The success of species depends critically on their ability to process and extract sensory information under a wide range of ecological conditions. For example, on a normal day, the luminance impinging on the retina varies within a dynamic range of 220 dB. Stimulus contrast can also vary drastically across the visual field due to shading, camouflage, etc. Given the limited dynamic range of human neurons, the brain deploys both structural and functional mechanisms that work in tandem to cope with these changes. Here, using a few canonical neural computations, such as shunting (Hodgkin-Huxley) dynamics, center-surround receptive-field (RF) organization, and nonlinearities, we show how a two-layer biologically-plausible neural architecture can model these mechanisms. The first layer accomplishes contrast-normalization as an emergent property of RF organization in shunting dynamics (Grossberg, 1988). The second layer implements contrast-dependent spatial processing, wherein distinct nonlinearities for center and surround control the dominance of summation and suppression according to contrast. Summation dominates at low contrast to improve weak signals whereas suppression dominates at high contrast to improve spatial resolution. We compared the predictions of the model with data (Tadin et al., 2003) showing that indeed increasing the spatial size of a low-contrast stimulus improves the discrimination of motion-direction whereas the opposite occurs with a high-contrast stimulus. Similarly, via a small modification, our model could account quantitatively (χ^2 (10)=1.07,p>0.99) for another set of behavioral data (Tadin et al., 2019) demonstrating opposite effects of contrast on motion discrimination and segregation, viz., as contrast increased motion discrimination became poorer whereas motion segmentation got better. Taken together our results show that this model is capable of capturing the trade-off between sensitivity and spatial resolution and highlights its implications for motion discrimination and segregation.