A Comparison between Harris and FAST - Corner Detection of Noisy Images Using Adaptive Non-Local Means

In this paper a comparison between Harris and FAST (Features from Accelerated Segment Test) corner detection has been presented that is track features within a noisy images where it is a challenging task in the field of image processing. As long as noisy image does not give the desired results in corner detection, de-noising is required. Adaptive non-local means are applied for salt and pepper, Gaussian and speckle noise before applying corner detection. FAST corner detection outperformed Harris in detecting actual and exact number of corners and more robust to noise than Harris, the obtained results shown a good satisfaction in this study especially in the numbers of real detected corners.

Many algorithms have been developed for corner detection and attracted many researchers for this issue.Corner detection is used in many application in real life like unmanned underwater vehicle (UUV), event-driven cameras and so on [4] [5], so the need for such a technique is required.Mathematically, it is required an algorithms to successfully detect a corner.In 1977, Moravec presented one of the premature corner detection algorithms and defined a point with low self-similarity as a corner [6].However, Moravec detector suffers from many problems, these problems are solved by Harris, 1988 with an algorithm based on Moravec's one [7].Later, Edward Rosten and Tom Drummond proposed another algorithm named FAST for corner detection which is applied in real time applications [8].The key point for any corner detection is the ability to detect the same corner in many images in different circumstances.One of the problems facing the corner recognition or detection is noise.Whereas noise is undesirable information in image or changing in image brightness or color or both.Image denoising is often used as a solution for degraded scene.Many types of noise exists in the field of image processing such as salt & pepper, Gaussian and speckle and these are the subjects in this paper.Non-local means for image de-noising will address noise issue with a cosine function acts as a weight function to improve the algorithm's efficiency and robustness.In this paper, a study Harris and FAST corner detectors will be present and provide an adaptive algorithm for noise problems that stand up to corner detection in noisy images and observe corners numbers where: • (, ) is the window function .
Harris coroner operator depends on high intensity for shifted window in order to detect the corner.To do that, expanding the term form ( 1): [( +  ,  +  ) -(, ) ] 2 using Taylor series to have high result of H [10] : Simplifying the equation which can be expressed in matrix form: Then shortening the matrix and denote it to be M: .

.. (4)
To be the equation: Calculation of measure of corner response by the following formula [11]: where: • K is empirical constant which is (0.04 -0.06) Note that H is closely related to the local autocorrelation function, let λ1 λ2 be the eigenvalues of H (, ).As before, there are three cases to be considered, if both λ1 and λ2 are small, flat area will occur, if λ1is high and λ2 is low or vice versa, an edge will appear and if both λ1 and λ2 are high, a corner will be detected [7].

Figure1: Feature detection in an image patch using FAST detector
The algorithm nominates p is a corner whether or not a corner with the intensity of the candidate pixel Ip and a suitable threshold t.Now p is a corner if there is a set of contiguous pixels n of the 16 pixels of the circle as shown in figure (1) which are all brighter than Ip+t or all darker than Ip-t .Where n was chosen to be twelve (12 pixels seem as white dash line within the Figure ( 1)) as a result of it admits a high-speed take a look at which might be accustomed exclude a really sizable amount of non-corners [13].
The test checks only four pixels at 1, 5, 9 and 13 (at clockwise direction) where it checks first 1 and 9 if they are too brighter or darker, if so it checks 5 and 13.If p could be a corner, then a minimum of 3 of those should all be brighter than Ip+t or darker than Ip-t.If neither of those is that the case, then p can't be a corner.Although, the algorithm demonstrate a high effectiveness but there are several weaknesses.The high-speed test don't reject as several candidates for n < 12.The choice of pixels isn't best as a result of its potency rely on ordering of the queries and features are observed contiguous one to another [13].Machine learning approach is given to handle initial 3 points whereas the last one is handled by non-maximal suppression.For each pixels (p→x) of the 16 pixels can have on of the following states: Using the ID3 algorithm (decision tree classifier) to question every 16 pixels using the variable Kp for the most information concerning verity pixel [13].A score function C has been computed, where C is the sum of absolute difference between p and 16 surrounding pixels values.C is generated by [14]: The weights then can be defined by the following formula [18]:

Non-local means
where G(x) is the normalization constant and defined as: and h is the weight decay of exponential function control parameter.

Proposed Method
In the original non-local means algorithm, to make the neighborhoods with similar texture gets a larger weight, it uses the exponential function [17].In this paper, cosine function is used and expressed as:  [20].The size and contrast plays an important role in preserving features in the processed image which the filter rely on them .Also, the weights of this algorithm is depended on Euclidean distance.In this way, the edges, corners and some other details preserved efficiently.The bilateral filter is defined as [20]: The proposed method is sketched in figure (3) below depending on the new weight function in equation ( 19), the steps of the proposed method is briefed as: Step1.Load noisy image.

