Harris Corners

Detailed Description

Computes the Harris Corners of an image.

The Harris Corners are computed with several parameters

\begin{eqnarray} I &=& \text{input image} \\ T_c &=& \text{corner strength threshold} \\ r &=& \text{euclidean radius} \\ k &=& \text{sensitivity threshold} \\ w &=& \text{window size} \\ b &=& \text{block size} \\ \end{eqnarray}

The computation to find the corner values or scores can be summarized as [R00060]:

\begin{eqnarray} G_x &=& Sobel_x(w, I) \\ G_y &=& Sobel_y(w, I) \\ A &=& window_{G_{x,y}}(x-b/2,y-b/2,x+b/2,y+b/2) \\ trace(A) &=& \sum^{A}{G_x^{2}} + \sum^{A}{G_y^{2}} \\ det(A) &=& \sum^{A}{G_x^{2}} \sum^{A}{G_y^{2}} - {\left(\sum^{A}{(G_x G_y)}\right)}^{2} \\ M_c(x,y) &=& det(A) - k*trace(A)^{2} \\ V_c(x,y) &=& \begin{cases} M_c(x,y) \text{ if } M_c(x,y) > T_c \\ 0 \text{ otherwise} \\ \end{cases} \end{eqnarray}

\[ \text{where } V_c \text{ is the thresholded corner value}. \]

The normalized Sobel kernels used for the gradient computation shall be as shown below:

• For gradient size 3 [R00061]:

  \[ \mathbf{Sobel}_{x}(Normalized)= \frac{1}{4*255*b}* \begin{vmatrix} -1 & 0 & 1\\ -2 & 0 & 2\\ -1 & 0 & 1 \end{vmatrix} \]

  \[ \mathbf{Sobel}_{y}(Normalized)= \frac{1}{4*255*b}*transpose({sobel}_{x})= \frac{1}{4*255*b}* \begin{vmatrix} -1 & -2 & -1\\ 0 & 0 & 0\\ 1 & 2 & 1 \end{vmatrix} \]

• For gradient size 5 [R00062]:

  \[ \mathbf{Sobel}_{x}(Normalized)= \frac{1}{16*255*b}* \begin{vmatrix} -1 & -2 & 0 & 2 & 1\\ -4 & -8 & 0 & 8 & 4\\ -6 & -12 & 0 & 12 & 6\\ -4 & -8 & 0 & 8 & 4\\ -1 & -2 & 0 & 2 & 1\\ \end{vmatrix} \]

\[ \mathbf{Sobel}_{y}(Normalized)= \frac{1}{16*255*b}*transpose({sobel}_{x}) \]

• For gradient size 7 [R00063]:

  \[ \mathbf{Sobel}_{x}(Normalized)= \frac{1}{64*255*b}* \begin{vmatrix} -1 & -4 & -5 & 0 & 5 & 4 & 1\\ -6 & -24 & -30 & 0 & 30 & 24 & 6\\ -15 & -60 & -75 & 0 & 75 & 60 & 15\\ -20 & -80 & -100 & 0 & 100 & 80 & 20\\ -15 & -60 & -75 & 0 & 75 & 60 & 15\\ -6 & -24 & -30 & 0 & 30 & 24 & 6\\ -1 & -4 & -5 & 0 & 5 & 4 & 1\\ \end{vmatrix} \]

\[ \mathbf{Sobel}_{y}(Normalized)= \frac{1}{64*255*b}*transpose({sobel}_{x}) \]

\( V_c \) is then non-maximally suppressed, returning the same results as using the following algorithm [R00064]:

• Filter the features using the non-maximum suppression algorithm defined for vxFastCornersNode.
• Create an array of features sorted by \( V_c \) in descending order: \(V_c(j) > V_c(j+1)\).
• Initialize an empty feature set \(F = \{\}\)
• For each feature \(j\) in the sorted array, while \(V_c(j) > T_c\):
  • If there is no feature i in \(F\) such that the Euclidean distance between pixels i and j is less than \(r\), add the feature \(j\) to the feature set \(F\).

An implementation shall support all values of Euclidean distance \( r \) that satisfy [R00065]:

 0 <= max_dist <= 30 

The feature set \(F\) is returned as a vx_array of vx_keypoint_t structs.

Functions
vx_node VX_API_CALL	vxHarrisCornersNode (vx_graph graph, vx_image input, vx_scalar strength_thresh, vx_scalar min_distance, vx_scalar sensitivity, vx_int32 gradient_size, vx_int32 block_size, vx_array corners, vx_scalar num_corners)
	[Graph] Creates a Harris Corners Node. More...

Function Documentation

vxHarrisCornersNode()

vx_node VX_API_CALL vxHarrisCornersNode	(	vx_graph	graph,
		vx_image	input,
		vx_scalar	strength_thresh,
		vx_scalar	min_distance,
		vx_scalar	sensitivity,
		vx_int32	gradient_size,
		vx_int32	block_size,
		vx_array	corners,
		vx_scalar	num_corners
	)

[Graph] Creates a Harris Corners Node.

Parameters

[in]	graph	The reference to the graph [R00357].
[in]	input	The input VX_DF_IMAGE_U8 image [R00358].
[in]	strength_thresh	The VX_TYPE_FLOAT32 minimum threshold with which to eliminate Harris Corner scores (computed using the normalized Sobel kernel) [R00359].
[in]	min_distance	The VX_TYPE_FLOAT32 radial Euclidean distance for non-maximum suppression [R00360].
[in]	sensitivity	The VX_TYPE_FLOAT32 scalar sensitivity threshold \( k \) from the Harris-Stephens equation [R00361].
[in]	gradient_size	The gradient window size to use on the input [R00362]. The implementation must support at least 3, 5, and 7.
[in]	block_size	The block window size used to compute the Harris Corner score [R00363]. The implementation must support at least 3, 5, and 7.
[out]	corners	The array of VX_TYPE_KEYPOINT objects [R00364]. The order of the keypoints in this array is implementation dependent.
[out]	num_corners	The total number of detected corners in image [R00365](optional). Use a VX_TYPE_SIZE scalar [R00366].

Returns

vx_node [R00367].

Return values

vx_node

A node reference. Any possible errors preventing a successful creation should be checked using vxGetStatus