import networkx as nx import numpy as np from scipy import ndimage as ndi from scipy import sparse import math from .. import measure, segmentation, util, color from .._shared.version_requirements import require def _edge_generator_from_csr(csr_array): """Yield weighted edge triples for use by NetworkX from a CSR matrix. This function is a straight rewrite of `networkx.convert_matrix._csr_gen_triples`. Since that is a private function, it is safer to include our own here. Parameters ---------- csr_array : scipy.sparse.csr_array The input matrix. An edge (i, j, w) will be yielded if there is a data value for coordinates (i, j) in the matrix, even if that value is 0. Yields ------ i, j, w : (int, int, float) tuples Each value `w` in the matrix along with its coordinates (i, j). Examples -------- >>> dense = np.eye(2, dtype=float) >>> csr = sparse.csr_array(dense) >>> edges = _edge_generator_from_csr(csr) >>> list(edges) [(0, 0, 1.0), (1, 1, 1.0)] """ nrows = csr_array.shape[0] values = csr_array.data indptr = csr_array.indptr col_indices = csr_array.indices for i in range(nrows): for j in range(indptr[i], indptr[i + 1]): yield i, col_indices[j], values[j] def min_weight(graph, src, dst, n): """Callback to handle merging nodes by choosing minimum weight. Returns a dictionary with `"weight"` set as either the weight between (`src`, `n`) or (`dst`, `n`) in `graph` or the minimum of the two when both exist. Parameters ---------- graph : RAG The graph under consideration. src, dst : int The verices in `graph` to be merged. n : int A neighbor of `src` or `dst` or both. Returns ------- data : dict A dict with the `"weight"` attribute set the weight between (`src`, `n`) or (`dst`, `n`) in `graph` or the minimum of the two when both exist. """ # cover the cases where n only has edge to either `src` or `dst` default = {'weight': np.inf} w1 = graph[n].get(src, default)['weight'] w2 = graph[n].get(dst, default)['weight'] return {'weight': min(w1, w2)} def _add_edge_filter(values, graph): """Create edge in `graph` between central element of `values` and the rest. Add an edge between the middle element in `values` and all other elements of `values` into `graph`. ``values[len(values) // 2]`` is expected to be the central value of the footprint used. Parameters ---------- values : array The array to process. graph : RAG The graph to add edges in. Returns ------- 0 : float Always returns 0. The return value is required so that `generic_filter` can put it in the output array, but it is ignored by this filter. """ values = values.astype(int) center = values[len(values) // 2] for value in values: if value != center and not graph.has_edge(center, value): graph.add_edge(center, value) return 0.0 class RAG(nx.Graph): """The Region Adjacency Graph (RAG) of an image, subclasses :obj:`networkx.Graph`. Parameters ---------- label_image : array of int An initial segmentation, with each region labeled as a different integer. Every unique value in ``label_image`` will correspond to a node in the graph. connectivity : int in {1, ..., ``label_image.ndim``}, optional The connectivity between pixels in ``label_image``. For a 2D image, a connectivity of 1 corresponds to immediate neighbors up, down, left, and right, while a connectivity of 2 also includes diagonal neighbors. See :func:`scipy.ndimage.generate_binary_structure`. data : :obj:`networkx.Graph` specification, optional Initial or additional edges to pass to :obj:`networkx.Graph` constructor. Valid edge specifications include edge list (list of tuples), NumPy arrays, and SciPy sparse matrices. **attr : keyword arguments, optional Additional attributes to add to the graph. """ def __init__(self, label_image=None, connectivity=1, data=None, **attr): super().