Step2. Apply Adaptive Non-local means
Step3.Apply Harris/FAST corner detection.Harris and FAST corner detection is done in order to obtain the final results of the work, the numbers of corners detected for both cases is shown in table (1) and figure (6) and figure (7).
As shown in table (1), the desired numbers of corners is obtained from the de-noised images and it is close to the numbers detected in the original image.… (20) PSNR is the ratio between power of a signal and the power of corrupting noise that affects the image.It can be defined as [21]: where   2 is the maximum value of pixel in image.Also SSIM is used for measuring the similarity between two images, it can give a ratio similarity between original image and any processed image and it can be expressed as [22]: The results of MSE, PSNR and SSIM are shown in table (2).

Conclusion
In

Introduction
In human visual system, a corner nothing but another feature in the scene can be identified easily without any efforts.A corner is an intersection of two edges, the edge is the change in image brightness sharply.Also, a corner can be defined as an interest point and it can strongly detected.Interest point detection could be a recent nomenclature in computer vision that refers to the detection of interest points for future processing.Corner detection is important and used in many fields such as computer vision and pattern recognition like face recognition, in and motion detection by exploiting the advantages of matching points and in 3D reconstruction such as piecewise-planar [1] [2] [3].Vol: 13 No:4 , October 2017 DOI : http://dx.doi.org/10.24237/djps.1304.307AP-ISSN: 2222-8373 E-ISSN: 2518-9255 before and after de-noising.Section 2 describes Harris corner detection.Whereas section 3 describes Fast corner detection.Concerning section 4, Non-local means for image de-noising are explained with an adaptivity by computing a cosine function (section 4.2) as a new weight function.Finally, section 6 gives the results of the images and tables obtained from the experiments.Harris Corner Detection Harris corner detection algorithm was proposed by Harris C and Stephens MJ 1988 [9].Harris's detector is a well-known corner detector due its robust stability in image noise.The local autocorrelation function measures the variation of the intensity with window moved by a small amount in different directions given a shift (Δx, Δy) and a point(, ) [10].The auto-correlation function is defined as [9]: Vol: 13 No:4 , October 2017 DOI : http://dx.doi.org/10.24237/djps.1304.307AP-ISSN: 2222-8373 E-ISSN: 2518-9255  (, ) = ∑ ,  (, ) [ ( +  ,  +  ) -(, ) ] 2 … (1)

Fast
Corner Detection FAST (Features from Accelerated Segment Test) is a corner detector developed by Rosten and Drummondn in (2006) [12].In real video application, FAST algorithm shows a good results in detection corners.The segment test standard run by taking into account a circle of sixteen pixels (Bresenham circle) around the corner candidate p [8].
By analyzing the exponential function and the cosine function, a new weight function is achieved: Where () = ∑  − ||(  )−(  )|| 2 , 2 ℎ 2 ()  Furthermore (C.Tomasi et al) proposed bilateral filtering, bilateral filtering change the intensity of each pixel with the closest neighbor pixel

Figure3:
Figure3: Scheme for corner detection of De-noised images
this paper, adaptive non-local means plays an important role in image de-noising for images including salt & pepper, Gaussian and speckle noise.FAST corner detection has superior over Harris in detecting actual and precise number of corners.FAST corner detection is more robust to noise than Harris.The proposed weight function shows a good results in number of corners detected by de-noised images is roughly equal to the same number of Harris and FAST corner detected for obtained corner from the original image especially in the case of Gaussian and speckle for FAST noise and salt & pepper noise for Harris using the new weight function in Non-local means algorithm.MSE and PSNR indicates relief values of high PSNR and low MSEfor de-noised images and the similarity between original image and de-noised images estimated using SSIM after de-noising salt and pepper, Gaussian and speckle noise from corrupted images was 81%, 85% and 85% respectively.The plane for future work is to minimize computation burden of FAST and Harris algorithms in motion scene.

Table ( 2): MSE, PSNR and SSIM values of de-noised images of the three types on noise
(2)ed on the results obtained from table(1), FAST corner detection shows better results than Harris corner detection in finding the actual numbers of corners in Gaussian and speckle noise cases while Harris corner detection surpassed FAST in salt and pepper noise case.In addition, FAST corner detection performs in more flexible ways than Harris in noisy environments, in other words FAST is more robust to noise than Harris.In table(2), PSNR values compared to MSE values demonstrates that the new weight function for non-local means gives the desired results, also SSIM values shows a good matching between original image and de-noised image of the three types of noise subjected in this work.