diff --git a/vidocp/table_parsing.py b/vidocp/table_parsing.py
index 5b811b8..c23aa5b 100644
--- a/vidocp/table_parsing.py
+++ b/vidocp/table_parsing.py
@@ -57,7 +57,7 @@ def parse_table(image: np.array):
     rects = stats[:, :-1][2:]
 
     # FIXME: For some reason some isolated rects remain.
-    rects = remove_isolated(rects)
+    rects = remove_isolated(rects, input_sorted=True)
 
     return rects
 
diff --git a/vidocp/utils/post_processing.py b/vidocp/utils/post_processing.py
index c05ab03..13f3149 100644
--- a/vidocp/utils/post_processing.py
+++ b/vidocp/utils/post_processing.py
@@ -1,6 +1,6 @@
 from collections import namedtuple
 from functools import partial
-from itertools import starmap
+from itertools import starmap, compress
 
 
 def remove_overlapping(rectangles):
@@ -29,24 +29,73 @@ def remove_included(rectangles):
     return rectangles
 
 
+def adjacent1d(n, m, tolerance=1):
+    return abs(n - m) <= tolerance
+
+
+def adjacent(a, b):
+    """Two rects (v1, v2), (w1, w2) are adjacent if either of:
+    - the x components of v2 and w1 match and the y components of w1 or w2 are in the range of the y components of v1 and v2
+    - the x components of v1 and w2 match and the y components of w1 or w2 are in the range of the y components of v1 and v2
+    - the y components of v2 and w1 match and the x components of w1 or w2 are in the range of the x components of v1 and v2
+    - the y components of v1 and w2 match and the x components of w1 or w2 are in the range of the x components of v1 and v2
+    """
+
+    def adjacent2d(g, h, i, j, k, l):
+        return adjacent1d(g, h) and any(k <= p <= l for p in [i, j])
+
+    if any(x is None for x in (a, b)):
+        return False
+
+    v1 = a.xmin, a.ymin
+    v2 = a.xmax, a.ymax
+
+    w1 = b.xmin, b.ymin
+    w2 = b.xmax, b.ymax
+
+    return any(
+        (
+            adjacent2d(v2[0], w1[0], w1[1], w2[1], v1[1], v2[1]),
+            adjacent2d(v1[0], w2[0], w1[1], w2[1], v1[1], v2[1]),
+            adjacent2d(v2[1], w1[1], w1[0], w2[0], v1[0], v2[0]),
+            adjacent2d(v1[1], w2[1], w1[0], w2[0], v1[0], v2[0]),
+        )
+    )
+
+
 # FIXME: For some reason some isolated rects remain.
-def remove_isolated(rectangles):
-    def are_neighbours(a, b):
-
-        def adjacent(n, m):
-            return abs(n - m) <= 1
-
-        return any(starmap(adjacent, [(b.xmin,  a.xmax), (b.ymin, a.ymax), (b.xmax, a.xmin), (b.ymax, a.ymin)]))
-
+def __remove_isolated_unsorted(rectangles):
     def is_connected(rect, rectangles):
-        return any(are_neighbours(r2, rect) for r2 in rectangles if not rect == r2)
+        return any(adjacent(r2, rect) for r2 in rectangles if not rect == r2)
 
     rectangles = list(map(xywh_to_vec_rect, rectangles))
     rectangles = filter(partial(is_connected, rectangles=rectangles), rectangles)
     rectangles = map(vec_rect_to_xywh, rectangles)
+
     return rectangles
 
 
+def __remove_isolated_sorted(rectangles):
+    def is_connected(left, center, right):
+        # if center == Rectangle(xmin=337, ymin=154, xmax=512, ymax=187) or center == Rectangle(xmin=719, ymin=188, xmax=781, ymax=251):
+        return any(starmap(adjacent, [(left, center), (center, right)]))
+
+    rectangles = list(map(xywh_to_vec_rect, rectangles))
+
+    lefts = [None, *rectangles[:-1]]
+    rights = [*rectangles[1:], None]
+
+    mask = starmap(is_connected, zip(lefts, rectangles, rights))
+    rectangles = compress(rectangles, mask)
+    rectangles = map(vec_rect_to_xywh, rectangles)
+
+    return rectangles
+
+
+def remove_isolated(rectangles, input_sorted=False):
+    return (__remove_isolated_sorted if input_sorted else __remove_isolated_unsorted)(rectangles)
+
+
 Rectangle = namedtuple("Rectangle", "xmin ymin xmax ymax")