The warm/hot intergalactic medium (WHIM) in the cosmic web may help solve the missing baryon problem. X-ray absorption observations of a WHIM component in the Local Group and at higher redshift, numerous detections of WHIM OVI absorption features in quasar spectra, as well as recent observations of the cosmic X-ray background in the Chandra Deep Fields North and South compel us to revisit earlier theoretical predictions for the WHIM. We use an algorithm adapted from computer vision to ferret out and extract structures in a higher resolution large scale simulation which includes the effects of galactic superwind feedback and non-equilibrium ionization. The predicted temperature-density phase diagrams for the intergalactic medium point to a new definition for the WHIM. We obtain a better understanding of the physical properties and extent of the WHIM (and therefore of the interpretation of its signature in current and future observations) by progressing beyond a threshold-based definition of this component to look at the morphology of this substantial baryon reservoir.