To calculate the Average Precision and Ranking for a Content-Based Image Retrieval (CBIR) system, you can follow these steps:

1. Collect a set of query images that you will use to evaluate the CBIR system.
2. For each query image, retrieve the top-k images from the database that are most similar to the query image, where k is a predetermined value (e.g., 10 or 20).
3. Determine the relevance of each of the retrieved images with respect to the query image. You can do this by using a binary relevance judgment, where a retrieved image is either relevant (1) or irrelevant (0) to the query image. You can obtain the ground truth relevance judgments by having human annotators label the images or by using a pre-existing dataset with ground truth relevance labels.
4. Calculate the precision and recall values for each query image. Precision is the proportion of retrieved relevant images among all retrieved images, while recall is the proportion of retrieved relevant images among all relevant images in the database.
5. Calculate the Average Precision (AP) for each query image. AP is the average precision value calculated at each relevant image in the ranked list of retrieved images.
6. Calculate the Mean Average Precision (MAP) across all query images. MAP is the average of AP values calculated for all query images.

Here's an example calculation for a single query image:

Suppose the CBIR system retrieves 10 images for a query image, and the ground truth relevance labels for those 10 images are as follows: 

The precision and recall values at each retrieved image are as follows: 

The Average Precision (AP) value for this query image is calculated as follows:

AP = (1.0 + 0.67 + 0.6 + 0.57 + 0.5) / 5 = 0.668

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