Remote Sensing & GIS 2 Flashcards

Question

Give the mathematical definitions of gradient and Laplacian filters.

Answer 1

* Prewitt filters * Sobel filters

Answer 2

* Standard Laplacian filter * Laplacian filter * Edge sharpening filter

Answer 3

In order to remove random noise with the minimum degradation of **resolution**, various edge preserved filters have been developed such as adaptive median filter.

Answer 4

* As PCs are independent without information redundancy, colour composites of PCs are often very _effective to highlight particular ground objects and minerals that are not distinguishable in colour composites of the original bands_. * However, in PC colour composites, the **noise may be exaggerated** because the **high rank PCs contain significantly less information** than lower rank PCs and have **very low SNR**. * When PC images are stretched and displayed in the same value range, the **noise in higher rank PCs is improperly enhanced**. * We would like to use three _PCs with comparable information levels_ for colour composite generation. * **Selective Principal Component Analysis** (SPCA) techniques can produce PC colour composites **condensing maximum information of either topographic or spectral features** and meantime makes the _information content in each PC displayed in RGB **better balanced**_. * There are two types of SPCA: **dimensionality and colour confusion reduction** and **spectral contrast mapping**.

Answer 5

* The spectral bands of a multi‐spectral image are arranged into three groups and **each group is composed of highly correlated bands**. * **PCA is performed on each group** and then **the three PC1s derived from these three groups are used to generate an RGB colour composite**. * As bands in each group are highly correlated, the PC1 **concentrates the maximum information of each group**. * For six reflective spectral bands of a TM or ETM+ image, the technique may condense more than 98% variance (information) in the derived PC1 colour composite. The recommended groups for six reflective spectral bands of TM or ETM+ images are shown in the Table. * The approach is actually equivalent to **generating a colour composite using broader spectral bands, given that a PC1 is a positively weighted summation of the bands involved in the PCA**. * It essentially creates a **colour composite of a broad visible band in blue, an NIR band in green and broad SWIR band in red**.

Answer 6

* The spectral bands of a multi‐spectral image are arranged into three groups and **each group is composed of highly correlated bands**. * **PCA is performed on each group** and then **the three PC1s derived from these three groups are used to generate an RGB colour composite**. * As bands in each group are highly correlated, the PC1 **concentrates the maximum information of each group**. * For six reflective spectral bands of a TM or ETM+ image, the technique may condense more than 98% variance (information) in the derived PC1 colour composite. The recommended groups for six reflective spectral bands of TM or ETM+ images are shown in the Table. * The approach is actually equivalent to **generating a colour composite using broader spectral bands, given that a PC1 is a positively weighted summation of the bands involved in the PCA**. * It essentially creates a **colour composite of a broad visible band in blue, an NIR band in green and broad SWIR band in red**.

Answer 7

* A more interesting and useful approach (as opposed to DCCR) is spectral contrast mapping, where the primary objective is to **map the contrast between different parts of the spectrum**, and so to **identify information unique to each band** rather than information in common. * For this purpose, **PC2s derived from band pairs** are used instead of PC1s. * By using only **two bands as inputs**, the information that is common to both bands is mapped to PC1 and the **unique information is mapped to PC2**. * In general, _low or medium correlation_ between the bands in each pair is preferred for this approach. * The recommended grouping for the six reflective spectral bands of TM/ETM+ is listed in the Table. * Based on the above principle, groups of **three or more bands** may also be used for spectral contrast mapping. * The technique can **generate spectrally informative colour composites** with **significantly reduced topographic shadow effects** and **better SNR**.

Answer 8

* The idea of PCADS is to stretch multidimensional imagery data along their PC axes (the axes of the data ellipsoid cluster) rather than original axes representing image bands. * In this way, the volume of data cluster can be effectively increased and the inter-band correlation is reduced. * The PCADS technique is similar to the HSIDS in results (both increase the three dimensionality of the data cluster) though based on quite different principles. * PCADS is statistically scene dependent as the whole operation starts from the image covarience matrix. * It can be operated on all image bands by one go. * Both PCADS and HSIDS involve complicated forward and inverse coordinate transformations. * In particular, the PCADS requires quite complicated inverse operations of eigenvector matrix for inverse PC transformation and t.f. not widely used.

