Thank you Dr. Dafda, for the image-processing videos, would you please continue lossy image compression techniques such as vector quantization, fractal, etc.
Yes, the conversion of scales to frequencies in Hz in wavelet transform involves some mathematical relationships. In wavelet analysis, the scale parameter s is related to frequency (f) by the following formula: f=1/s This means that as the scale increases, the frequency decreases, and vice versa. The scale parameter is essentially inversely proportional to the frequency. This relationship is derived from the wavelet transform equation, where s is the scale parameter, and ψ(t) is the mother wavelet function: Wavelet Transform=∫-∞ to ∞ x(t)⋅ψ∗((t−τ)/s )dt. Here, s is the scale, and f is the frequency. The relationship f=1/s, helps understand how the scale parameter influences the frequency content of the wavelet. As for the frequency content of the wavelet itself, it depends on the specific wavelet function being used. Different wavelet functions have different frequency characteristics. For example, in the case of the Morlet wavelet often used in continuous wavelet transform (CWT), it is a complex sinusoidal wave modulated by a Gaussian envelope. The frequency content of the Morlet wavelet is related to the central frequency of the sinusoidal component. In summary, the relationship between scale and frequency in wavelet transform is f=1/s , and the frequency content of the wavelet is determined by the specific form of the wavelet function being used.
Can you please explain, how LL gives Approximation, LH gives Vertical details, HL gives Horizontal details and HH gives Diagnol ....? Like why LH is not give Horizontal or diagonal??
In wavelet-based image compression, the LL, LH, HL, and HH refer to the subbands obtained after applying a wavelet transform to an image. These subbands represent different types of information present in the image. LL (Low-Low) Subband: The LL subband contains the approximation or low-frequency components of the image. It represents the coarse details and overall structure of the image. LH (Low-High) Subband: The LH subband contains the horizontal details of the image. It represents the high-frequency components in the horizontal direction. This subband captures the information related to edges and transitions that occur horizontally in the image. HL (High-Low) Subband: The HL subband contains the vertical details of the image. It represents the high-frequency components in the vertical direction. This subband captures the information related to edges and transitions that occur vertically in the image. HH (High-High) Subband: The HH subband contains the diagonal details of the image. It represents the high-frequency components in both the horizontal and vertical directions. This subband captures the information related to diagonal edges and transitions in the image. The reason why LH represents horizontal details instead of horizontal or diagonal details is due to the way the wavelet transform is defined. The wavelet basis functions used in the transform have specific characteristics that separate the frequency content in different directions. The LH subband captures the high-frequency information in the horizontal direction, while the HL subband captures the high-frequency information in the vertical direction. The HH subband captures the high-frequency information in both the horizontal and vertical directions, resulting in diagonal details. Therefore, LH is used to represent the horizontal details in wavelet-based image compression.
Thank you Dr. Dafda, for the image-processing videos, would you please continue lossy image compression techniques such as vector quantization, fractal, etc.
Hi, is there a clear approach to convert the scales to the frequency in Hz? what is/are the frequency content of the wavelet itself?
Yes, the conversion of scales to frequencies in Hz in wavelet transform involves some mathematical relationships. In wavelet analysis, the scale parameter
s is related to frequency (f) by the following formula:
f=1/s
This means that as the scale increases, the frequency decreases, and vice versa. The scale parameter is essentially inversely proportional to the frequency. This relationship is derived from the wavelet transform equation, where s is the scale parameter, and ψ(t) is the mother wavelet function:
Wavelet Transform=∫-∞ to ∞ x(t)⋅ψ∗((t−τ)/s )dt. Here, s is the scale, and f is the frequency. The relationship f=1/s, helps understand how the scale parameter influences the frequency content of the wavelet.
As for the frequency content of the wavelet itself, it depends on the specific wavelet function being used. Different wavelet functions have different frequency characteristics. For example, in the case of the Morlet wavelet often used in continuous wavelet transform (CWT), it is a complex sinusoidal wave modulated by a Gaussian envelope. The frequency content of the Morlet wavelet is related to the central frequency of the sinusoidal component.
In summary, the relationship between scale and frequency in wavelet transform is f=1/s , and the frequency content of the wavelet is determined by the specific form of the wavelet function being used.
Can you please explain, how LL gives Approximation, LH gives Vertical details, HL gives Horizontal details and HH gives Diagnol ....? Like why LH is not give Horizontal or diagonal??
In wavelet-based image compression, the LL, LH, HL, and HH refer to the subbands obtained after applying a wavelet transform to an image. These subbands represent different types of information present in the image.
LL (Low-Low) Subband: The LL subband contains the approximation or low-frequency components of the image. It represents the coarse details and overall structure of the image.
LH (Low-High) Subband: The LH subband contains the horizontal details of the image. It represents the high-frequency components in the horizontal direction. This subband captures the information related to edges and transitions that occur horizontally in the image.
HL (High-Low) Subband: The HL subband contains the vertical details of the image. It represents the high-frequency components in the vertical direction. This subband captures the information related to edges and transitions that occur vertically in the image.
HH (High-High) Subband: The HH subband contains the diagonal details of the image. It represents the high-frequency components in both the horizontal and vertical directions. This subband captures the information related to diagonal edges and transitions in the image.
The reason why LH represents horizontal details instead of horizontal or diagonal details is due to the way the wavelet transform is defined. The wavelet basis functions used in the transform have specific characteristics that separate the frequency content in different directions. The LH subband captures the high-frequency information in the horizontal direction, while the HL subband captures the high-frequency information in the vertical direction. The HH subband captures the high-frequency information in both the horizontal and vertical directions, resulting in diagonal details. Therefore, LH is used to represent the horizontal details in wavelet-based image compression.
ua-cam.com/video/T0Zhgc4BZl8/v-deo.html