Corner Detection

Calculate corner metric matrix and find corners in images

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Libraries:
Computer Vision Toolbox / Analysis & Enhancement

Description

The Corner Detection block finds corners in an image by using the Harris corner detection (by Harris and Stephens), minimum eigenvalue (by Shi and Tomasi), or local intensity comparison (based on the Accelerated Segment Test, (FAST) method by Rosten and Drummond) method. The block finds the corners in the image based on the pixels that have the largest corner metric values.

Examples

Detect Corners in Image

Detect corners in an image using the Corner Detection block.

• Open Model

Ports

Input

I — Input image

matrix of intensity values

Input image, specified as a matrix of intensity values.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Output

Loc — Corner locations

M-by-2 matrix

Corner locations, returned as an M-by-2 matrix of [x y] coordinates. M represents the number of corners and is less than or equal to the Maximum number of corners parameter.

Dependencies

To enable this port, set the Output parameter to one of these:

• Corner location

• Corner location and metric matrix

Data Types: uint32

Count — Number of detected corners

scalar

Number of detected corners, returned as a scalar.

Dependencies

To enable this port, set these block parameters:

• Output: Corner location | Corner location and metric matrix

• Output variable size signal: off

Data Types: uint32

Metric — Corner metric values

matrix

Corner metric values, returned as a matrix of intensity values. The returned matrix is the same size as the input image.

Dependencies

To enable this port, set the Output parameter to one of these:

• Corner location and metric matrix

• Metric matrix

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Parameters

Main

Method — Corner detection method

Harris corner detection (Harris & Stephens) (default) | Minimum eigenvalue (Shi & Tomasi) | Local intensity comparison (Rosten & Drummond)

Specify the corner detection method as Harris corner detection (Harris & Stephens), Minimum eigenvalue (Shi & Tomasi), or Local intensity comparison (Rosten & Drummond).

To get the most accurate results, use Minimum eigenvalue (Shi & Tomasi). For the fastest computation, use Local intensity comparison (Rosten & Drummond). For a balance between accuracy and computation speed, use Harris corner detection (Harris & Stephens). For more information on each method, see the Algorithms section.

Sensitivity factor (0<k<0.25) — Sensitivity factor

0.04 (default) | scalar

Specify the sensitivity factor, k. As k decreases, the likelihood that the algorithm can detect sharp corners increases.

Tunable: Yes

Dependencies

To enable this parameter, set the Method parameter to Harris corner detection (Harris & Stephens).

Coefficients for separable smoothing filter — Filter coefficients

fspecial('gaussian', [1 5], 1.5) (default) | vector

Specify a vector of filter coefficients for the smoothing filter.

Dependencies

To enable this parameter, set the Method parameter to one of these:

• Harris corner detection (Harris & Stephens)

• Minimum eigenvalue (Shi & Tomasi)

Intensity comparison threshold — Intensity threshold

0.1 (default) | scalar

Specify the intensity threshold value used to find valid surrounding pixels.

Tunable: Yes

Dependencies

To enable this parameter, set the Method parameter to Local intensity comparison (Rosten & Drummond).

Maximum angle to be considered a corner (in degrees) — Maximum corner angle

157.5 (default) | scalar

Specify the maximum corner angle.

Tunable: Yes

Dependencies

• To enable this parameter, set the Method parameter to Local intensity comparison (Rosten & Drummond).

• This parameter is tunable for simulation only.

Output — Block output

Corner location (default) | Corner location and metric matrix | Metric matrix

Specify the block output as Corner location, Corner location and metric matrix, and Metric matrix.

Set this parameter to Corner location or Corner location and metric matrix to expose the Maximum number of corners, Minimum metric value that indicates a corner, and Neighborhood size (suppress region around detected corners) parameters.

Maximum number of corners — Maximum number of corners

200 (default) | integer

Specify the maximum number of corners you want the block to find.

Dependencies

To enable this parameter, set the Output parameter to one of these:

• Corner location

• Corner location and metric matrix

Minimum metric value that indicates a corner — Minimum corner metric

0.0005 (default) | scalar

Specify the minimum corner metric value.

Tunable: Yes

Dependencies

To enable this parameter, set the Output parameter to one of these:

• Corner location

• Corner location and metric matrix

Neighborhood size — Neighborhood size

[11 11] (default) | 2-element vector

Specify the neighborhood size as a two-element vector of positive odd integers, [row, column]. The block uses this parameter to suppress the region around a valid corner point with the largest corner metric value.

Dependencies

To enable this parameter, set the Output parameter to one of these:

• Corner location

• Corner location and metric matrix

Output variable size signal — Variable size signal

on (default) | off

Select this parameter to output a variable size signal.

Dependencies

To enable this parameter, set the Output parameter to one of these:

• Corner location

• Corner location and metric matrix

Data Types

For details on the fixed-point block parameters, see Specify Fixed-Point Attributes for Blocks (DSP System Toolbox).