Answer 9

* The HSIDS technique is similar to the PCADS in results (both increase the three dimensionality of the data cluster) though based on quite different principles. * The HSIDS is not statistically scene dependent and only operates on three bands. * Both HSIDS and PCADS involve complicated forward and inverse coordinate transformations.

Answer 10

The Direct Decorrelation Stretch (DDS) is the most efficient technique and it can be quantitatively controlled based on the saturation level of the image.

Answer 11

* As PC1 is mainly topography, colour composites excluding PC1 may better present spectral information with topography subdued. * PCs represent condensed and independent image information and therefore produce more colourful (i.e. informative) colour composites. * However, here we have a problem in that a PC is a linear combination of the original spectral bands, so its relationship to the original spectral signatures of targets representing ground objects is no longer apparent. * To solve this problem, a feature‐oriented PC selection (FPCS) method for colour composition was proposed.

Answer 12

* In general, for multi-spectral imagery, the reflective bands are highly correlated, and, for example, if there is a correlation of 0.99 between two bands, this means that there is 99% information redundancy between the two bands, with only 1% of unique information. * As such, multi-spectral imagery is not efficient for information storage. * As shown by the 2D illustration, suppose the image data points form an elliptic cluster; * The aim of PCA is to **rotate the orthogonal co‐ordinate system of band 1 and band 2 to match the two axes of the ellipsoid**, the **PC1 and PC2**. * The coordinates of each data point in the PC co-ordinate system will be the DNs of the corresponding pixels in the PC images. * The first PC is represented by the longest axis of the data cluster and the second PC the second longest, and so on. * The axes representing high order PCs may be too short to represent any substantial information, and then the apparent m-dimensional ellipsoid is effectively degraded to n (n\<=m) independent dimensions. * In this way, PCA reduces image dimensionality and represent the nearly same imagery information with fewer independent dimensions in a smaller dataset without redundancy.

Answer 13

A process that transforms a single input image, *X*, to a single output image, *Y*, through a function *f*, in such a way that the DN of an output pixel, y_ij, depends only on the DN of the corresponding input pixel x_ij. **y_ij = f(x_ij)** When *X* represents a digital image and x_ij, the DN of any pixel in the image at the i^th line and j^th column, *Y* represents the image derived from *X* by a function, *f*, and y_ij is the output value corresponding to x_ij.

Answer 14

* Point operation is also called histogram modification because the operation only alters the histogram. *h(x)*, of an image but not spatial relationship of image pixels. * For pixels with the same input DN, x, but different locations, the function, f, will produce the same output DN, y. * T.f. point operation can be more concisely defined as: y = f(x)

Answer 15

* Sometimes called radiometric enhancement or histogram modification, contrast enhancement is the most basic but very effective and efficient technique to optimise the image contrast and brightness for visualization or highlight information in particualr DN ranges. * Contrast enhancement is a point operation that modifies the image brightness and contrast but does not alter the image size and textures.

Answer 16

If image bands displayed in red, green and blue do not match the spectra of these three primary colours, a false colour compositeimage is produced. A typical example is the so called standard false colour compositein which nearer infrared band is displayed in red, red band in green and green band in blue.

Answer 17

* A SAR interferometer acquires two SLC images of the same scene with the antenna separated by a distance *B* called the *baseline*. * For a **single-pass** SAR interferometer, such as a SAR interferometer on board an aircraft or the space shuttle (e.g. SRTM mission), two images are acquired simultaneously via **two separate antennas**; **one sends and receives microwave signals while the other receives only** (Figure 1a). * In contrast, a _repeat-pass_ SAR interferometer acquires a single image of the same area twice from _two separate obits with minor drift which forms the baseline B_ (Figure 1b); this is the case for most SAR EO satellites.

