MASK_TO_CELL Returns the cells from a BW image with ridges.

MainScripts/mask_to_objects.m

+function [ objects, junction_graph ] = mask_to_objects( I )
+%% MASK_TO_CELL Returns the cells from a BW image with ridges.
+% This function takes as input an image that was generated e.g. with the
+% morphological segmentation technique, where each object is white and
+% separated from its neighbor by a black ridge. It then returns the a
+% struct array, 1 element per object, containing the object boundary, the
+% junction id this object touches and its center.
+% As a second output it returns the junction graph.
+%
+% This function only works for object in white with a ridge in black. The
+% ridge must be connected using 8-connectivity.
+%
+% Jean-Yves Tinevez - Institut Pasteur - Nov 2019.
+
+
+%% Create mask.
+
+% Boundary mask.
+M = I == 0;
+
+%% Get dilated bounds.
+% Bounds like we would not have the black ridge in between cells.
+
+CC = bwconncomp( ~M, 4 );
+n_cells = CC.NumObjects;
+B = cell( n_cells, 1 );
+
+% 4-connectivity strel.
+se = strel( 'diamond', 1 );
+
+for i = 1 : n_cells
+    temp = false( CC.ImageSize );
+    temp( CC.PixelIdxList{ i } ) = true;
+    temp = imdilate( temp, se, 'same' );
+    bounds = bwboundaries( temp, 4, 'noholes' );
+    B{ i } = bounds{ 1 };
+end
+
+%% Remove cells touching the border.
+
+[ width, height ] = size( M );
+touching_border = cellfun( @(x) ...
+    any( x(:) == 1 ) ...
+    ||  any(x(:,1) == width ) ...
+    ||  any(x(:,2) == height ),...
+    B );
+B( touching_border ) = [];
+n_cells = numel( B );
+
+%% Get the position of junction points.
+
+% Define a function that only returns true for middle pixel of a 3x3
+% neighborhood is >0 and with number of white neighbors >= 4.
+f = @(x) (x(5) > 0 & sum(x(:)) >= 4);
+
+% Make it a binary LUT for 3x3 neighborhood:
+lut = makelut(f, 3);
+
+% Apply the LUT to the mask image:
+J = bwlookup( M, lut );
+
+% Make label image with the junctions.
+LJ = bwlabel( J );
+
+% Measure junction centroids.
+junction_table = regionprops('table', LJ, 'Centroid');
+n_junctions = size(junction_table, 1 );
+
+% Add junction id.
+junction_table.ID = ( 1 : n_junctions )';
+
+%% Link junctions together and create the output struct.
+
+% Struct, one per cell.
+
+% Junction graph.
+junction_graph = graph( false( n_junctions, n_junctions ), junction_table );
+
+
+% Loop over cells.
+for i = n_cells : -1 : 1
+    
+    boundary = B{ i };
+    n_pixels = size( boundary, 1 );
+    previous_junction_id = -1;
+    
+    visited_junctions = [];
+    
+    for k = 1 : n_pixels
+        
+        x = boundary( k , 1 );
+        y = boundary( k , 2 );
+        junction_id = LJ( x, y );
+        
+        if  junction_id > 0
+            
+            visited_junctions = [
+                visited_junctions
+                junction_id ]; %#ok<AGROW>
+            
+            if previous_junction_id < 0
+                first_junction_id = junction_id;
+            end
+            
+            if previous_junction_id > 0 && previous_junction_id ~= junction_id
+                % Link this junction to the previous one.
+                idx = findedge( junction_graph, previous_junction_id, junction_id );
+                
+                if numel( idx ) <= 1 && idx <= 0
+                    junction_graph = addedge( junction_graph, previous_junction_id, junction_id );
+                end
+            end
+            
+            previous_junction_id = junction_id;
+        end
+        
+    end
+    
+    % Loop.
+    if previous_junction_id > 0 && previous_junction_id ~= first_junction_id
+        % Link this junction to the previous one.
+        idx = findedge( junction_graph, previous_junction_id, first_junction_id );
+        
+        if numel( idx ) <= 1 && idx <= 0
+            junction_graph = addedge( junction_graph, previous_junction_id, first_junction_id );
+        end
+    end
+    
+    objects( i ).junctions = unique( visited_junctions );
+    objects( i ).boundary = boundary;
+    objects( i ).center = mean( boundary );
+    
+end
+
+end
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