(Eng.) Weighted Felzenszwalb and Huttenlocher method (WFH)

Image segmentation is a fundamental step in a wide range of image processing tasks. One of the many image segmentation methods is the Felzenszwalb and Huttenlocher method (FH), which is a segmentation method based on graph theory. A new segmentation approach based on the FH method called Weighted Felzenszwalb and Huttenlocher method (WFH) is shown. This method is guided by a non-linear discrimination function, the Polynomial Mahalanobis distance, which captures the user-inference, prioritizing during the connecting process the regions with higher similarity to the user selected pattern. The WFH presents pattern-oriented segmentation results, showing better coherence among the segments with higher similarity to the selected pattern. All obtained segmentation results use the third degree of projection for the Polynomial Mahalanobis. To show the improvement of WFH in comparison with FH, two experiments were performed.

First Experiment

The first experiment was the comparison, first visual than quantitative of the results for both methods.

Segmentation Results obtained using 60 images from Berkeley Dataset:

Table below shows the values of Rand index for each of the 60 images, used for validation and quantitative analysis:

Table comparing the Rand index results between FH and WFH for all the 60 selected images. The column image is the reference number of the image on the Berkeley dataset.

Statistical comparison between the values of Rand index for the two approaches:

Comparison of FH and WFH performance. (a) box-plot comparing FH and WFH Rand index dissimilarity to GT results. (b) paired comparison image sequence related to GT.

Second Experiment

The second experiment uses the results obtained previously for both methods (FH and WFH) and compares with other segmentation algorithms (Color Structure Code, Edge Detection and Image Segmentation (EDISON), Mumford-Shah (MS), Watershed (WS), JSEG, Recursive Hierarchical Segmentation (RHSEG)).

Figure below shows the comparison between segmentation results for all the algorithms used and the graph result from Rand index value for each method.

Comparison between segmentation methods on image 368068. (A) original image, (B) Ground Truth, (C) WFH, (D) FH, (E) CSC, (F) Edison, (G) MS, (H) RHSEG, (I) JSEG and (J) WS.

Graph showing the Rand index score for the image 368068 for each method tested.

To summarize the comparison between methods, we show in Figure below the boxplot of the Rand index obtained for 16 images with each tested method and the values of Rand index used to build the boxplot. This plot shows that WFH has the lowest mean value, indicating that among the 16 images, the proposed approach, according to the validation method, obtained best segmentation results.

Table comparing the Rand index results between segmentation methods for 16 images. The column image is the reference number of the image on the Berkeley dataset.

Graph showing the boxplot of Rand index for 16 images for each method tested.

The link below contains all the patterns and images used:
Images, Patterns and Statistical Results