Recent advances in 3D modeling provide us with real 3D datasets to answer queries, such as "What is the best position for a new billboard?" and "Which hotel room has the best view?" in the presence of obstacles. These applications require measuring and differentiating the visibility of an object (target) from different viewpoints in a dataspace, e.g., a billboard may be seen from two viewpoints but is readable only from the viewpoint closer to the target. In this paper, we formulate the above problem of quantifying the visibility of (from) a target object from (of) the surrounding area with a visibility color map (VCM). A VCM is essentially defined as a surface color map of the space, where each viewpoint of the space is assigned a color value that denotes the visibility measure of the target from that viewpoint. Measuring the visibility of a target even from a single viewpoint is an expensive operation, as we need to consider factors such as distance, angle, and obstacles between the viewpoint and the target. Hence, a straightforward approach to construct the VCM that requires visibility computation for every viewpoint of the surrounding space of the target, is prohibitively expensive in terms of both I/Os and computation, especially for a real dataset comprising of thousands of obstacles. We propose an efficient approach to compute the VCM based on a key property of the human vision that eliminates the necessity of computing the visibility for a large number of viewpoints of the space. To further reduce the computational overhead, we propose two approximations; namely, minimum bounding rectangle and tangential approaches with guaranteed error bounds. Our extensive experiments demonstrate the effectiveness and efficiency of our solutions to construct the VCM for real 2D and 3D datasets.