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Is there any previous work on computing some sort of prominence score based on the prevalence of features in an image?

For example, let's say I am classifying images based on whether or not they have dogs in them. Is there a way to compute how prominent that feature is?

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Saliency is typically discussed more in object detection or scene understanding than prominence. There are lots of papers on saliency models. "What do different evaluation metrics tell us about saliency models?" is a good paper on various metrics on saliency models. It covers the following metrics:

  1. Similarity or histogram intersection (SIM)
  2. Pearson's Correlation Coefficient (CC)
  3. Normalized Scanpath Saliency (NSS)
  4. Area Under ROC Curve (AUC)
  5. Information Gain (IG)
  6. Kullback-Leibler divergence (KL)
  7. Earth Mover's Distance (EMD)

Some other papers you may find interesting:

  1. Saliency, attention, and visual search: An information theoretic approach
  2. Towards Instance Segmentation with Object Priority: Prominent Object Detection and Recognition
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