__init__(data, **attr) if self.number_of_nodes() == 0: self.max_id = 0 else: self.max_id = max(self.nodes()) if label_image is not None: fp = ndi.generate_binary_structure(label_image.ndim, connectivity) # In the next ``ndi.generic_filter`` function, the kwarg # ``output`` is used to provide a strided array with a single # 64-bit floating point number, to which the function repeatedly # writes. This is done because even if we don't care about the # output, without this, a float array of the same shape as the # input image will be created and that could be expensive in # memory consumption. output = np.broadcast_to(1.0, label_image.shape) output.setflags(write=True) ndi.generic_filter( label_image, function=_add_edge_filter, footprint=fp, mode='nearest', output=output, extra_arguments=(self,), ) def merge_nodes( self, src, dst, weight_func=min_weight, in_place=True, extra_arguments=None, extra_keywords=None, ): """Merge node `src` and `dst`. The new combined node is adjacent to all the neighbors of `src` and `dst`. `weight_func` is called to decide the weight of edges incident on the new node. Parameters ---------- src, dst : int Nodes to be merged. weight_func : callable, optional Function to decide the attributes of edges incident on the new node. For each neighbor `n` for `src` and `dst`, `weight_func` will be called as follows: `weight_func(src, dst, n, *extra_arguments, **extra_keywords)`. `src`, `dst` and `n` are IDs of vertices in the RAG object which is in turn a subclass of :obj:`networkx.Graph`. It is expected to return a dict of attributes of the resulting edge. in_place : bool, optional If set to `True`, the merged node has the id `dst`, else merged node has a new id which is returned. extra_arguments : sequence, optional The sequence of extra positional arguments passed to `weight_func`. extra_keywords : dictionary, optional The dict of keyword arguments passed to the `weight_func`. Returns ------- id : int The id of the new node. Notes ----- If `in_place` is `False` the resulting node has a new id, rather than `dst`. """ if extra_arguments is None: extra_arguments = [] if extra_keywords is None: extra_keywords = {} src_nbrs = set(self.neighbors(src)) dst_nbrs = set(self.neighbors(dst)) neighbors = (src_nbrs | dst_nbrs) - {src, dst} if in_place: new = dst else: new = self.next_id() self.add_node(new) for neighbor in neighbors: data = weight_func( self, src, dst, neighbor, *extra_arguments, **extra_keywords ) self.add_edge(neighbor, new, attr_dict=data) self.nodes[new]['labels'] = ( self.nodes[src]['labels'] + self.nodes[dst]['labels'] ) self.remove_node(src) if not in_place: self.remove_node(dst) return new def add_node(self, n, attr_dict=None, **attr): """Add node `n` while updating the maximum node id. .. seealso:: :obj:`networkx.Graph.add_node`.""" if attr_dict is None: # compatibility with old networkx attr_dict = attr else: attr_dict.update(attr) super().add_node(n, **attr_dict) self.max_id = max(n, self.max_id) def add_edge(self, u, v, attr_dict=None, **attr): """Add an edge between `u` and `v` while updating max node id. .. seealso:: :obj:`networkx.Graph.add_edge`.""" if attr_dict is None: # compatibility with old networkx attr_dict = attr else: attr_dict.update(attr) super().add_edge(u, v, **attr_dict) self.max_id = max(u, v, self.max_id) def copy(self): """Copy the graph with its max node id. .. seealso:: :obj:`networkx.Graph.copy`.""" g = super().copy() g.max_id = self.max_id return g def fresh_copy(self): """Return a fresh copy graph with the same data structure. A fresh copy has no nodes, edges or graph attributes. It is the same data structure as the current graph. This method is typically used to create an empty version of the graph. This is required when subclassing Graph with networkx v2 and does not cause problems for v1. Here is more detail from the network migrating from 1.x to 2.x document:: With the new GraphViews (SubGraph, ReversedGraph, etc) you can't assume that ``G.__class__()`` will create a new instance of the same graph type as ``G``. In fact, the call signature for ``__class__`` differs depending on whether ``G`` is a view or a base class. For v2.x you should use ``G.fresh_copy()`` to create a null graph of the correct type---ready to fill with nodes and edges. """ return RAG() def next_id(self): """Returns the `id` for the new node to be inserted. The current implementation returns one more than the maximum `id`. Returns ------- id : int The `id` of the new node to be inserted. """ return self.max_id + 1 def _add_node_silent(self, n): """Add node `n` without updating the maximum node id. This is a convenience method used internally. .. seealso:: :obj:`networkx.Graph.add_node`.""" super().add_node(n) def rag_mean_color(image, labels, connectivity=2, mode='distance', sigma=255.0): """Compute the Region Adjacency Graph using mean