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Here we consider generic object localization in digital images where the goal is to find a tight bounding box enclosing the instances of object of interest. Traditional object localization methods treat this problem as building a binary classification that distinguishes between the object class and the background. The trained classifier is usually turned into a detector by sliding it across the image at different scales and classifying each window. In this study we also use the sliding window approach, but as opposed to the traditional methods, we approximate object class by using a convex class model, and each window is assigned to the object class or background based on the distance to this convex model. Our experiments demonstrate that using such models in a cascade for object localization with linear Support Vector Machines significantly improves the real-time efficiency with maintaining high classification accuracies.