Stereotomography is a slope-based tomographic method that uses seismic reflection data, consisting of traveltimes and slopes, to estimate the subsurface velocity macro-model. Here, we interpret the macro-model as the large-scale components of the acoustic velocity model of the subsurface. Tomographic methods are often solved with local optimization techniques, which are dependent on the initial input data. In that sense, selecting the correct input data by estimating and picking slopes is a crucial part of the stereotomography problem. In this paper, we address the problem of slope estimation and picking in stereotomography. Our central proposal uses the attributes obtained from the common-offset common-reflection-surface method as input data for stereotomography. We use the global optimization method known as differential evolution to estimate these attributes, resulting in gathers of attributes estimated for the complete seismic data. This strategy presents reliable estimates when the seismic data are highly corrupted by random noise or present geological features that may lead to the failure of classical methods. We also propose an automatic picking strategy to extract the traveltimes and slopes from the common-offset common-reflection-surface attributes gathers. We illustrate with synthetic examples the benefits of using the proposed framework for obtaining input data for stereotomography.