Capturing the essential characteristics of visual objects by considering how their features are inter-related is a recent philosophy of object classification. In this paper, we embed this principle in a novel image descriptor, dubbed Heterogeneous Auto-Similarities of Characteristics (HASC). HASC is applied to heterogeneous dense features maps, encoding linear relations by co variances and nonlinear associations through information-theoretic measures such as mutual information and entropy. In this way, highly complex structural information can be expressed in a compact, scale invariant and robust manner. The effectiveness of HASC is tested on many diverse detection and classification scenarios, considering objects, textures and pedestrians, on widely known benchmarks (Caltech-101, Brodatz, Daimler Multi-Cue). In all the cases, the results obtained with standard classifiers demonstrate the superiority of HASC with respect to the most adopted local feature descriptors nowadays, such as SIFT, HOG, LBP and feature co variances. In addition, HASC sets the state-of-the-art on the Brodatz texture dataset and the Daimler Multi-Cue pedestrian dataset, without exploiting ad-hoc sophisticated classifiers.