We discuss deinterlacing results in a computationally constrained and varied environment. The proposed computation-aware algorithm selection approach (CASA) for fast interlaced to progressive conversion algorithm consists of three methods: the line-averaging (LA) method for plain regions, the modified edge-based line-averaging (MELA) method for medium regions, and the proposed covariance-based adaptive deinterlacing (CAD) method for complex regions. The proposed CASA uses two criteria, mean-squared error (MSE) and CPU time, for assigning the method. We proposed a CAD method. The principle idea of CAD is based on the correspondence between the high and low-resolution covariances. We estimated the local covariance coefficients from an interlaced image using Wiener filtering theory and then used these optimal minimum MSE interpolation coefficients to obtain a deinterlaced image. The CAD method, though more robust than most known methods, was not found to be very fast compared to the others. To alleviate this issue, we proposed an adaptive selection approach using a fast deinterlacing algorithm rather than using only one CAD algorithm. The proposed hybrid approach of switching between the conventional schemes (LA and MELA) and our CAD was proposed to reduce the overall computational load. A reliable condition to be used for switching the schemes was presented after a wide set of initial training processes. The results of computer simulations showed that the proposed methods outperformed a number of methods presented in the literature.