Digital Signal Processing Reference
In-Depth Information
2.
EXTRACTION USING THE HOUGH
TRASNFORM
2.1
Hough Transform
The Hough transform is a technique to robustly extract parametric patterns,
such as lines, circles, and ellipses, from a noisy image[3].
The Hough transform method to extract a significant line from an image on
the
plane can be formulated as follows. Suppose the image consists of
pixels at
Every pixel on the
plane is transformed to
a line on the
plane as
A brightness value of the pixel on the plane is accumulated at every
point on the line. This process is called “voting” to the plane. After voting
for all the pixels, the maximum accumulated voting value on the
plane is
detected, and the peak point
is transformed to a line on the
plane by
the following equation:
2.2 Extraction Using the Hough Transform
Cepstral peaks extracted independently for each short period of speech have
been widely used to extract values. This method often causes errors, includ-
ing half pitch, double pitch and drop outs, for noisy speech. Since contours
have temporal continuity in voiced periods, the Hough transform, taking ad-
vantage of its continuity, applied to time-cepstrum images is expected to have
robustness in extracting pitch in the noisy environment.
Speech waveforms are sampled at 16kHz and transformed to 256 dimensional
cepstra. A 32ms-long Hamming window is used to extract frames every 10ms.
For reducing noise effects of a high frequency domain, we extract and use time-
cepstrum images which are limited to 60~256 dimensions and liftered accord-
ing to the following formula:
where is the original cepstrum and is the liftered cepstrum.
To the liftered time-cepstrum image, a nine-frame moving window is applied
at every frame interval to extract an image for line information detection. The
time-cepstrum image is used as the pixel brightness image for the Hough trans-
form. An
value is obtained from a cepstrum index of the center point for the
