The location of this LandSat Imagery is in San Francisco. First, the LandSAT imagery was visualized using an online repository where the LandSAT imagery has been published. Data collected from (USGS, n.d.)
Figure 1 displays Band 4 of the LandSAT 7 imagery, which corresponds to the Red band in the visible spectrum. When visualized, this image displays the intensity of the reflectance in the red wavelength for each pixel of the image.
What does the Visualization Represent?
Grayscale Image: The image that has been generated will be a grayscale representation of the Red band. Higher pixel values (lighter areas) represent stronger reflectance in the red portion of the spectrum, while lower values (darker areas) represent weaker reflectance.
Single Spectral Band: This is a single-band image representing reflectance in a narrow range of the red wavelength (Band 4, wavelength ~0.63-0.69µm)
Reflectance: The pixel values indicate the amount of light n the red spectrum being reflected by the Earth's surface. Vegetation, for example, tends to reflect more in the near-infrared (NIR) than in the red band, but some vegetation may still have moderate reflectance in red.
How Band 4 (Red) is Typically Used:
Vegetation Studies: In combination with the NIR band, the red band is utilized to compute indices such as the NDVI(Normalized Difference Vegetation Index), which assists in analyzing vegetation health.
Urban and Soil Studies: Urban areas, bare soil, and built-up zones usually reflect more red light than vegetated areas, so they tend to appear brighter in the red band.
Figure 1 - Red Band in GreyScale
Next, the LandSat imagery was classified in PCA, which is the Principal Component Analysis (PCA).
What is Principal Component Analysis?
Principal Component Analysis (PCA) is a dimensionality reduction technique used to reduce the number of variables in a dataset while retaining as much variability (or information) as possible. It does this by transforming the data into a new coordinate system where the new axes (called principal components) are ordered by the amount of variance they capture from the original dataset.
PCA is widely used in fields like machine learning, statistics, and remote sensing (e.g., LandSAT imagery analysis) because it helps simplify complex datasets by identifying patterns and reducing noise, making them easier to analyze.
Key Concepts in PCA
Variance:
In PCA, the goal is to maximize the variance explained by the new axes (principal components). Variance represents how much the data is spread out, and capturing this variance is key to retaining important information from the original dataset.
Principal Components:
Principal Components (PCs) are new axes that are linear combinations of the original variables (e.g., spectral bands in remote sensing). The first principal component explains the most variance, the second explains the next most, and so on.
Each principal component is orthogonal (perpendicular) to the others, meaning they are uncorrelated and represent different aspects of the variance in the data.
Dimensionality Reduction:
By transforming data into fewer principal components, PCA reduces the number of dimensions (or variables) in the dataset while still preserving most of the important information. For example, instead of analyzing 10 variables, you may only need 2 or 3 principal components to capture most of the variance.
Eigenvalues and Eigenvectors:
Eigenvalues represent the amount of variance captured by each principal component.
Eigenvectors define the direction of the principal components in the new coordinate system. They are linear combinations of the original variables and help identify how the original features contribute to the principal components.
Steps in PCA:
Standardize the Data:
PCA works best when the data is standardized (mean of 0 and variance of 1 for each variable) to ensure that all features contribute equally.
Compute the Covariance Matrix:
The covariance matrix describes how each variable varies with the others. It is used to measure relationships between the different features.
Calculate Eigenvalues and Eigenvectors:
Eigenvalues tell us how much variance each principal component captures.
Eigenvectors give the direction of the principal components.
Sort the Principal Components:
Principal components are sorted based on the eigenvalues. The first principal component captures the most variance, the second captures the next most, and so on.
Transform the Data:
The original data is projected onto the new principal component axes, resulting in a lower-dimensional dataset that still captures most of the variance from the original dataset.
Applications of PCA:
Dimensionality Reduction:
In high-dimensional datasets, PCA helps reduce the number of variables, simplifying the analysis and making it computationally less expensive while retaining the most important information.
Data Visualization:
PCA is often used to visualize high-dimensional data by projecting it into 2D or 3D spaces, allowing for easier exploration of patterns, clusters, and outliers.
Noise Reduction:
By capturing the most important components and ignoring those that contribute little variance (often due to noise), PCA can help in reducing the noise in datasets.
Image Compression and Remote Sensing:
In image processing (e.g., remote sensing using LandSAT), PCA is used to reduce the number of spectral bands into principal components. This can enhance image interpretation and make it easier to classify land cover types.
PCA Example in LandSAT Imagery:
When dealing with LandSAT imagery, you might have multiple spectral bands (e.g., red, green, blue, NIR, SWIR). Applying PCA to these bands can help:
Reduce the number of bands while still capturing most of the spectral information.
Identify new combinations of spectral information that can highlight certain features (e.g., vegetation, water, urban areas).
Reduce redundancy and noise in the data, making it easier to classify or interpret.
Benefits of PCA:
Simplifies data: Reduces the number of features or variables to only the most important ones.
Removes correlations: The principal components are uncorrelated, reducing redundancy in the data.
Visualizes high-dimensional data: Makes it easier to visualize and interpret complex datasets by projecting them onto fewer dimensions.
Limitations of PCA:
Linear method: PCA only captures linear relationships in the data. If the data has complex, non-linear relationships, PCA may not capture all the information.
Loss of interpretability: The principal components are linear combinations of the original variables, so the transformed data may be harder to interpret in terms of the original features.
Sensitive to scaling: If the data isn't properly standardized, the principal components can be dominated by variables with larger scales.
