import numpy as np from ._find_contours_cy import _get_contour_segments from collections import deque _param_options = ('high', 'low') def find_contours( image, level=None, fully_connected='low', positive_orientation='low', *, mask=None ): """Find iso-valued contours in a 2D array for a given level value. Uses the "marching squares" method to compute 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 ---------- image : (M, N) ndarray of double Input image in which to find contours. level : float, optional Value along which to find contours in the array. By default, the level is set to (max(image) + min(image)) / 2 .. versionchanged:: 0.18 This parameter is now optional. 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 : str, {'low', '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.) mask : (M, N) ndarray of bool or None A boolean mask, True where we want to draw contours. Note that NaN values are always excluded from the considered region (``mask`` is set to ``False`` wherever ``array`` is ``NaN``). Returns ------- contours : list of (K, 2) ndarrays Each contour is a ndarray of ``(row, column)`` coordinates along the contour. See Also -------- skimage.measure.marching_cubes Notes ----- The marching squares algorithm is a special case of the marching cubes algorithm [1]_. A simple explanation is available here: https://users.polytech.unice.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 or a masked-off region (either where mask is False or where array is NaN) 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). :DOI:`10.1145/37401.37422` 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. ]])] """ if fully_connected not in _param_options: raise ValueError( 'Parameters "fully_connected" must be either ' '"high" or "low".' ) if positive_orientation not in _param_options: raise ValueError( 'Parameters "positive_orientation" must be either ' '"high" or "low".' ) if image.shape[0] < 2 or image.shape[1] < 2: raise ValueError("Input array must be at least 2x2.") if image.ndim != 2: raise ValueError('Only 2D arrays are supported.') if mask is not None: if mask.shape != image.shape: raise ValueError('Parameters "array" and "mask"' ' must have same shape.') if not np.can_cast(mask.dtype, bool, casting='safe'): raise TypeError('Parameter "mask" must be a binary array.') mask = mask.astype(np.uint8, copy=False) if level is None: level = (np.nanmin(image) + np.nanmax(image)) / 2.0 segments = _get_contour_segments( image.astype(np.float64), float(level), fully_connected == 'high', mask=mask ) contours = _assemble_contours(segments) if positive_orientation == 'high': contours = [c[::-1] for c in contours] return contours def _assemble_contours(segments): current_index = 0 contours = {} starts = {} ends = {} for from_point, to_point in segments: # 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 degenerate vertex will be picked up later by neighboring # squares. if from_point == to_point: continue tail, tail_num = starts.pop(to_point, (None, None)) head, head_num = ends.pop(from_point, (None, None)) if tail is not None and head is not None: # We need to connect these two contours. if tail is head: # We need to closed a contour: add the end point head.append(to_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 tail from the detected contours contours.pop(tail_num, None) # Update starts and ends starts[head[0]] = (head, head_num) ends[head[-1]] = (head, head_num) else: # tail_num <= head_num # head was created second. Prepend head to tail. tail.extendleft(reversed(head)) # Remove head from the detected contours starts.pop(head[0], None) # head[0] can be == to_point! contours.pop(head_num, None) # Update starts and ends starts[tail[0]] = (tail, tail_num) ends[tail[-1]] = (tail, tail_num) elif tail is None and head is None: # We need to add a new contour new_contour = deque((from_point, to_point)) contours[current_index] = new_contour starts[from_point] = (new_contour, current_index) ends[to_point] = (new_contour, current_index) current_index += 1 elif head is None: # tail is not None # tail first element is to_point: the new segment should be # prepended. tail.appendleft(from_point) # Update starts starts[from_point] = (tail, tail_num) else: # tail is None and head is not None: # head last element is from_point: the new segment should be # appended head.append(to_point) # Update ends ends[to_point] = (head, head_num) return [np.array(contour) for _, contour in sorted(contours.items())]