import numpy as np from . import _find_contours_cy from collections import deque _param_options = ('high', 'low') def find_contours(array, level, fully_connected='low', positive_orientation='low'): """Find iso-valued contours in a 2D array for a given level value. Uses the "marching squares" method to compute a the iso-valued contours of the input 2D array for a particular level value. Array values are linearly interpolated to provide better precision for the output contours. Parameters ---------- array : 2D ndarray of double Input data in which to find contours. level : float Value along which to find contours in the array. fully_connected : str, {'low', 'high'} Indicates whether array elements below the given level value are to be considered fully-connected (and hence elements above the value will only be face connected), or vice-versa. (See notes below for details.) positive_orientation : either 'low' or 'high' Indicates whether the output contours will produce positively-oriented polygons around islands of low- or high-valued elements. If 'low' then contours will wind counter- clockwise around elements below the iso-value. Alternately, this means that low-valued elements are always on the left of the contour. (See below for details.) Returns ------- contours : list of (n,2)-ndarrays Each contour is an ndarray of shape ``(n, 2)``, consisting of n ``(row, column)`` coordinates along the contour. Notes ----- The marching squares algorithm is a special case of the marching cubes algorithm [1]_. A simple explanation is available here:: http://www.essi.fr/~lingrand/MarchingCubes/algo.html There is a single ambiguous case in the marching squares algorithm: when a given ``2 x 2``-element square has two high-valued and two low-valued elements, each pair diagonally adjacent. (Where high- and low-valued is with respect to the contour value sought.) In this case, either the high-valued elements can be 'connected together' via a thin isthmus that separates the low-valued elements, or vice-versa. When elements are connected together across a diagonal, they are considered 'fully connected' (also known as 'face+vertex-connected' or '8-connected'). Only high-valued or low-valued elements can be fully-connected, the other set will be considered as 'face-connected' or '4-connected'. By default, low-valued elements are considered fully-connected; this can be altered with the 'fully_connected' parameter. Output contours are not guaranteed to be closed: contours which intersect the array edge will be left open. All other contours will be closed. (The closed-ness of a contours can be tested by checking whether the beginning point is the same as the end point.) Contours are oriented. By default, array values lower than the contour value are to the left of the contour and values greater than the contour value are to the right. This means that contours will wind counter-clockwise (i.e. in 'positive orientation') around islands of low-valued pixels. This behavior can be altered with the 'positive_orientation' parameter. The order of the contours in the output list is determined by the position of the smallest ``x,y`` (in lexicographical order) coordinate in the contour. This is a side-effect of how the input array is traversed, but can be relied upon. .. warning:: Array coordinates/values are assumed to refer to the *center* of the array element. Take a simple example input: ``[0, 1]``. The interpolated position of 0.5 in this array is midway between the 0-element (at ``x=0``) and the 1-element (at ``x=1``), and thus would fall at ``x=0.5``. This means that to find reasonable contours, it is best to find contours midway between the expected "light" and "dark" values. In particular, given a binarized array, *do not* choose to find contours at the low or high value of the array. This will often yield degenerate contours, especially around structures that are a single array element wide. Instead choose a middle value, as above. References ---------- .. [1] Lorensen, William and Harvey E. Cline. Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics (SIGGRAPH 87 Proceedings) 21(4) July 1987, p. 163-170). Examples -------- >>> a = np.zeros((3, 3)) >>> a[0, 0] = 1 >>> a array([[ 1., 0., 0.], [ 0., 0., 0.], [ 0., 0., 0.]]) >>> find_contours(a, 0.5) [array([[ 0. , 0.5], [ 0.5, 0. ]])] """ array = np.asarray(array, dtype=np.double) if array.ndim != 2: raise ValueError('Only 2D arrays are supported.') level = float(level) if (fully_connected not in _param_options or positive_orientation not in _param_options): raise ValueError('Parameters "fully_connected" and' ' "positive_orientation" must be either "high" or "low".') point_list = _find_contours_cy.iterate_and_store(array, level, fully_connected == 'high') contours = _assemble_contours(_take_2(point_list)) if positive_orientation == 'high': contours = [c[::-1] for c in contours] return contours def _take_2(seq): iterator = iter(seq) while True: try: n1 = next(iterator) n2 = next(iterator) yield (n1, n2) except StopIteration: return def _assemble_contours(points_iterator): current_index = 0 contours = {} starts = {} ends = {} for from_point, to_point in points_iterator: # Ignore degenerate segments. # This happens when (and only when) one vertex of the square is # exactly the contour level, and the rest are above or below. # This degnerate vertex will be picked up later by neighboring squares. if from_point == to_point: continue tail_data = starts.get(to_point) head_data = ends.get(from_point) if tail_data is not None and head_data is not None: tail, tail_num = tail_data head, head_num = head_data # We need to connect these two contours. if tail is head: # We need to closed a contour. # Add the end point, and remove the contour from the # 'starts' and 'ends' dicts. head.append(to_point) del starts[to_point] del ends[from_point] else: # tail is not head # We need to join two distinct contours. # We want to keep the first contour segment created, so that # the final contours are ordered left->right, top->bottom. if tail_num > head_num: # tail was created second. Append tail to head. head.extend(tail) # remove all traces of tail: del starts[to_point] try: del ends[tail[-1]] except KeyError: pass del contours[tail_num] # remove the old end of head and add the new end. del ends[from_point] ends[head[-1]] = (head, head_num) else: # tail_num <= head_num # head was created second. Prepend head to tail. tail.extendleft(reversed(head)) # remove all traces of head: del starts[head[0]] del ends[from_point] del contours[head_num] # remove the old start of tail and add the new start. del starts[to_point] starts[tail[0]] = (tail, tail_num) elif tail_data is None and head_data is None: # we need to add a new contour current_index += 1 new_num = current_index new_contour = deque((from_point, to_point)) contours[new_num] = new_contour starts[from_point] = (new_contour, new_num) ends[to_point] = (new_contour, new_num) elif tail_data is not None and head_data is None: tail, tail_num = tail_data # We've found a single contour to which the new segment should be # prepended. tail.appendleft(from_point) del starts[to_point] starts[from_point] = (tail, tail_num) elif tail_data is None and head_data is not None: head, head_num = head_data # We've found a single contour to which the new segment should be # appended head.append(to_point) del ends[from_point] ends[to_point] = (head, head_num) # end iteration over from_ and to_ points return [np.array(contour) for (num, contour) in sorted(contours.items())]