Lock data type settings against change by the fixed-point tools — Data type override

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in this block. For more information, see Lock the Output Data Type Setting (Fixed-Point Designer).

Block Characteristics

Data Types	Booleana | double | fixed point | integer | single
Multidimensional Signals	no
Variable-Size Signals	yes
a This data type is not supported for the Local Intensity Comparison method.

More About

These diagrams show the data types used in the Corner Detection block for fixed-point signals. These diagrams apply to the Harris corner detection and minimum eigenvalue methods only.

The following table summarizes the variables used in the previous diagrams.

Variable Name	Definition
IN_DT	Input data type
MEM_DT	Memory data type
OUT_DT	Metric output data type
COEF_DT	Coefficients data type

Algorithms

Determine final corner values

To determine the final corner values, the block follows this process:

1. Find the pixel with the largest corner metric value.

2. Verify that the metric value is greater than or equal to the value you specified for the Minimum metric value that indicates a corner parameter.

3. Suppress the region around the corner value by the size defined in the Neighborhood size (suppress region around detected corners) parameter.

The block repeats this process until it finds all the corners in the image or it finds the number of corners you specified in the Maximum number of corners parameter.

The corner metric values computed by the Minimum eigenvalue and Local intensity comparison methods are always nonnegative. The corner metric values computed by the Harris corner detection method can be negative.

Minimum Eigenvalue Method

The method is more computationally expensive than the Harris corner detection algorithm because it directly calculates the eigenvalues of the sum of the squared difference matrix, M.

The sum of the squared difference matrix, M, is defined as follows:

$$M=\left[\begin{array}{cc}A& C\\ C& B\end{array}\right]$$

The previous equation is based on the following values:

$$\begin{array}{c}A={(I_x)}^2\otimes w\\ B={(I_y)}^2\otimes w\\ C={(I_x{I}_y)}^2\otimes w\end{array}$$

where $$I_x$$ and $$I_y$$ are the gradients of the input image, I, in the x and y direction. The $$\otimes$$ symbol denotes a convolution operation.

Use the Coefficients for separable smoothing filter parameter to define a vector of filter coefficients. The block multiplies this vector of coefficients by its transpose to create a matrix of filter coefficients, w.

The block calculates the smaller eigenvalue of the sum of the squared difference matrix. This minimum eigenvalue corresponds to the corner metric matrix.

Harris Corner Method

The Harris corner detection method avoids the explicit computation of the eigenvalues of the sum of squared differences matrix by solving for the corner metric matrix, R:

$$R=AB-C^2-k{(A+B)}^2$$

See the Minimum Eigenvalue Method section for the definitions of A, B, and C.

The variable k corresponds to the sensitivity factor. You can specify its value using the Sensitivity factor (0<k<0.25) parameter. As k decreases, the likelihood that the algorithm can detect sharp corners increases.

Use the Coefficients for separable smoothing filter parameter to define a vector of filter coefficients. The block multiplies this vector of coefficients by its transpose to create a matrix of filter coefficients, w.

Local Intensity Method

The method determines that a pixel is a possible corner if it has either, N contiguous valid bright surrounding pixels, or N contiguous dark surrounding pixels.

Suppose that p is the pixel under consideration and j is one of the pixels surrounding p. The locations of the other surrounding pixels are denoted by the shaded areas in the following figure. The shaded areas in this figure denote the locations of other surrounding pixels.

$$I_p$$ and $$I_j$$ are the intensities of pixels p and j, respectively. Pixel j is a valid bright surrounding pixel if $$I_j-I_p\ge T$$. Similarly, pixel j is a valid dark surrounding pixel if $$I_p-I_j\ge T$$. In these equations, T is the value you specified for the Intensity comparison threshold parameter.

The block repeats this process to determine whether the block has N contiguous valid surrounding pixels. The value of N is related to the value you specify for the Maximum angle to be considered a corner (in degrees) parameter, as shown in this table.

Number of Valid Surrounding Pixels and Angle

Number of Valid Surrounding Pixels	Angle (degrees)
15	22.5
14	45
13	67.5
12	90
11	112.5
10	135
9	157.5

After the block determines that a pixel is a possible corner, it computes its corner metric using the following equation:

$$R=\max \left({\displaystyle \sum _{j:I_j\ge I_p+T}\left|I_p-I_j\right|-T,{\displaystyle \sum _{j:I_j\le I_p-T}\left|I_p-I_j\right|-T}}\right)$$

References

[1] Harris, C. and M Stephens. “A Combined Corner and Edge Detector.” Proceedings of the 4th Alvey Vision Conference, 147-151. August 1988.

[2] Shi, J. and C. Tomasi. “Good Features to Track.” Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 593-600. June 1994.

[3] Rosten, E. and T. Drummond. “Fusing Points and Lines for High Performance Tracking.” Proceedings of the IEEE International Conference on Computer Vision Vol. 2, 1508-1511. October 2005.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2007b