Answer 18

An SLC image is composed of pixels of complex numbers which record not only the intensity (the energy of microwave signals returned from targets) but also the phase of the signal which is determined by the distance between the corresponding ground position and the radar antenna. Given a complex number of an SLC pixel: c = a + ib, the magnitude of c (the SAR intensity image) is: M_c = (a² + b²)^½

Answer 19

* InSAR (interferometric Synthetic Aperture Radar) technology exploits the phase information in SAR single look complex (SLC) images for earth and pletary observations. * A **SAR interferogram** shows the phase differences between the corresponding pixels of the same object in two SAR images taken from two slightly different positions. It represents topography as fringes of interference. * Based on this principle, InSAR technology has been developed and applied successfully for topographic mapping, measurement of terrain deformation caused by earthquakes, subsidence, volcano deflation and glacial flow. * The purpose of InSAR is to derive an SAR interferogram, ø, which is the **phase difference between the two coherent SLC images** (often called a *fringe pair*). ø = ø₁ - ø₂ * The applications of InSAR are largely based on the relationships between the interferogram, topography and terrain deformation, for which the baseline B, especially the perpendicular baseline, B₁, plays a key role.

Answer 20

* **InSAR interferogram** is used for **DEM generation**. * The **single pass** configeration of InSAR is preferred for the complete _elimination of temporal decorrelation_ and to ensure _high quality_ interferogram.

Answer 21

* _Differential_ InSAR (DInSAR) is used for the ***measurement* of terrain deformation**. * This uses **repeat pass InSAR** with at least one pair of _across-deformation event_ SAR acquisitions.

Answer 22

* InSAR coherence technique is for **random change *detection***. * It is very important to note that this technique is for **_detection_** rather than *measurement*. * A coherence technique must be based on **repeat pass InSAR**.

Answer 23

* The InSAR measured phase difference is a **variable in the 2π period**, or is **2π-modulo wrapped**, with fringes that occur in repeating 2π cycles and _do not give the actual phase differences_ which could be *n* times of 2π, plus the InSAR measured phase difference. * The interferometric phase therefore needs to be **unwrapped** to remove the 2π-modulo ambiguity in order to generate DEM data. * There are also other corrections necessary such as the **removal of the ramps** caused by the earth’s curvature and by the direction angle between the two paths as they are usually not strictly parallel. * For InSAR, the wider the perpendicular baseline, B_l, the higher the elevation resolution. However, a **too wide B_l introduces more severe spatial decorrelation** which **degrades the quality of the interferogram and then the DEM**. * Usually a B_l of several 10's - 1000 m is used for C band in InSAR. * **The elevation resolution of InSAR, is t.f., for C-band for example, no better than 10 m in general.**

Answer 24

(a) InSAR technique can be used to produce DEMs of NO BETTER THAN 10 M level accuracy of elevation. (b) Differential InSAR technique can be used FOR THE MEASUREMENT OF TERRAIN DEFORMATION AS CASUED BY EARTHQUAKES, SUBSIDENCE, GLACIAL MOTION AND VOLCANO DEFLATION. **(c) Differential InSAR technique can _measure_ better than cm level _deformation of land surface_.** (d) SAR coherence image can DETECT up to cm level (half radar wavelength) RANDOM CHANGES of land surface.

Answer 25

a. InSAR technique can be used to produce DEMs of NO BETTER THAN 10 M level accuracy of elevation. b. Differential InSAR technique can be used FOR THE MEASUREMENT OF TERRAIN DEFORMATION AS CASUED BY EARTHQUAKES, SUBSIDENCE, GLACIAL MOTION AND VOLCANO DEFLATION. c. Differential InSAR technique can MEASURE up to cm level (half radar wavelength) DEFORMATION of land surface. **d. SAR coherence image can _detect_ up to cm level (half radar wavelength) _random changes of land surface_.**

