This is an improved Sobel operator mainly used in edge detection. It uses 3×3 convolution matrix to compute the gradient in the x-direction (\\(G_x\\)) and y-direction (\\(G_y\\)):
\n\\[
\nG_x =
\n\\begin{bmatrix}
\n-1 & 0 & 1\\\\
\n-\\sqrt 2 & 0 & \\sqrt 2 \\\\
\n-1 & 0 & 1
\n\\end{bmatrix} * A
\n~~~~~~~~~~~~
\nG_y =
\n\\begin{bmatrix}
\n-1 & -\\sqrt 2 & -1\\\\
\n0 & 0 & 0 \\\\
\n1 & \\sqrt 2 & 1
\n\\end{bmatrix} * A
\n\\]<\/p>\n
As with the gradient vector \\( (G_x,\u00a0 G_y) \\), we can compute the absolute magnitude of the gradient using:<\/p>\n
\\[
\nG = \\sqrt{G_x^2 + G_y^2}
\n\\]<\/p>\n
For example,\u00a0 if A is the input image<\/p>\n
\\[
\nA =
\n\\begin{bmatrix}
\nP_1 & P_2 & P_3\\\\
\nP_4 &\u00a0P_5 &\u00a0P_6 \\\\
\nP_7 &\u00a0P_8 &\u00a0P_9
\n\\end{bmatrix}
\n\\]<\/p>\n
We can calculate the gradient vector components<\/span>:<\/p>\n \\[ <\/p>\n","protected":false},"excerpt":{"rendered":" This is an improved Sobel operator mainly used in edge detection. It uses 3×3 convolution matrix to compute the gradient in the x-direction (\\(G_x\\)) and y-direction (\\(G_y\\)): \\[ G_x = \\begin{bmatrix} -1 & 0 & 1\\\\ -\\sqrt 2 & 0 & \\sqrt 2 \\\\ -1 & 0 & 1 \\end{bmatrix} * A ~~~~~~~~~~~~ G_y = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-428","post","type-post","status-publish","format-standard","hentry","category-graphics"],"_links":{"self":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts\/428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/comments?post=428"}],"version-history":[{"count":0,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts\/428\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/media?parent=428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/categories?post=428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/tags?post=428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nG_x = P_3 –\u00a0P_1 + \\sqrt{2}(P_6 – P_4) +\u00a0P_9 –\u00a0P_7 \\\\
\nG_y = P_7 – P_1 + \\sqrt{2}(P_8 – P_2) + P_9 – P_3
\n\\]<\/p>\n