Spatial omics maps molecular features within tissues to study their organization across biological contexts, including disease and development. Interpreting these maps requires distinguishing patterns from noise and comparing them across samples. Yet pattern detection remains unresolved, and comparisons based on regional summaries lose spatial detail. Here we show that spatial frequency provides a common basis for detecting and comparing these patterns. Our framework, SONIC, unifies spatial detection tests through a common quadratic form, establishes conditions for reliable detection and explains how kernel choice determines sensitivity to different spatial patterns. It also separates changes in spatial organization from changes in overall abundance without aligning tissues. Fast, memory-efficient algorithms make detection and comparison practical across large datasets. Applying SONIC, we identify plaque-associated responses in Alzheimer's disease and differences in the spatial expression of blood-clotting genes between glioma subtypes. We further construct a gene-centric atlas that traces changes in spatial expression through mouse and human embryogenesis and supports retrieval of related patterns across species. These results extend spatial analysis from identifying individual patterns to following their changes across anatomically different tissues. Together, SONIC establishes a shared language for integrating molecular maps across studies and technologies.

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