Invariant object recognition is a remarkable ability of primates visual system that its underlying mechanism has constantly been under intense investigations. Computational modeling is a valuable tool toward understanding the processes involved in invariant object recognition. Although recent computational models have shown outstanding performances on challenging image databases, they fail to perform well in image categorization under more complex image variations. Studies have shown that making sparse representation of objects by extracting more informative visual features through a feedforward sweep can lead to higher recognition performances. Here, however, we show that when the complexity of image variations is high, even this approach results in poor performance compared to humans. To assess the performance of models and humans in invariant object recognition tasks, we built a parametrically controlled image database consisting of several object categories varied in different dimensions and levels, rendered from 3D planes. Comparing the performance of several object recognition models with human observers shows that only in low-level image variations the models perform similar to humans in categorization tasks. Furthermore, the results of our behavioral experiments demonstrate that, even under difficult experimental conditions (i.e., briefly presented masked stimuli with complex image variations), human observers performed outstandingly well, suggesting that the models are still far from resembling humans in invariant object recognition. Taken together, we suggest that learning sparse informative visual features, although desirable, is not a complete solution for future progresses in object-vision modeling. We show that this approach is not of significant help in solving the computational crux of object recognition (i.e., invariant object recognition) when the identity-preserving image variations become more complex.