with the help of similarity transform, to relatively simpler ODE. The consequent non-linear equation is complicated enough to have an exact solution. We have solved that with the help of variation of parameters method. The results are displayed with the help of graphs and are decorated with suitable physical explanation.

An Extension of Phase Correlation-Based Image Registration to Estimate Similarity Transform Using Multiple Polar Fourier Transform

Image registration is a core technology of many different image processing areas and is widely used in the remote sensing community. The accuracy of image registration largely determines the effect of subsequent applications. In recent years, phase correlation-based image registration has drawn much attention because of its high accuracy and efficiency as well as its robustness to gray difference and even slight changes in content. Many researchers have reported that the phase correlation method can acquire a sub-pixel accuracy of 1 / 10 or even 1 / 100 . However, its performance is acquired only in the case of translation, which limits the scope of the application of the method. However, there are few reports on the estimation of scales and angles based on the phase correlation method. To take advantage of the high accuracy property and other merits of phase correlation-based image registration and extend it to estimate the similarity transform, we proposed a novel algorithm, the Multilayer Polar Fourier Transform (MPFT), which uses a fast and accurate polar Fourier transform with different scaling factors to calculate the log-polar Fourier transform. The structure of the polar grids of MPFT is more similar to the one of the log-polar grid. In particular, for rotation estimation only, the polar grid of MPFT is the calculation grid. To validate its effectiveness and high accuracy in estimating angles and scales, both qualitative and quantitative experiments were carried out. The quantitative experiments included a numerical simulation as well as synthetic and real data experiments. The experimental results showed that the proposed method, MPFT, performs better than the existing phase correlation-based similarity transform estimation methods, the Pseudo-polar Fourier Transform (PPFT) and the Multilayer Fractional Fourier Transform method (MLFFT), and the classical feature-based registration method, Scale-Invariant Feature Transform (SIFT), and its variant, ms-SIFT.

IMAGE STITCHING WITH PERSPECTIVE-PRESERVING WARPING

Image stitching algorithms often adopt the global transform, such as homography, and work well for planar scenes or parallax free camera motions. However, these conditions are easily violated in practice. With casual camera motions, variable taken views, large depth change, or complex structures, it is a challenging task for stitching these images. The global transform model often provides dreadful stitching results, such as misalignments or projective distortions, especially perspective distortion. To this end, we suggest a perspective-preserving warping for image stitching, which spatially combines local projective transforms and similarity transform. By weighted combination scheme, our approach gradually extrapolates the local projective transforms of the overlapping regions into the non-overlapping regions, and thus the final warping can smoothly change from projective to similarity. The proposed method can provide satisfactory alignment accuracy as well as reduce the projective distortions and maintain the multi-perspective view. Experimental analysis on a variety of challenging images confirms the efficiency of the approach.

IMAGE STITCHING WITH PERSPECTIVE-PRESERVING WARPING

Image stitching algorithms often adopt the global transform, such as homography, and work well for planar scenes or parallax free camera motions. However, these conditions are easily violated in practice. With casual camera motions, variable taken views, large depth change, or complex structures, it is a challenging task for stitching these images. The global transform model often provides dreadful stitching results, such as misalignments or projective distortions, especially perspective distortion. To this end, we suggest a perspective-preserving warping for image stitching, which spatially combines local projective transforms and similarity transform. By weighted combination scheme, our approach gradually extrapolates the local projective transforms of the overlapping regions into the non-overlapping regions, and thus the final warping can smoothly change from projective to similarity. The proposed method can provide satisfactory alignment accuracy as well as reduce the projective distortions and maintain the multi-perspective view. Experimental analysis on a variety of challenging images confirms the efficiency of the approach.

Uniform Flow Over a Bi-axial Stretching Surface

The uniform flow over a bi-axial stretching surface is studied by similarity transform of the Navier–Stokes equations and an efficient numerical integration of the resulting ordinary differential equations. The uniform flow induces a net shear stress (and drag), which is increased by lateral stretching. Heat transfer from the surface is also determined.