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We introduce a new model-based approach for automatic quantification of colocalizations in multichannel 3D microscopy images. The approach uses different 3D parametric intensity models in conjunction with a model fitting scheme to localize and quantify subcellular structures with high accuracy. The central idea is to determine colocalizations between different channels based on the estimated geometry of the subcellular structures as well as to differentiate between different types of colocalizations. A statistical analysis was performed to assess the significance of the determined colocalizations. This approach was used to successfully analyze about 500 three-channel 3D microscopy images of human soft tissue tumors and controls.