1. Introduction

In the last two decades mobile robots are attracting more attention of scientists because their range of use is increasing in various fields such as space research, underwater exploration, automotive, military, medical, service robots, robots for serving and entertainment, etc. Mobile robots have to possess some autonomy, intelligence and ability to navigate in an unknown surrounding, which is a fundamental problem for mobile robots. Robot navigation requires guidance of mobile robot through desired path to the desired goal avoiding obstacles and hazards encountered in an unknown environment. [1] Detection and avoidance of obstacles, collisions and hazardous situations is in the first place, however, path planning and arrival at the desired goal is also a very important part of reliable and secure navigation of mobile robots. Planning the optimal path requires optimization of specific performance of navigation, such as minimum time until robot reaches desired goal with a minimum of control, but also requires to comply with certain restrictions in robot motion, such as avoiding obstacles with the maximum speed of the robot.

Generally, all obstacles or hazards in the urban surrounding of the robot, can be classified as [2]:

* Drop offs (sidewalk curbs, downward stairs, steps);

* Static obstacles (walls, furniture);

* Dynamic obstacles (people, doors);

* Invisible obstacles (glass doors and glass walls);

* Overhangs (table tops, railings, tree branches);

* Inclines (wheelchair ramps, curb cuts);

* Rough surfaces (travel paths, grass beds).

* Narrow regions (doorways, elevators).

To avoid collision with obstacles in the environment, robots should be equipped with sensor system that will enable detection of these obstacles. Informations obtained from sensors are used in obstacle avoidance strategies, or in strategies for finding best solution in case of emergency stop of robot before collision. [1] Obstacle detection can be classified into two types [3]:

* Ranged-based obstacle detection.

* Appearance-based obstacle detection.

Obstacle criterion is important difference between these two obstacle detection systems. In range-based systems, obstacles are objects that protrude a minimum distance from the ground. In appearance-based systems, obstacles are objects that differ in appearance from the ground. [4] In case of range-based obstacle detection, sensors scan the area and detect any obstacle within the range, also sensors calculate the range between the robot and the obstacle. In appearance based obstacle detection, the physical appearance of the obstacle is detected from the environment, usually by image processing. [3] Vision sensors provide large quantity of data from the environment that are useful for obstacles detection. However, this large quantity of data also represents great computational complexity for processing circuitry of the mobile robot, so it is necessary to extract only the most important details. one way to extract only the most important details are methods for detecting the edges of obstacles placed in the robot's surrounding. In this paper we will present comparison of the four most commonly used methods for edge detection: Sobel, Prewitt, Roberts and Canny.

These edge detection methods were used in various systems for edge detection in different environments and scenarios. Each method has strengths and weaknesses and its particularities. Sobel, Prewitt and Roberts methods uses derivatives on an intensity map to calculate the maximum change in the gradient at an edge [5]. Canny algorithm has the ability to achieve a low error-rate by eliminating almost all non-edges and improving the localization of all identified edges [6]. Various authors have compared these methods on a variety of examples in the application of detected edges to perform different tasks. on the example of edge detection for mobile robot on lunar surface and surroundings [5] it is noticed that Canny edge algorithm results in highly detailed edges but it is not desirable in a defined textured scene, good result provided Sobel operator for detecting high concentration edges. Comparison of these methods was done through a navigation system of a mobile robot using Pan Tilt Zoom network camera mounted on the robot as the primary sensor for robot navigation [7]. Application and comparison of these methods is presented trough edge detection algorithm for vision guided robotics which showed that Canny's edge detection algorithm gives better result and minimum error [8]. The edge detection techniques Canny, Prewitt, Roberts and Sobel are compared in paper to detect the obstacles with the precision of free Google Maps API [9]. In the papers [10]--[12] through various experiments, comparisons of these four methods have shown that Canny algorithm is computationally more expensive compared to Sobel, Prewitt and Robert methods. However, the Canny algorithm performs better in different environments and scenarios, also under noisy conditions and indicates better performance.

This paper presents comparison of Sobel, Prewitt, Roberts and Canny methods to select best edge detection method that will be used for mobile robot indoor navigation. Future work is based on the development of mobile robot navigation system with a fusion of infrared sensors and camera, where most suitable of these edge detecting methods will be used.

