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The goal of this project is to determine if there is a difference between planar and volumetric numerical observers. The motivation comes from the use of a volumetric (3-D) display of image data (i.e., three orthogonal views through a volume image) to assess whole-body PET images in most, if not all, clinical PET centers. Studies of correlations between numerical observers and human observers (e.g., using receiver operating characteristic (ROC) detection analysis), however, typically use a planar (2-D) display and analysis methodology. In particular, planar implementations of the nonprewhitening matched filter (NPWMF) and the channelized Hotelling observer (CHO) have been extensively investigated as surrogates for measuring human detection task performance. To determine if there is a difference between planar and volumetric numerical observers, we analyzed the behavior of 2-D and 3-D implementations of the NPWMF and CHO numerical observers with multiple realizations of images with noise properties similar to those of whole-body PET oncology imaging. The results indicate that there is a significant increase in SNR or detectability of volumetric numerical observers relative to planar observers. This implies that volumetric and planar numerical observers may have different strengths of correlation with human observer performance, and that these correlations should be determined prior to using numerical observers to optimize algorithm or protocol performance for whole-body PET imaging. When axial smoothing is applied, however, to impose isotropic target resolution or to simulate fully 3-D PET data, the detectabilities of planar numerical observers are increased and the differences between planar and volumetric numerical observers become less significant.