# Hough Transform

Find lines in images

## Library

Transforms

`visiontransforms`

## Description

Use the Hough Transform block to find straight lines in an image. The block outputs
the Hough space matrix and, optionally, the *rho*-axis and
*theta*-axis vectors. Peak values in the matrix represent
potential straight lines in the input image. Generally, the Hough
Transform block precedes the Hough Lines block which uses the
output of this block to find straight lines in an image. You can instead use a custom
algorithm to locate peaks in the Hough space matrix in order to identify potential
straight lines.

Port | Input/Output | Supported Data Types | Supported Complex Values |
---|---|---|---|

BW | Matrix that represents a binary image | Boolean | No |

Hough | Parameter space matrix |
Double-precision floating point Single-precision floating point Fixed point (unsigned, fraction length equal to 0) 8-, 16-, 32-bit unsigned integer
| No |

Theta | Vector of theta values |
Double-precision floating point Single-precision floating point Fixed point (signed) 8-, 16-, 32-bit signed integer
| No |

Rho | Vector of rho values | Same as Theta port | No |

## Parameters

**Theta resolution (radians)**Specify the spacing of the Hough transform bins along the

*theta*-axis.**Rho resolution (pixels)**Specify the spacing of the Hough transform bins along the

*rho*-axis.**Output theta and rho values**If you select this check box, the

**Theta**and**Rho**ports appear on the block. The block outputs theta and rho-axis vector values at these ports.**Output data type**Specify the data type of your output signal.

**Rounding mode**Select the rounding mode for fixed-point operations.

**Overflow mode**Select the overflow mode for fixed-point operations.

**Sine table**Choose how to specify the word length of the values of the sine table:

When you select

`Binary point scaling`

, you can enter the word length of the sine table values, in bits.When you select

`Slope and bias scaling`

, you can enter the word length of the sine table values, in bits.

The sine table values do not obey the

**Rounding mode**and**Overflow mode**parameters; they always saturate and round to`Nearest`

.**Rho**Choose how to specify the word length and the fraction length of the rho values:

When you select

`Binary point scaling`

, you can enter the word length and the fraction length of the rho values, in bits.When you select

`Slope and bias scaling`

, you can enter the word length, in bits, and the slope of the rho values. All signals in Computer Vision Toolbox™ blocks have a bias of 0.

**Product output**. Use this parameter to specify how to designate the product output word and fraction lengths:

When you select

`Binary point scaling`

, you can enter the word length and the fraction length of the product output, in bits.When you select

`Slope and bias scaling`

, you can enter the word length, in bits, and the slope of the product output. All signals in Computer Vision Toolbox blocks have a bias of 0.

See Multiplication Data Types for illustrations depicting the use of the product output.

**Accumulator**Use this parameter to specify how to designate this accumulator word and fraction lengths:

When you select

`Same as product output`

, these characteristics match the characteristics of the product output.When you select

`Binary point scaling`

, you can enter the word length and the fraction length of the accumulator, in bits.When you select

`Slope and bias scaling`

, you can enter the word length, in bits, and the slope of the accumulator. All signals in Computer Vision Toolbox blocks have a bias of 0.See Multiplication Data Types for illustrations depicting the use of the accumulator data type in this block.

**Lock data type settings against change by the fixed-point tools**Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see

`fxptdlg`

(Fixed-Point Designer), a reference page on the Fixed-Point Tool in the Simulink^{®}documentation.**Hough output**Choose how to specify the word length and fraction length of the Hough output of the block:

When you select

`Binary point scaling`

, you can enter the word length of the Hough output, in bits. The fraction length always has a value of 0.When you select

`Slope and bias scaling`

, you can enter the word length, in bits, of the Hough output. The slope always has a value of 0. All signals in Computer Vision Toolbox blocks have a bias of 0.

**Theta output**Choose how to specify the word length and fraction length of the theta output of the block:

When you select

`Binary point scaling`

, you can enter the word length and the fraction length of the theta output, in bits.When you select

`Slope and bias scaling`

, you can enter the word length, in bits, and the slope of the theta output. All signals in Computer Vision Toolbox blocks have a bias of 0.

## Algorithm

The Hough Transform block implements the Standard Hough Transform (SHT). The SHT uses the parametric representation of a line:

The upper-left corner pixel is assumed to be at x=0,y=0.

The variable *rho* indicates the perpendicular distance from the
origin to the line.

The variable *theta* indicates the angle of inclination of the
normal line from the x-axis. The range of *theta* is $$-\frac{\pi}{2}\le \theta <+\frac{\pi}{2}$$ with a step-size determined by the **Theta resolution
(radians)** parameter. The SHT measures the angle of the line clockwise
with respect to the positive x-axis.

The Hough Transform block creates an accumulator matrix. The
(*rho, theta*) pair represent the location of a cell in the
accumulator matrix. Every valid (logical true) pixel of the input binary image
represented by (*R,C*) produces a rho value for all theta values. The
block quantizes the rho values to the nearest number in the rho vector. The rho vector
depends on the size of the input image and the user-specified rho resolution. The block
increments a counter (initially set to zero) in those accumulator array cells
represented by (*rho, theta*) pairs found for each pixel. This
process validates the point (*R,C*) to be on the line defined by
(*rho, theta*). The block repeats this process for each logical
true pixel in the image. The **Hough** block outputs the resulting
accumulator matrix.

## See Also

Computer Vision Toolbox | |

Computer Vision Toolbox | |

Image Processing Toolbox™ | |

Image Processing Toolbox | |

Image Processing Toolbox |

## Extended Capabilities

## Version History

**Introduced before R2006a**