2. METHOD USED

2.1. Hardware and Software Used

Hardware used in this paper includes a mobile robot Robotino 2 (Fig. 1.) and a laptop, while the application algorithms were implemented in MATLAB/Simulink programming environment. Robotino is a fully functional, high quality mobile robotic system with omnidirectional wheel drive. The system can work independently but also linked to an external computer system (Wi-Fi connection). Robotino possesses different types of sensors. Some of these sensors are built-in as standard equipment, such as: VGA camera, infrared sensors, incremental encoder and bumper. Other sensors come as an upgrade, such as: analog inductive distance sensor, gyroscope or a navigation system. Robotino controller unit consists of 3 components [13], [14]:

* PC 104 processor, 300 MHz, and Linux operating system with real-time kernel, SDRAM 128 MB

* Compact flash card with C++ API for controlling Robotino

* Wireless LAN access point

Controller unit is equipped with the following interfaces: Ethernet, 2 ea. USB and VGA. Power is supplied by two rechargeable 12 V batteries. Robotino is equipped with a camera system. Its height and inclination can be adjusted, and connects to Robotino via USB port. The camera makes it possible to display live images using different programming interfaces, including MATLAB/Simulink. Technical specifications of the camera are shown in Table 1.

2.2. Edge Detection Methods

Edge detection is one of the most important parts in the image processing systems of mobile robots navigation. It allows the extraction and display of features such as curves, lines and angles for the purposes of identifying images from the environment. Images represented by edges are widely used to simplify the process of identifying and interpreting images to the navigation systems of mobile robots which use camera as primary sensor. [15]

Main idea in edge detection process is based on an abrupt change in the intensity of pixels between adjacent pixels in the image. The edge represents a location that forms the border between the pixels of high and low intensity. Abrupt transition in the intensity of pixels requires the application of derivative operators to create a gradient images. The edge detector can be defined as a mathematical operator that corresponds to spatial variations and discontinuities in the grayscale pixel set in the image. The edge is indicated with a rapid changes within the picture that shows the characteristic features and can therefore be characterized as a set of pixels whose intensity of environmental follows continuous variation.

The quality of edge detection largely depends on light conditions, the presence of objects of similar intensity, density of edges in the scene and noises. Different edge detectors work better under different conditions, and therefore there is no uniform algorithm that can be adapted to all conditions in the environment. An "optimal" edge detector means [16]:

* Good detection--the algorithm should mark real edges in the image as possible.

* Good localization--Marked edges should be as close as possible to the edge in the real image.

* Minimal response--a given edge in the image should only be noticeable once, and where possible, image noise should not generate false edges.

Ideal would be to use an algorithm that simultaneously uses different detectors applying each of them when conditions in environment are ideal for that particular method. This paper will present comparison of four methods for detecting edges of obstacles that mobile robot encounters. These methods are: Sobel, Prewitt, Roberts and Canny.

Sobel Edge Detector

Sobel operator uses two 3 x 3 kernels which are convolved with the original image to calculate approximations of the derivatives, one for horizontal changes, and one for vertical changes. To produce separate measurements of the gradient component in each orientation, kernels can be applied separately to the input image (Gx--in direction of the X-axis; Gy --in direction of Y-axis), as follows: [18]

[mathematical expression not reproducible] (1)

The x-coordinate is defined as increasing in the "right"-direction, and the y- coordinate is defined as increasing in the "down"--direction. These can then be combined together to find the resulting gradient approximations at each point in the image, to give the gradient magnitude:

G = [square root of [G.sup.2.sub.x] + [G.sup.2.sub.y]] (2)

Then, it is possible to calculate the gradient's direction:

[theta] = arctan ([G.sub.y]/[G.sub.x]) (3)

Prewitt edge detector

Prewitt operator is very similar to the Sobel operator, and also utilizes two masks which enable calculation of pixel intensity gradient in the vertical and horizontal directions. The overall gradient and edge orientation is calculated in the same way [17], [18]:

G = [square root of [G.sup.2.sub.x] + [G.sup.2.sub.y]] and [theta] = arctan([G.sub.y]/[G.sub.x]) (4)

Horizontal (Gx) and vertical (Gy) derivative approximations are computed as:

[mathematical expression not reproducible] (5)

Roberts edge detector

The Roberts detector performs a simple, quick to compute, 2-D spatial gradient measurement on an image. Pixel values at each point in the output represent the estimated absolute magnitude of the spatial gradient of the input image at that point. The operator consists of a pair of 2 x 2 convolution kernels. These kernels are designed to respond maximally to edges running at 45[degrees] to the pixel grid, one kernel for each of the two perpendicular orientations. The kernels can be applied separately to the input image, to produce separate measurements of the gradient component in each orientation (Gx and Gy). This is very similar to the Sobel operator. In order to perform edge detection with the Roberts operator initially it is necessary to convolve the original image, with the following two kernels [11], [17]:

[mathematical expression not reproducible] (6)

These can then be combined together to find the absolute magnitude of the gradient at each point and the orientation of that gradient:

G = [square root of [G.sup.2.sub.x] + [G.sup.2.sub.y]] (7)

The direction of the gradient can also be defined as follows:

[theta] = arctan([G.sub.y]/[G.sub.x]) - [3[pi]/4] (8)

