A Fast and Reliable Corner Detector for Non-Uniform Illumination Mineshaft Images

2.1 Corner Region Detection

Corner detection is the most time-consuming process in image processing [17]. Trajkovic and Hedley [18] advanced that there should be an obvious variety of gray values in a neighborhood of corners. Moreover, most images are mainly composed of regions with similar intensity and brightness, which are defined as flat regions, and the other regions are defined as corner regions. To avoid unnecessary detection and calculation, a mask with four pixels will scan the nucleus first and then go directly to the next pixel if the nucleus is located on the flat region. As a result, only the corner regions are detected, which will drastically improve the efficiency.

We presented a new mask in this article to determine the corner and flat regions in an image. In Figure 1, assume X is the nucleus and then a mask is put on X. We found that the use of only four pixels, P, P′, Q, and Q′, of the mask could fulfill the requirements of both time consumption and classification quality. According to the geometrical characteristics of the corners, if X is a corner candidate, at most two of the four pixels of the mask will be similar to X; otherwise, X is located on a flat region. The difference between X and P is defined as

Figure 1.

A Mineshaft Image and the Neighborhood of a Corner.

where f_P and f_X are the gray values of P and X, respectively, and T_d is the threshold of difference. If n_P is 1, there will be a big difference between P and X; otherwise, P is similar to X.

The value of T_d has a strong effect on the accuracy and efficiency of the algorithm in that oversized values will possibly cause the algorithm to miss the true corners and the undersized value may lower down computation efficiency.

The corner regions are defined as

If the value of F_Corner is 1, pixel X is located on the corner region, which requires further detection. Figure 2 shows the corner regions of two mineshaft images. The corner regions are marked black in Figure 2. The areas of the corner regions in the two mineshaft images accounted for are 20.59% and 28.69%, respectively. We have investigated 15 non-uniform illumination mineshaft images, and the percentage of the area of the corner regions is 26.32%.

Figure 2.

The Corner Regions: (A) One Non-Uniform Illumination Image, (B) The Corner Region of (A) with T_d = 5, (C) Another Image, and (D) The Corner Region of (C) With T_d = 5.

2.2 Corner Region State

Mineshaft images are fuzzy because they are captured on a moving cage by artificial illumination, and the gradient of gray level changes slowly on the edge of the object. In Figure 1, X relative to the pixels of the mask can have one of three states [15]:

where T_C is the corner threshold. The other three pixels on the mask are similarly defined as P. Let S_X be the corner region state of X, and each corner region state of the nucleus on corner regions can be computed as

S_X can be positive, zero, or negative. Positive and negative values represent a corner located on a bright region and a dark region, respectively. If S_X is 0, the mask needs to be rotated by 45° for state recomputation.

3.1 Corner Detection

We presented a circular mask, including 32 pixels for corner region scan. The circular mask only includes the boundary pixels to reduce the time consumption. The diameter of the circle can be 9, 11, 13, and 15 pixels, of which the 13-pixel diameter mask was found to have the detection performance. Figure 3 shows the circular corner mask proposed in this article.

Let X₁, X₂, X₃, . . . , X₃₂ be the pixels covered by the mask. When the corner state is bright, there is a set of n-continuous pixels in the mask that are brighter than the intensity of X or that have similar intensity as X. When the corner state is dark, there is a set of n-continuous pixels in the mask that are darker than X or that have similar intensity as X, as shown in Figure 3. The set of n-continuous pixels in the mask is defined as the CCSN. The contribution function point P to X is defined as follows:

Figure 3.

The Circle Corner Mask.

The shape of the corner can be X, Y, etc., and the number of CCSN is >1. Let CCSN_k represent the k^th CCSN, and it is given by

In CCSN_k, each F_S(X_m, X) (m = i, i + 1, . . . , j) should be equal to 1. Considering the resistance to noise, at most, only two F_S(X_m, X) can be 0.

Let N_C represent the largest number of CCSN, which means

where the function num computes the number of pixels in CCSN_k.

