Enhancing haptic sensing allows more efficient control of interaction with unstructured and changing environments. Meanwhile, rich haptic information obtained during the interaction is useful for recognizing the environment. The haptic information contains distinctive physical features like friction, surface texture, local geometry, etc. However, how to combine these features for recognizing the environment is underexplored. Our previous work demonstrated that with accurate estimation of contact locations, and the direction and magnitude of the normal and tangential forces, a finger can follow unknown surfaces even with large changes in curvature while keeping a desired normal force. In this letter, we propose an object recognition method, using a multivariate Gaussian-Bayesian classifier that collectively combines the haptic information, including friction coefficients and surface roughness, with the local geometry to recognize the object after surface haptic exploration. Eighteen objects with different materials and shapes were tested, and results show that the method achieved a recognition accuracy of 92.3% on an average. In addition, we compared the method with six other classifiers, and concluded that it is easier to use while having high accuracy. Most importantly, it can show the levels of similarities between the features of different objects and provide a causal explanation of the recognition accuracy. This paves a way toward active and adaptive exploration where highly efficient recognition can be realized by selectively probing the most distinguishable features.