1 Introduction
In image processing, segmentation is a a set of techniques that separate regions from a scene based on similarity. There are several techniques available for this process Rodrigues2011 ; Erdmann2015 . Segmentation is usually based on attributes such as color, brightness contrast or continuity of pixel regions. In the particular case of threshold based techniques, one ore more threshold values is determined. Pixels of similar brightness levels are then grouped as below or above such threshold levels gonzalez2002digital .
Fig. 1 shows an example of a scene containing a simple foreground and a background. Fig. 2 shows it’s corresponding gray level histogram with an obtained threshold level at . The resulting image of a threshold based segmentation algorithm can is shown at Fig. 3, where pixels below are set to . Conversely, pixels of brightness level above are set to . In this case, pixels labeled as (0) and (255) can be treated as the background and foreground, respectively.
Such techniques are often used at preprocessing step in high level computer vision based systems as it reduces the amount of irrelevant information by similarity grouping of the pixels in the same region. The objective of threshold algorithms is to detect the threshold level that separates an image in regions of interest more accurately. The main problem is that the quality evaluation of such algorithms lacks an objective parameter and cannot be determined automatically.
There are many proposals for a generic metric of segmentation algorithms. Such metric is often difficult to describe making an objective evaluation method potentially unreliable. The evaluation methods can be divided in two main categories: analytic and empirical cardoso2005toward . The analytic methods are based in properties obtained from the segmented image which can be used in order to obtain a quantitative quality measurement. These methods are not very reliable as determining the quality of a segmentation based purely in analytic parameters can be difficult cardoso2005toward . The empirical methods are based on the comparison of the resulting segmented image with predefined desirable results determined by human operators, and can be further divided into two subcategories, goodness methods and discrepancy methods. Goodness methods are uses preestablished parameters such as as region uniformity or inter region contrast. The discrepancy methods rely on the comparison of the segmentation result with a reference image known as ground truth, which is established by an human operator cardoso2005toward .
Despite it’s limitations, the PSNR has been used as an analytic metric by several authors of threshold based algorithms. chen2011gray ; horng2011multilevel ; arora2008multilevel . As subject to study we performed some experiments to verify if PSNR can be used reliably as an analytic metric for image segmentation.
2 Psnr
The PSNR is a signal processing measurement that compares a given received or processed signal to it’s original source signal. This comparison allows us to quantify how much a processed signal is faithful to the original, also allowing us to identify possible noises or distortions to the signal. We can say that the PSNR represents a direct relationship of a signal before and after a degradation process.
(1) 
(2) 
where is the highest possible value of the signal. In the case of a gray scale image of 8 bits, . As demonstrated in Eq. (1), the is inversely proportional to the MSE (Mean Squared Error). The final value of the is given in decibel.
The PSNR is generally used to evaluate the quality if transmission and compression of image or video signals, based on de mean square error of the received or processed image in comparison to the source image. However, it also has been used as an analytic metric for segmentation algorithm evaluation chen2011gray ; horng2011multilevel . In the case of multithreshold algorithms, it was also used as a metric to determine the number of thresholds arora2008multilevel as well as it’s values yun2011multi .
3 Objective
The purpose of this paper is to evaluate the PSNR itself as a reliable analytic method for evaluation of image segmentation algorithms.
4 Methodology
Since we are not trying to evaluate an algorithm but the metric itself, we cannot rely on some existing study that used the PSNR as an analytic method for evaluation. Instead, we propose the adoption of ground truth data that would normally be suitable for empiric methods as results of a segmentation algorithm. Then, we use the PSRN as an analytic method to evaluate such results.
For the experiments, we used the set of images from the Berkeley BSR300 Database MartinFTM01 . It comprises of 300 images containing several types of scenes where every image has it’s corresponding ground truth image . The ground truth is an image contained contours of objects from each scene defined by volunteers as the most relevant ones. Fig. 4 shows an example of an image (a) of the database and it’s respective ground truth image (b).
From each ground truth image , a region mask is obtained, separating the background from the foreground. The mask was obtained by automatically filling of the closed contours with the white color (), thus creating masks with the most relevant regions of interest. After applying a threshold algorithm to this mask, a binary mask is obtained. Since computer vision techniques are strongly inspired by the human vision, we can assume that such binary masks are close to an ideal segmentation algorithm. Fig. 5 shows an example of a filled ground truth (a) and the corresponding binary mask (b) after threshold.
