jaccard

Jaccard similarity coefficient for image segmentation

Description

example

similarity = jaccard(BW1,BW2) computes the intersection of binary images BW1 and BW2 divided by the union of BW1 and BW2, also known as the Jaccard index. The images can be binary images, label images, or categorical images.

example

similarity = jaccard(L1,L2) computes the Jaccard index for each label in label images L1 and L2.

similarity = jaccard(C1,C2) computes the Jaccard index for each category in categorical images C1 and C2.

Examples

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Read an image containing an object to segment. Convert the image to grayscale, and display the result.

I = im2gray(A);
figure
imshow(I)
title('Original Image') Use the active contours (snakes) method to segment the hand.

Read in the ground truth against which to compare the segmentation.

Compute the Jaccard index of this segmentation.

similarity = jaccard(BW, BW_groundTruth);

Display the masks on top of each other. Colors indicate differences in the masks.

figure
imshowpair(BW, BW_groundTruth)
title(['Jaccard Index = ' num2str(similarity)]) This example shows how to segment an image into multiple regions. The example then computes the Jaccard similarity coefficient for each region.

Read in an image with several regions to segment.

Create scribbles for three regions that distinguish their typical color characteristics. The first region classifies the yellow flower. The second region classifies the green stem and leaves. The last region classifies the brown dirt in two separate patches of the image. Regions are specified by a 4-element vector, whose elements indicate the x- and y-coordinate of the upper left corner of the ROI, the width of the ROI, and the height of the ROI.

region1 = [350 700 425 120]; % [x y w h] format
BW1 = false(size(RGB,1),size(RGB,2));
BW1(region1(2):region1(2)+region1(4),region1(1):region1(1)+region1(3)) = true;

region2 = [800 1124 120 230];
BW2 = false(size(RGB,1),size(RGB,2));
BW2(region2(2):region2(2)+region2(4),region2(1):region2(1)+region2(3)) = true;

region3 = [20 1320 480 200; 1010 290 180 240];
BW3 = false(size(RGB,1),size(RGB,2));
BW3(region3(1,2):region3(1,2)+region3(1,4),region3(1,1):region3(1,1)+region3(1,3)) = true;
BW3(region3(2,2):region3(2,2)+region3(2,4),region3(2,1):region3(2,1)+region3(2,3)) = true;

Display the seed regions on top of the image.

figure
imshow(RGB)
hold on
visboundaries(BW1,'Color','r');
visboundaries(BW2,'Color','g');
visboundaries(BW3,'Color','b');
title('Seed Regions') Segment the image into three regions using geodesic distance-based color segmentation.

Load a ground truth segmentation of the image.

Visually compare the segmentation results with the ground truth.

figure
imshowpair(label2rgb(L),label2rgb(L_groundTruth),'montage')
title('Comparison of Segmentation Results (Left) and Ground Truth (Right)') Compute the Jaccard similarity index (IoU) for each segmented region.

similarity = jaccard(L, L_groundTruth)
similarity = 3×1

0.8861
0.5683
0.8414

The Jaccard similarity index is noticeably smaller for the second region. This result is consistent with the visual comparison of the segmentation results, which erroneously classifies the dirt in the lower right corner of the image as leaves.

Input Arguments

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First binary image, specified as a logical array of any dimension.

Data Types: logical

Second binary image, specified as a logical array of the same size as BW1.

Data Types: logical

First label image, specified as an array of nonnegative integers, of any dimension.

Data Types: double

Second label image, specified as an array of nonnegative integers, of the same size as L1.

Data Types: double

First categorical image, specified as a categorical array of any dimension.

Data Types: category

Second categorical image, specified as a categorical array of the same size as C1.

Data Types: category

Output Arguments

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Jaccard similarity coefficient, returned as a numeric scalar or numeric vector with values in the range [0, 1]. A similarity of 1 means that the segmentations in the two images are a perfect match. If the input arrays are:

• binary images, similarity is a scalar.

• label images, similarity is a vector, where the first coefficient is the Jaccard index for label 1, the second coefficient is the Jaccard index for label 2, and so on.

• categorical images, similarity is a vector, where the first coefficient is the Jaccard index for the first category, the second coefficient is the Jaccard index for the second category, and so on.

Data Types: double

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Jaccard Similarity Coefficient

The Jaccard similarity coefficient of two sets A and B (also known as intersection over union or IoU) is expressed as:

jaccard(A,B) = | intersection(A,B) | / | union(A,B) |

where |A| represents the cardinal of set A. The Jaccard index can also be expressed in terms of true positives (TP), false positives (FP) and false negatives (FN) as:

jaccard(A,B) = TP / (TP + FP + FN)

The Jaccard index is related to the Dice index according to:

jaccard(A,B) = dice(A,B) / (2 - dice(A,B) )