diff --git a/dlib/statistics/average_precision.h b/dlib/statistics/average_precision.h
index 978a2c4c6..87408904d 100644
--- a/dlib/statistics/average_precision.h
+++ b/dlib/statistics/average_precision.h
@@ -28,17 +28,28 @@ namespace dlib
     )
     {
         using namespace dlib::impl;
-        double precision_sum = 0;
         double relevant_count = 0;
+        // find the precision values
+        std::vector<double> precision;
         for (unsigned long i = 0; i < items.size(); ++i)
         {
             if (get_bool_part(items[i]))
             {
                 ++relevant_count;
-                precision_sum += relevant_count / (i+1);
+                precision.push_back(relevant_count / (i+1));
             }
         }
 
+        double precision_sum = 0;
+        double max_val = 0;
+        // now sum over the interpolated precision values
+        for (std::vector<double>::reverse_iterator i = precision.rbegin(); i != precision.rend(); ++i)
+        {
+            max_val = std::max(max_val, *i);
+            precision_sum += max_val;
+        }
+
+
         relevant_count += missing_relevant_items;
 
         if (relevant_count != 0)
diff --git a/dlib/statistics/average_precision_abstract.h b/dlib/statistics/average_precision_abstract.h
index 147c3ea8f..daf95619b 100644
--- a/dlib/statistics/average_precision_abstract.h
+++ b/dlib/statistics/average_precision_abstract.h
@@ -29,6 +29,12 @@ namespace dlib
               the second true has a precision of 0.5, giving an average of 0.75).
             - As a special case, if item contains no true elements then the average
               precision is considered to be 1.
+            - Note that we use the interpolated precision.  That is, the interpolated
+              precision at a recall value r is set to the maximum precision obtained at any
+              higher recall value.  Or in other words, we interpolate the precision/recall
+              curve so that precision is monotonically decreasing.  Therefore, the average
+              precision value returned by this function is the area under this interpolated
+              precision/recall curve.
             - This function will add in missing_relevant_items number of items with a
               precision of zero into the average value returned.  For example, the average
               precision of the ranking [true, true] if there are 2 missing relevant items
diff --git a/dlib/test/statistics.cpp b/dlib/test/statistics.cpp
index ab2e4c3e7..d7e0d7cbe 100644
--- a/dlib/test/statistics.cpp
+++ b/dlib/test/statistics.cpp
@@ -446,6 +446,11 @@ namespace
             items.push_back(true);
 
             DLIB_TEST(std::abs(average_precision(items) - (2.0+3.0/4.0)/3.0) < 1e-14);
+
+            items.push_back(true);
+
+            DLIB_TEST(std::abs(average_precision(items)   - (2.0 + 4.0/5.0 + 4.0/5.0)/4.0) < 1e-14);
+            DLIB_TEST(std::abs(average_precision(items,1) - (2.0 + 4.0/5.0 + 4.0/5.0)/5.0) < 1e-14);
         }
 
         void perform_test (