Canny Edge Detector

The Canny edge detector is known as the optimal edge detector. John F. Canny in 1986 introduced a multi-stage algorithm for detecting a wide range of edges. He discussed a mathematical problem of derivation of optimal smoothing filter with respect to the criteria of detection, localization and minimization of multiple responses of one edge. [19] Canny saw the edge detection problem as a signal processing optimization problem, so he developed an objective function to be optimized. The solution to this problem was a rather complex exponential function, but Canny found several ways to approximate and optimize the edge-searching problem. Steps in the canny edge detector are as follows [17], [19]:

1. Smoothing: Blurring of the image to remove noise.

2. Finding gradients: The edges should be marked where the gradients of the image has large magnitudes.

3. Non-maximum suppression: Only local maxima should be marked as edges.

4. Double thresholding: Potential edges are determined by thresholding.

5. Edge tracking by hysteresis: Final edges are determined by suppressing all edges that are not connected to a very certain (strong) edge.

The block diagram of Canny edge detection algorithm is shown in Figure 2.

3. Implementation

Sobel, Prewitt, Roberts and Canny edge detection algorithms are implemented using MATLAB Simulink models by using Video and Image Processing Blocksets from Simulink of MATLAB 7.10 (2010a). Manufacturer (Festo) of mobile robot Robotino has provided an upgrade for MATLAB/Simulink. This also includes Simulink Blockset with blocks for connecting to Robotino and to control all its components, including the camera, motors, sensors, etc.

Exactly the same blocks and the same structure is used for Sobel, Prewitt and Roberts edge detector Simulink models (Fig. 3.).

The only thing that was changed for each method is the selection of exactly preferred method in the "Function Block Parameters" of "Edge Detection" block (Fig. 4.). For Sobel, Prewitt, and Roberts, the "Edge Detection" block finds the edges in an input image by approximating the gradient magnitude of the image. The block convolves the input matrix with the Sobel, Prewitt, or Roberts kernel, and outputs two gradient components of the image, which are the result of this convolution operation. Alternatively, the block can perform a thresholding operation on the gradient magnitudes and output a binary image, which is a matrix of Boolean values. If a pixel value is 1, it is an edge. [16], [17]

After starting the simulation, Robotino is moving and observing with a camera various obstacles in the environment. Image from the camera passes through the "Edge Detection" block and appears as an image with edges in the "Video Viewer" block. For comparison, on other monitor is possible to see real image of the obstacle.

Canny edge detector Simulink model is created with the same blocks as in the previous case and with some new blocks (Fig. 5.). [20] Fixed-point input is not supported for Canny edge method in Simulink. "Gaussian Noise Generator" and "Median Filter" blocks are used. It is necessary to add noise to the image using a Gaussian noise generator in the order to test the model in noisy environment. "Median Filter" is used to reduce the effect on noise present in the image. [21] For Canny method, the "Edge Detection" block finds edges by looking for the local maxima of the gradient of the input image. It calculates the gradient using the derivative of the Gaussian filter. The Canny method uses two thresholds to detect strong and weak edges. It includes the weak edges in the output only if they are connected to strong edges. As a result, the method is more robust to noise, and more likely to detect true weak edges. [17], [21], [22]

4. Results

Results of edge detection of some characteristic obstacles are presented in this section. First of all, the Simulink models of Sobel, Prewitt, Roberts and Canny edge detector were tested with different parameters, under different lighting conditions, and thereafter edge detection was performed with the best configuration for each model. Sobel, Prewitt and Roberts Simulink model were tested with different values of "'Threshold scale factor" (TSF), which is used to automatically calculate threshold value. Threshold scale factor was combined with the option "Edge thinning" (ET). Values of the Threshold scale factor were from 1 to 4. Canny model was tested with different values of "Approximate percentage of weak edge and nonedge pixels" (APP), which is used to automatically calculate threshold value. Values of Approximate percentage of weak edge and nonedge pixels were from 70 to 99. Value of "Standard deviation of Gaussian filter" whole time of the testing was set to 1, because in the previous use of these tools it has been proved that this is the most appropriate value. Fig. 6. shows testing of all edge detecting methods on the example of detecting edges while the robot passes through the narrow passage between the wall and the desk.

After testing on different scenes, it is possible to notice that the following parameters are most suitable:

* Sobel, Prewitt and Roberts: TSF: 1 or 4plus ET

* Canny: APP: 95-97

Following images show detection of edges in the accordance with previously adopted parameters. These settings provide the best edge detection of the obstacles that Robotino encounters.

