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Mapless navigation has emerged as a promising approach for enabling autonomous robots to navigate in environments where pre-existing maps may be inaccurate, outdated, or unavailable. In this work, we propose an image-based local representation of the environment immediately around a robot to parse navigability. We further develop a local planning and control framework, a Pareto-optimal mapless visual navigator (POVNav), to use this representation and enable autonomous navigation in various challenging and real-world environments. In POVNav, we choose a Pareto-optimal sub-goal in the image by evaluating all the navigable pixels, finding a safe visual path, and generating actions to follow the path using visual servo control. In addition to providing collision-free motion, our approach enables selective navigation behavior, such as restricting navigation to select terrain types, by only changing the navigability definition in the local representation. The ability of POVNav to navigate a robot to the goal using only a monocular camera without relying on a map makes it computationally light and easy to implement on various robotic platforms. Real-world experiments in diverse challenging environments, ranging from structured indoor environments to unstructured outdoor environments such as forest trails and roads after a heavy snowfall, using various image segmentation techniques demonstrate the remarkable efficacy of our proposed framework.