It is challenging to detect the presence of Psoriasis using subjective means. Its objective determination can help to understand the coverage and severity of the disease and consequently offer the appropriate treatment. Deep learning methods like U-Net are very popular methods for segmenting disease regions for objective analysis. U-Net is an encode-decode under-complete convolution network that focuses on learning high-level features and fails in detecting fine boundaries and smaller lesions. Hence in this paper, the overcomplete version of U-Net and its variants Residual U-Net, and Attention U-Net are studied for psoriasis lesions segmentation from the full body color images. The overcomplete versions are found sensitive focusing from larger to smaller regions providing more precision in identifying the impacted Psoriasis skin lesions. They showed significant performance measured using the Dice similarity index as 0.9280, 0.9780, and 0.9834 for Overcomplete U-Net, Overcomplete Residual U-Net, and Overcomplete Attention U-Net, respectively. Among them, Overcomplete Attention U-Net has demonstrated superior performance compared to others.