According to the shape of the corner, the corner response function is given by

The shaper the corner angle is, the stronger the detector response will be. Besides, a non-maximum suppression has been performed to enhance corner detection.

3.2 Threshold Processing

The background of mineshaft images has low contrast, and the foreground has high contrast. Therefore, using a common threshold, background will miss corners and the foreground will detect too many false corners. In this article, we separated the corner regions into background and foreground, and low and high thresholds will be used for the background and foreground, respectively [4].

The separation was carried out based on the maximum entropy algorithm because the maximum entropy is insensitive to initial condition and has good feasibility in the separation of mineshaft images. A and B denote the background and the foreground, respectively, and the algorithm is as follows:

1. Record the histogram of the gray image and the probability of each gray value p_i.

2. Smooth the image histogram, with GV_L and GV_H as the smallest and the highest gray values, respectively.

3. Compute the region probability of A and B:

   

4. Define the evaluation function according to the maximum entropy algorithm:

   

5. The separation threshold T is obtained when F_H reaches the maximum.

   The gray value of mineshaft video images changes little during the same interval. To reduce time consumption, the mean threshold can only be obtained in the first few frames. Experimental results showed that the value of T_C in Eq. (3) can be computed using

   

3.3 Removal of False Corners

In this section, the false corners will be removed, and the examples of three main types of false corners are given in Figure 4:

1. A false corner with a nucleus located on a noisy pixel, as shown in Figure 4A;

2. A false corner with a nucleus located on a salient pixel, as shown in Figure 4B;

3. A false corner with a nucleus located on a thin band, as shown in Figure 4C.

Figure 4.

Three Types of False Corner with a Nucleus on a (A) Noisy Point, (B) Salient Point, and (C) Thin-Band Point.

Next, we present some corresponding methods to determine and remove these false corners.

4.1 Performance Analysis

In this section, the proposed algorithm is tested and compared with the existing corner detectors developed by SUSAN [17], Harris [5], and Lan and Zhang [8]. The SUSAN algorithm is a classical corner detector. The FAST detector uses machine learning to derive a very fast, high-quality corner detector. Recently, Lan and Zhang produced a fast corner detector. An artificial image, a noisy image, and mineshaft images were chosen to obtain the best results for each detector and to evaluate the performance of the algorithm proposed in this article. Tables 1–4 present the quantitative results of each algorithm in the test images. Four parameters, including the number of detected true corners (T_DC), missed corners (M_C), false corners (F_C), and detecting accuracy (D_a), were used for image evaluation.

The detection accuracy is defined as

where T_C stands for the number of all the true corners of each image.

Figure 5 is an artificial image that has a good quality with some obvious corners, and it has a size of 256×256 pixels at 256 gray levels. Table 1 gives the corresponding results obtained for this image. We found that the SUSAN algorithm mainly detects the area of USAN and results in the largest number of false corners, especially on the circumference; it also cannot detect some cross-shaped corners. The Harris algorithm detects the least number of true corners, with only 67, but there was no false corner detection because the result is sensitive to the threshold. A small threshold obtains a large number of true corners but makes a larger number of false corners. The method of Lan and Zhang uses an outer mask to detect corners and an inner circle mask to remove false corners; it performs well in true corner detection, and there were only three false corner detections. The method proposed in this article detects all the true corners, with only one round false corner. The proposed method obtains a detecting accuracy of 0.988 and gives the best performance among the four algorithms.

Figure 5.

Corner-Detection Results on an Artificial Image Obtained with the Use of (A) SUSAN, (B) Harris, (C) Lan and Zhang, and (D) The Proposed Method.

