PERF: Use binary search for threshold in ThresholdLabelerImageFilter

Modules/Filtering/Thresholding/include/itkThresholdLabelerImageFilter.h

@@ -78,25 +78,28 @@ class ITK_TEMPLATE_EXPORT ThresholdLabeler
   inline TOutput
   operator()(const TInput & A) const
   {
-    size_t size = m_Thresholds.size();
-
-    if (size == 0)
-    {
-      return m_LabelOffset;
-    }
-    if (A <= m_Thresholds[0])
+    // When there are N thresholds, they divide values into N+1 buckets, which we number
+    // 0, ..., N.  Each bucket represents a half-open interval of values (A, B].  The
+    // variables low, mid, and high refer to buckets.  The inclusive range [low, high]
+    // are the buckets that are not yet ruled out.  We repeatedly bisect this range
+    // using the variable `mid`.  In the case of ties, this method returns the lowest
+    // bucket index for which `A` is less than or equal to the bucket's upper limit.
+    size_t low = 0;
+    size_t high = m_Thresholds.size();
+    while (low < high)
     {
-      return m_LabelOffset;
-    }
-    for (size_t i = 0; i < size - 1; ++i)
-    {
-      /* Value is in this class if it equals the upper bound. */
-      if (m_Thresholds[i] < A && A <= m_Thresholds[i + 1])
+      const size_t mid = (low + high) / 2;
+      if (A <= m_Thresholds[mid])
+      {
+        high = mid;
+      }
+      else
       {
-        return static_cast<TOutput>(i + 1) + m_LabelOffset;
+        low = mid + 1;
       }
     }
-    return static_cast<TOutput>(size) + m_LabelOffset;
+    // The computed bucket index is relative to m_LabelOffset.
+    return static_cast<TOutput>(low) + m_LabelOffset;
   }
 
 private: