Spatial information plays a very important role in high-level image understanding tasks. Contextual models that exploit spatial information through the quantification of region spatial relationships can be used for resolving the uncertainties in low-level features used for image classification and object detection. We describe intuitive, flexible and efficient methods for modeling pairwise directional spatial relationships and the ternary between relationship using fuzzy mathematical morphology. These methods define a fuzzy landscape where each image point is assigned a value that quantifies its relative position with respect to the reference object(s) and the type of the relationship. Directional mathematical dilation with fuzzy structuring elements is used to compute this landscape. We provide flexible definitions of fuzzy structuring elements that are tunable along both radial and angular dimensions. Examples using synthetic images show that our models produce more intuitive results than the competitors. We also illustrate the use of the models described in this chapter as spatial contextual constraints for two image analysis tasks. First, we show how these spatial relationships can be incorporated into a Bayesian classification framework for land cover classification to reduce the amount of commission among spectrally similar classes. Then, we show how the use of spatial constraints derived from shadow regions improves building detection accuracy. The significant improvement in accuracy in these applications confirms the importance of spatial information and the effectiveness of the relationship models described in this chapter in modeling and quantifying this information.

Purpose: Use of strict scoring criteria to study the inter‐observer variability of image quality between megavoltage cone‐beam cat scan (MV CBCT) and megavoltage helical fan‐beam computed tomography (TomoTherapy). Method and Materials: A Siemens MVCB QA phantom was utilized for all image acquisitions. Sections 2 and 4 of this phantom contain low contrast objects, and section 3 contains a line pair array for spatial resolution determination. The phantom was imaged on a 20‐slice Siemens SOMATOM® Sensation Open (CT‐Sim) as the “gold standard” for image quality. The phantom was also imaged on a TomoTherapy machine utilizing the three available imaging modes of fine, normal, and coarse. The imaging was repeated on a Siemens OnCor Avant‐Garde linear accelerator utilizing the MVCB‐CT option. Five observers were asked to score each image modality. A scoring scheme and rules were developed to allow all of the observers to use the same criteria to judge these image attributes. Each image was processed using a constant region of interest (ROI) and fixed window and level to reduce scoring bias. Results: The outcome was consistent among the observers concerning spatial resolution. There was a decrease in perceived resolution in the z‐axis compared to the x‐y directions for all three imaging units The Siemens MVCB scored higher compared to TomoTherapy in the z‐axis, but scored lower in the x‐y plane. The observer scoring for low contrast detection was most consistent in the phantom containing high‐density objects (1.56–1.02 g/cc) compared to lower density (1.09–1.02 g/cc). A comparison was made between low contrast scoring and quantitative contrast ratio. Conclusion: The results show consistent scoring of image spatial resolution by multiple observers regardless of modality. The largest variation occurred when scoring the lowest density objects. A noticeable trend was established between contrast ratio and observer scoring. Conflict of Interest: Partially supported by Siemens.