Analysing examples of the previous images it can be concluded that Sobel, Prewitt and Roberts produced thicker edges. Sobel, Prewitt and Roberts have shown simplicity in edge detection and their orientations, but Sobel gives some false edges in case when images have more details. However, they are quite sensitive to noises in the detection of the edges and their orientations, and have decreased accuracy as the gradient magnitude of the edges decreases. canny method gave the best results and provides sharpest and clearest obstacle edges, lines of edges are continuous and clear, and this is a very important feature in the application of edge detection method in the mobile robot navigation system. canny gives better results in case of noise conditions, and provides a thin lines using non-maximal suppression. use of the high threshold eliminates almost all the false edges. Canny edge detector algorithm is computationally more expensive compared to Sobel, Prewitt and Roberts. Also, main disadvantage is time consumption because of complex computation, and it is difficult to reach real time response. To improve real time response, these disadvantages will be compensated by using more powerful computer processing unit for mobile robot navigation system that will be implemented through this project. Finally, as confirmed in comparison with other studies referenced in this paper, Canny edge detector has the best results, Sobel and Prewitt mutually have very similar characteristics of the edges, Roberts has weakest results with the highest number of false edges.

It has been shown that the best settings for edge detection, compared to environmental conditions, are as follows:

* In the case of poor illumination, for Sobel, Prewitt and Roberts method, Threshold scale factor should have a lower value (in this simulation it is set to 1).

* When it comes to increased illumination, for the same methods, Threshold scale factor should have a higher value (in this simulation it is set to 4).

* Canny edge detector showed consistent results in both cases, whether it is a poor or increased illumination. The results are very similar, compared to lighting conditions, when the approximate percentage of weak edge and nonedge pixels is in the range 95-97.

5. Conclusion

This paper presents a Simulink models of Sobel, Prewitt, Roberts and the Canny edge detectors, used to compare the quality of edges applied on detection of obstacle edges in navigation system of mobile robot. For mobile robot navigation and detection of obstacles, it is very important that obstacles are visible, respectively, lines of edges must be clear without false edges. Since edge detection is the initial step in obstacles detection and recognition, it is very important to choose a method that will provide greatest number of correct data with least computational complexity. As shown through the examples in this paper, Canny edge detector has the best results and it is able to provide sharpest and clearest obstacle edges, with continuous and clear lines. Disadvantage of Canny method is computational complexities, so it is necessary that robot has a powerful computer system in order to detect obstacles in the real time. Future work will be focused on development of mobile robot navigation algorithm, which will be based on Canny edge detector.

DOI: 10.2507/27th.daaam.proceedings.035

6. References

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[18] N. H. Seng, "A comparison of various edge detection methods," Seberang Perai, 2013

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[22] J. K. Sahu, P. R. Mishra, P. K. Sethy, and S. Behera, "Edge detection of a still image using simulation and realtime implementation using TMS320C6713DSK," UGC Spons. Natl. Semin. Emerg. Trends Inf. Technol. Dev., no. March, 2014

Boris Crnokic, Snjezana Rezic, Slaven Pehar

University of Mostar, Faculty of Mechanical Engineering and Computing, Matice

hrvatske bb, 88000, Mostar, BiH

This Publication has to be referred as: Cmokic, B[oris]; Rezic, S[njezana] & Pehar, S[laven] (2016). Comparision of Edge Detection Methods for Obstacles Detection in a Mobile Robot Environment, Proceedings of the 27th DAAAM International Symposium, pp.0235-0244, B. Katalinic (Ed.), Published by DAAAM International, ISBN 978-3-902734-08-2, ISSN 1726-9679, Vienna, Austria

Caption: Fig. 1. Mobile robot Robotino 2 and VGA camera [13]

Caption: Fig. 2. Block diagram of Canny edge detector [19]

Caption: Fig. 3. Sobel edge detection Simulink model for Robotino

Caption: Fig. 4. Selection of methods for edge detection

Caption: Fig. 5. Canny edge detection Simulink model for Robotino

Caption: Fig. 6. Testing of edge detecting methods--Obstacle: passage between the wall and the desk; Room: poorly illuminated

Caption: Fig. 7. Edge detection--Obstacles: table and crosspiece; Room: moderately illuminated

Caption: Fig. 8. Edge detection--Obstacles: door, wall, doorstep; Room: very illuminated

Caption: Fig. 9. Edge detection--Obstacles: chair, closet, glass ashtray; Room: very illuminated

Caption: Fig. 10. Edge detection--Obstacles: upward stairs; Room: very illuminated

Caption: Fig. 11. Edge detection--obstacles: upward stairs; Room: moderately illuminated

Table 1. Technical specificatios of VGA camera [13]

Technical Specifications

Image Sensor           Colour VGA CMOS

Colour Depth           24 Bit True Colour

PC-connection          USB 2.0 (compatible with USB 1.1)

Video resolutions      320 x 240, (QVGA), 30 images/second
                       640 x 480, (VGA), 30 images/second

                       Robotino View can process this resolution
                       800 x 600(SVGA, software-interpolated),
                         30 images/second

Still image            640 x 480 (VGA)
resolutions            800 x 600(SVGA)
                       1024 x 768 (SXGA, software-interpolated)

Still capture          BMP, JPG
format