The results obtained by a single pass through an image of some 2-D kernels can be achieved also by two passes using 1-D kernels. For example, the same result of using a 3 x 3 smoothing kernel with coefficients 1/9 can be obtained by a pass of the kernel [11 1] through an image, followed by a pass of the result with the kernel [11 1'. The final result is then scaled by 1/9. Show that the response of Sobel kernels (Fig. 10.14) can be implemented similarly by one pass of the differencing kernel [-1 0 1] (or its vertical coun- terpart) followed by the smoothing kernel [1 2 1] (or its vertical counterpart).
The results obtained by a single pass through an image of some 2-D kernels can be achieved also by two passes using 1-D kernels. For example, the same result of using a 3 x 3 smoothing kernel with coefficients 1/9 can be obtained by a pass of the kernel [11 1] through an image, followed by a pass of the result with the kernel [11 1'. The final result is then scaled by 1/9. Show that the response of Sobel kernels (Fig. 10.14) can be implemented similarly by one pass of the differencing kernel [-1 0 1] (or its vertical coun- terpart) followed by the smoothing kernel [1 2 1] (or its vertical counterpart).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![10.14)
The results obtained by a single pass through an
image of some 2-D kernels can be achieved also
by two passes using 1-D kernels. For example,
the same result of using a 3 x 3 smoothing kernel
with coefficients 1/9 can be obtained by a pass
of the kernel [1 1 1] through an image, followed
by a pass of the result with the kernel [1 1 1]'.
The final result is then scaled by 1/9. Show that
the response of Sobel kernels (Fig. 10.14) can
be implemented similarly by one pass of the
differencing kernel [-1 0 1] (or its vertical coun-
terpart) followed by the smoothing kernel [1 2 1]
(or its vertical counterpart).
Fig. 10.14)
a
b c
de
f g
**
Roberts
-1
1-
Prewitt
--
-2
-2
21
1.
2.
--1
Sobel](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe09358e-0876-4919-81c1-67cd5ad8f5f7%2Fd2b8696b-eea8-4a9c-af2c-c08370d8883a%2Ff962fqj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10.14)
The results obtained by a single pass through an
image of some 2-D kernels can be achieved also
by two passes using 1-D kernels. For example,
the same result of using a 3 x 3 smoothing kernel
with coefficients 1/9 can be obtained by a pass
of the kernel [1 1 1] through an image, followed
by a pass of the result with the kernel [1 1 1]'.
The final result is then scaled by 1/9. Show that
the response of Sobel kernels (Fig. 10.14) can
be implemented similarly by one pass of the
differencing kernel [-1 0 1] (or its vertical coun-
terpart) followed by the smoothing kernel [1 2 1]
(or its vertical counterpart).
Fig. 10.14)
a
b c
de
f g
**
Roberts
-1
1-
Prewitt
--
-2
-2
21
1.
2.
--1
Sobel
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