To verify the efficacy of the PSNR as an analytic method for image segmentation, we generated poorly segmented masks based on binary masks with the use of salt and pepper noise. As the salt and pepper noise adds changes pixels randomly to either or we can use this to simulate a bad segmentation. The resulting mask
therefore, contains several pixels that are incorrectly classified as foreground (
) and background (). Fig. 6 shows an example of a binary mask (a) and it’s corresponding bad segmentation (b).When used as an analytic method, the PSNR is used between the resulting image and the original. Therefore, the PSNR must be calculated between each original image and the corresponding segmentation mask and bad segmentation mask .
For each image in the database, the PSNR is calculated between both and and and the results of the PSNR are calculated and stored for posterior analysis.
4.1 Proof
Let be the set of PSNR results calculated between each binary mask and it’s corresponding image . Le be the set of PSNR results calculated between each bad segmentation mask and it’s corresponding source image . If the PSNR is not an adequate analytic method, the average of PSNR values in should be significantly superior to those obtained in . For this paper, this condition is adopted as our main hypothesis.
5 Results and discussion
To confirm the main hypothesis, initially we proposed the use of Sudent’s T test with
of significance student1908probable between and. However this test requires the variance between the samples to be homogeneous. Firstly we used the Fisher’s F test for variance
fisher1941asymptotic to verify such homogeneity between and . Figs. 7 and 8shows the density of probability for the sets
and respectively. If the results from the F test indicate that the variance between the sets and is not homogeneous the Student’s T test cannot be applied. In this case, the Welch’s T test should be used instead welch1947generalization . These hypothesis tests were performed using the R language.5.1 Fisher’s F test for variance
As a null hypothesis for the F test, we adopt that the variances of the sets are homogeneous. As the alternative hypothesis, we adopt that the variances between the sets are not homogeneous. The results from the F test are shown on table
1.F  0.4618 

df  299 
df denominator  299 
P value  
Confidence interval  0.3679506 a 0.5795227 
Variance rates 
The value for the F test is in the region for acceptance of the alternative hypothesis. Therefore, is not safe to assume that the variances between and are homogeneous and the Student’s T test cannot be used reliably. The Welch’s T test is then used to determine if the difference between and is statistically significant.
5.2 Welch’s T test
As a null hypothesis, we adopt that and are equal and the difference between the means of both sets is zero (). As the alternative hypothesis, we adopt that the mean of is superior to the mean of . Should the alternative hypothesis be accepted, it would suggest that the bad segmentation masks were considered better then the ideal segmentation according to the PSNR metric.
The Welch’s T Test is then applied with of significance between both sets and . Table 2 shows the results of the Welch’s T test.
T statistics  7.6524 

df  526.607 
p value  
Confidence interval  
Mean of  
Mean of 
The value for the Welch’s T test is and is found in the area of rejection of the null hypothesis. We are left with the acceptance of the alternative hypothesis which indicate that the PSNR values calculated from the bad segmentation masks are superior to the ones calculated by human obtained masks .
6 Final considerations
We investigated the efficacy of the PSNR as an analytic method for segmentation algorithms the same way it’s adopted. We used human created segmentation masks as an ideal reference of a segmentation algorithm and compared the calculated PSNR values from these masks to those calculated from artificially inferior segmentation masks.
To verify if the PSNR is a good evaluation method we compared the values of two sets of calculated PSNR values from good and bad segmentation masks. The mask generation procedure can produce masks that would not be obtainable from threshold algorithms as the values for labels are usually determined by the values of the calculated thresholds. For example, a foreground object on a brighter background would have it’s pixels set to () in the binary mask while the background would be set to (). However, there is no rule for what levels each label should be set to and this could influence the PSNR as well. Some graph based algorithms even separate regions using random colors huang2012robust . Results from such such algorithms could not be verified with the PSNR as it is as they would change greatly from one execution to another.
We proposed the use of Welch’s T test to verify if the difference between the sets of PSNR values from good and bad segmentation is significant. Higher PSNR values for good segmentation masks would suggest the PSNR is in fact a good analytic method. However, the results from the Welch T test suggest exactly the opposite. The values of PSNR value for the bad segmentation masks are significantly superior than the ones for good segmentation masks. Therefore, the PSNR should not be considered an adequate method for evaluation of segmentation algorithms. However, the PSNR is still a good method to evaluate discrepancies between images and could be used to evaluate edge detection algorithms by comparing with ground truth images such as the ones present in the BSR300 database.
Future works could include the verification of multithreshold algorithms and the determination of the number of thresholds as well as the impact of the label values.
7 Acknowledgment
The authors would like to thank the Berkeley University for the creation and availability of the BSR300 database.
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