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jaccard

Jaccard similarity coefficient for image segmentation

Description

example

similarity= jaccard(BW1,BW2)computes the intersection of binary imagesBW1andBW2divided by the union ofBW1andBW2, also known as the Jaccard index. The images can be binary images, label images, or categorical images.

example

similarity= jaccard(L1,L2)计算农协ccard index for each label in label imagesL1andL2.

similarity= jaccard(C1,C2)计算农协ccard index for each category in categorical imagesC1andC2.

Examples

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

A = imread('hands1.jpg'); I = im2gray(A); figure imshow(I) title('Original Image')

Figure contains an axes object. The axes object with title Original Image contains an object of type image.

Use the active contours (snakes) method to segment the hand.

mask = false(size(I)); mask(25:end-25,25:end-25) = true; BW = activecontour(I, mask, 300);

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

BW_groundTruth = imread('hands1-mask.png');

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)])

Figure contains an axes object. The axes object with title Jaccard Index = 0.72158 contains an object of type image.

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.

RGB = imread('yellowlily.jpg');

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] formatBW1 = 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) holdonvisboundaries(BW1,'Color','r'); visboundaries(BW2,'Color','g'); visboundaries(BW3,'Color','b'); title('Seed Regions')

Figure contains an axes object. The axes object with title Seed Regions contains 7 objects of type line, image.

Segment the image into three regions using geodesic distance-based color segmentation.

L = imseggeodesic(RGB,BW1,BW2,BW3,'AdaptiveChannelWeighting',true);

Load a ground truth segmentation of the image.

L_groundTruth = double(imread('yellowlily-segmented.png'));

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)')

Figure contains an axes object. The axes object with title Comparison of Segmentation Results (Left) and Ground Truth (Right) contains an object of type image.

Compute the Jaccard similarity index (IoU) for each segmented region.

similarity = jaccard(L, L_groundTruth)
similarity =3×10.8861 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 asBW1.

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 asL1.

Data Types:double

First categorical image, specified as acategoricalarray of any dimension.

Data Types:category

第二个分类图像, specified as acategoricalarray of the same size asC1.

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]. Asimilarityof 1 means that the segmentations in the two images are a perfect match. If the input arrays are:

  • binary images,similarityis a scalar.

  • label images,similarityis 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,similarityis 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

More About

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Jaccard Similarity Coefficient

The Jaccard similarity coefficient of two setsAandB(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 setA. 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) )

Version History

Introduced in R2017b

See Also

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