colors. Given an image and its initial segmentation, this method constructs the corresponding Region Adjacency Graph (RAG). Each node in the RAG represents a set of pixels within `image` with the same label in `labels`. The weight between two adjacent regions represents how similar or dissimilar two regions are depending on the `mode` parameter. Parameters ---------- image : ndarray, shape(M, N[, ..., P], 3) Input image. labels : ndarray, shape(M, N[, ..., P]) The labelled image. This should have one dimension less than `image`. If `image` has dimensions `(M, N, 3)` `labels` should have dimensions `(M, N)`. connectivity : int, optional Pixels with a squared distance less than `connectivity` from each other are considered adjacent. It can range from 1 to `labels.ndim`. Its behavior is the same as `connectivity` parameter in ``scipy.ndimage.generate_binary_structure``. mode : {'distance', 'similarity'}, optional The strategy to assign edge weights. 'distance' : The weight between two adjacent regions is the :math:`|c_1 - c_2|`, where :math:`c_1` and :math:`c_2` are the mean colors of the two regions. It represents the Euclidean distance in their average color. 'similarity' : The weight between two adjacent is :math:`e^{-d^2/sigma}` where :math:`d=|c_1 - c_2|`, where :math:`c_1` and :math:`c_2` are the mean colors of the two regions. It represents how similar two regions are. sigma : float, optional Used for computation when `mode` is "similarity". It governs how close to each other two colors should be, for their corresponding edge weight to be significant. A very large value of `sigma` could make any two colors behave as though they were similar. Returns ------- out : RAG The region adjacency graph. Examples -------- >>> from skimage import data, segmentation, graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels) References ---------- .. [1] Alain Tremeau and Philippe Colantoni "Regions Adjacency Graph Applied To Color Image Segmentation" :DOI:`10.1109/83.841950` """ graph = RAG(labels, connectivity=connectivity) for n in graph: graph.nodes[n].update( { 'labels': [n], 'pixel count': 0, 'total color': np.array([0, 0, 0], dtype=np.float64), } ) for index in np.ndindex(labels.shape): current = labels[index] graph.nodes[current]['pixel count'] += 1 graph.nodes[current]['total color'] += image[index] for n in graph: graph.nodes[n]['mean color'] = ( graph.nodes[n]['total color'] / graph.nodes[n]['pixel count'] ) for x, y, d in graph.edges(data=True): diff = graph.nodes[x]['mean color'] - graph.nodes[y]['mean color'] diff = np.linalg.norm(diff) if mode == 'similarity': d['weight'] = math.e ** (-(diff**2) / sigma) elif mode == 'distance': d['weight'] = diff else: raise ValueError(f"The mode '{mode}' is not recognised") return graph def rag_boundary(labels, edge_map, connectivity=2): """Comouter RAG based on region boundaries Given an image's initial segmentation and its edge map this method constructs the corresponding Region Adjacency Graph (RAG). Each node in the RAG represents a set of pixels within the image with the same label in `labels`. The weight between two adjacent regions is the average value in `edge_map` along their boundary. labels : ndarray The labelled image. edge_map : ndarray This should have the same shape as that of `labels`. For all pixels along the boundary between 2 adjacent regions, the average value of the corresponding pixels in `edge_map` is the edge weight between them. connectivity : int, optional Pixels with a squared distance less than `connectivity` from each other are considered adjacent. It can range from 1 to `labels.ndim`. Its behavior is the same as `connectivity` parameter in `scipy.ndimage.generate_binary_structure`. Examples -------- >>> from skimage import data, segmentation, filters, color, graph >>> img = data.chelsea() >>> labels = segmentation.slic(img) >>> edge_map = filters.sobel(color.rgb2gray(img)) >>> rag = graph.rag_boundary(labels, edge_map) """ conn = ndi.generate_binary_structure(labels.ndim, connectivity) eroded = ndi.grey_erosion(labels, footprint=conn) dilated = ndi.grey_dilation(labels, footprint=conn) boundaries0 = eroded != labels boundaries1 = dilated != labels labels_small = np.concatenate((eroded[boundaries0], labels[boundaries1])) labels_large = np.concatenate((labels[boundaries0], dilated[boundaries1])) n = np.max(labels_large) + 1 # use a dummy broadcast array as data for RAG ones = np.broadcast_to(1.0, labels_small.shape) count_matrix = sparse.csr_array( (ones, (labels_small, labels_large)), dtype=int, shape=(n, n) ) data = np.concatenate((edge_map[boundaries0], edge_map[boundaries1])) graph_matrix = sparse.csr_array((data, (labels_small, labels_large))) graph_matrix.data /= count_matrix.data rag = RAG() rag.add_weighted_edges_from(_edge_generator_from_csr(graph_matrix), weight='weight') rag.add_weighted_edges_from(_edge_generator_from_csr(count_matrix), weight='count') for n in rag.nodes(): rag.nodes[n].update({'labels': [n]}) return rag @require("matplotlib", ">=3.3") def show_rag( labels, rag, image, border_color='black', edge_width=1.5, edge_cmap='magma', img_cmap='bone', in_place=True, ax=None, ): """Show a Region Adjacency Graph on an image. Given a labelled image and its corresponding RAG, show the nodes and edges of the RAG on the image with the specified colors. Edges are displayed between the centroid of the 2 adjacent regions in the image. Parameters ---------- labels : ndarray, shape (M, N) The labelled image. rag : RAG The Region Adjacency Graph. image : ndarray, shape (M, N[, 3]) Input image. If `colormap` is `None`, the image should be in RGB format. border_color : color spec, optional Color with which the borders between regions are drawn. edge_width : float, optional The thickness with which the RAG edges are drawn. edge_cmap : :py:class:`matplotlib.colors.Colormap`, optional Any matplotlib colormap with which the edges are drawn. img_cmap : :py:class:`matplotlib.colors.Colormap`, optional Any matplotlib colormap with which the image is draw. If set to `None` the image is drawn as it is. in_place : bool, optional If set, the RAG is modified in place. For each node `n` the function will set a new attribute ``rag.nodes[n]['centroid']``. ax : :py:class:`matplotlib.axes.Axes`, optional The axes to draw on. If not specified, new axes are created and drawn on. Returns ------- lc : :py:class:`matplotlib.collections.LineCollection` A collection of lines that represent the edges of the graph. It can be passed to the :meth:`matplotlib.figure.Figure.colorbar` function. Examples -------- .. testsetup:: >>> import pytest; _ = pytest.importorskip('matplotlib') >>> from skimage import data, segmentation, graph >>> import matplotlib.pyplot as plt >>> >>> img = data.coffee() >>> labels = segmentation.slic(img) >>> g = graph.rag_mean_color(img, labels) >>> lc = graph.show_rag(labels, g, img) >>> cbar = plt.colorbar(lc) """ from matplotlib import colors from matplotlib import pyplot as plt from matplotlib.collections import LineCollection if not in_place: rag = rag.copy() if ax is None: fig, ax = plt.subplots() out = util.img_as_float(image, force_copy=True) if img_cmap is None: if image.ndim < 3 or image.shape[2] not in [3, 4]: msg = 'If colormap is `None`, an RGB or RGBA image should be given' raise ValueError(msg) # Ignore the alpha channel out = image[:, :, :3] else: img_cmap = plt.get_cmap(img_cmap) out = color.rgb2gray(image) # Ignore the alpha channel out = img_cmap(out)[:, :, :3] edge_cmap = plt.get_cmap(edge_cmap) # Handling the case where one node has multiple labels # offset is 1 so that regionprops does not ignore 0 offset = 1 map_array = np.arange(labels.max() + 1) for n, d in rag.nodes(data=True): for label in d['labels']: map_array[label] = offset offset += 1 rag_labels = map_array[labels] regions = measure.regionprops(rag_labels) for (n, data), region in zip(rag.nodes(data=True), regions): data['centroid'] = tuple(map(int, region['centroid'])) cc = colors.ColorConverter() if border_color is not None: border_color = cc.to_rgb(border_color) out = segmentation.mark_boundaries(out, rag_labels, color=border_color) ax.imshow(out) # Defining the end points of the edges # The tuple[::-1] syntax reverses a tuple as matplotlib uses (x,y) # convention while skimage uses (row, column) lines = [ [rag.nodes[n1]['centroid'][::-1], rag.nodes[n2]['centroid'][::-1]] for (n1, n2) in rag.edges() ] lc = LineCollection(lines, linewidths=edge_width, cmap=edge_cmap) edge_weights = [d['weight'] for x, y, d in rag.edges(data=True)] lc.set_array(np.array(edge_weights)) ax.add_collection(lc) return lc