Figure 6 is a noisy synthetic image with a size of 320×240 pixels on which we checked the performance of the four detectors. Table 2 shows that the SUSAN and Harris algorithms detect the same number of true corners, but the Harris algorithm detects fewer false corners and has a higher noise resistance than the SUSAN algorithm. Lan and Zhang’s method falsely detects the least number of true corners and the most number of false corners, resulting in a detection accuracy of only 0.112, which is much lower than the other three algorithms. The reason is that the detector only uses the margins of the two circle masks but has no effective method in reducing noise. The method proposed in this article takes some measures to reduce the effects of noise, detects the most number of true corners, and has no false detections. The experiment on five noisy images shows that the proposed method has the best performance and is resistant to noise.

Figure 6.

Corner-Detection Results on a Noisy Image Obtained with the Use of (A) SUSAN, (B) Harris, (C) Lan and Zhang, and (D) The Proposed Method.

Figure 7 is a mineshaft image of a well rope with obvious corners, and the size is 350×190 pixels. The results show that the detectors of SUSAN, Harris, and Lan and Zhang could hardly detect the true corners and obtain false corners. The reason is that they only use a single threshold on the non-illumination images and take no measure to settle the fuzzy problems. The detecting accuracies of the SUSAN, Harris, and Lan and Zhang detectors are all very small (0.023, 0.019, and 0.045, respectively). Although the proposed method detects several false corners in Figure 7, a reasonable quantity of true corners is detected. The detection accuracy on this mineshaft images is 0.5.

Figure 7.

Corner-Detection Results on a Mineshaft Image Obtained with the Use of (A) SUSAN, (B) Harris, (C) Lan and Zhang, and (D) The Proposed Method.

An in-depth detection of the performance of the four algorithms is carried out on a large number of mineshaft images, and the results are basically consistent with the above experimental results. We provided the results of 15 images in this article. Figure 8 gives the detection results on five images that detect pulley and derrick. Figure 9 gives the results on five cable images, and Figure 10 gives the detection results on five ventilating shaft, wall, and drain line images. We found that SUSAN, Harris, and Lan and Zhang detectors all failed on the non-illumination and fuzzy mineshaft images. They detected many thin-band false corners and noisy false corners, with detecting accuracies of <0.2; meanwhile, our proposed method performed well. It is robust to noisy and non-uniform illumination, and the detecting accuracy is >0.45. The reason is that we used a separate threshold on low- and high-contrast regions and computed the continuous contributive segment based on corner region state; in addition, we adopted some measures to remove the false corners.

Figure 8.

Corner-Detection Results on Five Pulley and Derrick Mineshaft Images Obtained with the Use of (A) SUSAN, (B) Harris, (C) Lan and Zhang, And (D) The Proposed Method.

Figure 9.

Corner-Detection Results on Five Cable Mineshaft Images Obtained with the Use of (A) SUSAN, (B) Harris, (C) Lan and Zhang, and (D) The Proposed Method.

Figure 10.

Corner-Detection Results on Five Ventilating Shaft, Wall, and Drain Line Images Obtained with the Use of (A) SUSAN, (B) Harris, (C) Lan and Zhang, and (D) The Proposed Method.

4.2 Time Consumption

We recorded the time consumption of the SUSAN, Harris, Lan and Zhang detectors and the proposed method with all the algorithms running on a 2.4-GHz Intel Core Duo CPU, Pte. Ltd., China. The time consumption results are shown in Table 4 (in milliseconds).

The SUSAN detector uses a circular template, which means that the larger the template, the more time will be consumed. However, a too small template may result in many false corner detections. In most cases, the SUSAN detector uses a template with a diameter of 7 pixels (37 pixels included) and takes the longest time compared with the other three detectors. The Harris detector uses Gaussian filters and evaluates the second-order derivatives. Therefore, the Harris detector is a time-consuming algorithm. The Lan and Zhang detector adopts a double-circle mask that only involves the boundary and has recently been provide to be a fast corner detector. The proposed method takes the least time among the four algorithms because it only uses four pixels of the inner mask to recognize corner regions and flat regions and detects corners only on corner regions, which are always a small proportion of the whole image. It then only uses the margin pixels of the outer circle mask to detect corners.