Conclusion:
PCA is a powerful technique for reducing the complexity of datasets by finding new, uncorrelated principal components that capture the most variance. It’s widely used in data science, machine learning, and fields like remote sensing to improve data interpretation and efficiency.
Figure 2 - Various PCAs of LandSAT Imagery
Figure 3 - Optimal PCA of LandSAT Imagery
Figure 4 - Updated Various PCAs of LandSAT Inagery
Figure 5 - Refined PCA of LandSAT Imagery
What is a False Color Composite?
A False Color Composite (FCC) is a method of displaying satellite images by assigning non-visible wavelengths (such as infrared) to visible colors like red, green, and blue. This technique enhances specific features in the imagery that are not easily visible in a standard true-color image.
In remote sensing, different objects reflect different amounts of energy at various wavelengths. While human eyes can only see the visible part of the spectrum (red, green, blue), sensors on satellites (like LandSAT) capture a broader range of wavelengths, including infrared and shortwave infrared bands. By mapping these invisible wavelengths to visible colors, a false color composite helps reveal features such as vegetation, water bodies, and urban areas with greater clarity.
Why Use False Color Composite?
Highlighting Specific Features: False color composites are used to highlight features like vegetation, water, and urban areas that may not be easily distinguishable in natural-color (true-color) images.
Differentiate Surface Types: FCCs can help differentiate between surface materials (e.g., soil, vegetation, water) by enhancing spectral differences.
Analyzing Environmental Changes: False color composites are widely used to monitor environmental changes such as deforestation, urban expansion, or agricultural productivity.
Key Components in False Color Composites:
Spectral Bands: Instead of the usual red, green, and blue bands, a false color composite uses a combination of other spectral bands, like infrared (NIR) or short-wave infrared (SWIR).
Assignment of Bands: In an FCC, the NIR band is often assigned to the red color channel, the red band is assigned to the green channel, and the green band is assigned to the blue channel. This highlights vegetation, water bodies, and urban areas.
Color Enhancement: Features like vegetation reflect strongly in the infrared spectrum, so assigning the infrared band to red highlights vegetation in bright red. Similarly, water absorbs infrared, so it appears dark or blue when mapped to shorter wavelengths.
Common Band Combinations in False Color Composites:
1. NIR-R-G (Near-Infrared, Red, Green)
NIR Band (e.g., LandSAT Band 5) is assigned to Red.
Red Band (e.g., LandSAT Band 4) is assigned to Green.
Green Band (e.g., LandSAT Band 3) is assigned to Blue.
This combination is widely used to:
Vegetation: Vegetation appears in shades of red because it strongly reflects near-infrared light.
Water: Water bodies appear blue or dark because they absorb near-infrared light.
Urban Areas or Bare Soil: Appear green or brown.
2. SWIR-NIR-R (Shortwave Infrared, Near-Infrared, Red)
SWIR Band (e.g., LandSAT Band 7) is assigned to Red.
NIR Band (e.g., LandSAT Band 5) is assigned to Green.
Red Band (e.g., LandSAT Band 4) is assigned to Blue.
This combination is used for:
Water Content: Detecting moisture in soils and vegetation.
Burn Scar Detection: Highlights burned areas in different shades compared to other land cover types.
Example: False Color Composite (NIR-R-G)
In a false color composite using NIR (Band 5), Red (Band 4), and Green (Band 3):
Vegetation appears as red because plants reflect more near-infrared light (assigned to the red channel) than visible light.
Water bodies absorb infrared and appear as blue or dark.
Urban areas or bare soil appear in shades of green or brown.
Applications of False Color Composites:
Vegetation Analysis:
Since vegetation reflects strongly in the NIR band, it appears prominently in false color composites. Healthy vegetation appears bright red, while stressed or sparse vegetation appears darker or more muted.
Water Body Detection:
Water absorbs infrared light, so water bodies appear dark (sometimes blue) in false color composites. This helps in mapping and monitoring lakes, rivers, and coastlines.
Urban and Land Cover Mapping:
Urban areas and bare soil typically reflect more in the visible spectrum but less in the infrared, making them appear green or brown in false color composites. This helps distinguish between urban and natural land cover types.
Environmental Monitoring:
False color composites are commonly used for environmental monitoring, such as deforestation, desertification, or monitoring the health of ecosystems over time.
Comparison with True Color Composite:
True Color Composite: Uses the Red, Green, and Blue bands (as the human eye perceives). The image looks similar to what we would see in a photograph.
False Color Composite: Uses non-visible bands (such as NIR or SWIR) and assigns them to visible colors (R, G, B). This enhances certain features (like vegetation or water) that are not easily distinguishable in true color images.
Benefits of False Color Composite:
Enhanced Feature Detection: Allows for clearer identification of features like vegetation, water, and built-up areas.
Highlighting Invisible Information: Reveals important information from non-visible wavelengths like NIR and SWIR.
Improved Land Cover Classification: Helps in analyzing land cover types and changes that are not easily distinguishable in natural color imagery.
Figure 6 - Enhanced False Color Composite of LandSAT Imagery
Conclusion:
A False Color Composite is a powerful tool in remote sensing that enhances the visualization of satellite imagery by assigning non-visible wavelengths to visible colors. It helps reveal features like vegetation, water, and urban areas that may not be as easily visible in a standard true-color image. By using bands such as NIR and SWIR, FCCs highlight details crucial for environmental analysis, land cover classification, and ecosystem monitoring.
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