Answer 26

* A decision must be made based on the **level of acceptable risk** and the **degree of confidence** (error and uncertainty) in the available data: * Aiming for a _quantitative prediction_, with assurances of _minimised uncertainty_. 1. **Deterministic** Decision Making 2. **Probabilistic** Decision Making 3. **Fuzzy** Decision Making

Answer 27

* 'Controls' data and relationships between inputs, * Decisions and outcomes are understood with some certainty (rare!) * Categorical classes, rules and thresholds can be applied

Answer 28

* Environement, relationships and outcomes are uncertain. * In general, uncertainty is treated as 'randomness' (not normal in nature'). * Categorical classes, rules and thresholds should not be applied * Produces a true or false result - no degree of uncertainty is accommodated unless as a seperate and distinct state.

Answer 29

* Uncertainties are related to _natural variation_, _imprecision_, _lack of understanding_ or _insufficient data_ (or all of these). * Consider **variable class membership** (rather than true or false) - allowing _infinite number of states_, representing the _increasing possibility of being true_.

Answer 30

1. Criterion uncertainty (data quality) 2. Threshold uncertainty (data & class descriptions) 3. Decision Rule uncertainty (data handling) ## Footnote *Fuzzy logic can assist with 2 and 3*

Answer 31

* (data quality) * Arise from measurement and identification errors, and data quality

Answer 32

* (data & class descriptions) * Boundaries between classes are usually **artificially applied** but are **rarely rigid** in nature. * Concept of '**possibility**' would be useful in describing **natural variation** rather than categories, so **fuzzy boundaries** can be used.

Answer 33

* (data handling) * 'Hard' rules for firm evidence, plentiful knowledge and/or legal prescrption, or; * 'Soft' rules for circumstantial evidence, belief and plausibility.

Answer 34

* The criteria being evaluated are generally one of two types, * **constraints** that are inherently Boolean and limit the area within which the phenomenon is feasible, or * **factors** that are variable and are measured on a relative scale representing a variable degree of likelihood for the occurrence of the phenomenon. * Preperation of both types is important * Each has a different role within the model

Answer 35

* Discretely sampled phenomena (maybe Boolean) * Containing values on nominal or ordinal measurement scale (i.e. not real DN but symbols or 'pointers') * Often used to satisfy legally prescriptive requirements

Answer 36

* **Spatially variable**, **continuously sampled** phenomena (real DN) * Containing values on **interval, ratio and cycle scales** (*integer or floating point*) * Must be **scaled** to a **consistent value range** and **direction**

Answer 37

* Fuzzy membership or fuzzy sets provide an elegant solution to the **problem of threshold and decision rule uncertainty** by _allowing ‘soft’ thresholds and decisions_ to be made. * It converts criterion value ranges to consistent value range/type and incorporates uncertainties by.. * **Breaking the requirement of ‘total membership’ of a class**; * Instead of just two states of belonging for a class, a fuzzy variable can have one of an infinite number of states ranging from 0 (non‐membership) to 1 (complete membership) and the values in between represent the increasing possibility of membership. * The **fuzzy set membership function** (expressed on a continuous scale from 0 (non-member) to 1 (full membership)) can be most readily appreciated with reference to a **simple linear function** but it may also be sigmoidal or J‐shaped, and monotonic or symmetric in form (Fig. 18.3).

Answer 38

* e.g. for **slope instability** * Gentle slopes (\<4°) are unlikely to be associated with stability and so would have a fuzzy membership of 0, * whereas steeper slopes (\>10°) are likely to be associated with instability and so would have a fuzzy membeship of 1.0. * A **simple linar membership function**, µ_(x), is a good example, where x is the slope angle, and * every value of x is associated with a value of µ_(x), and the ordered pairs [x, µ_(x)] are collectively known as the **Fuzzy Set**.

Answer 39

* Increase resolution of data, * Improve standards and procedures * More rigorous sampling * Error assessment techniques (RMS)

Answer 40

* GIS data handling to create **soft** or **fuzzy boundaries** and **scaling**

Answer 41

Decision rule uncertaincies can be quanitfied and accommodated (to varying degrees) through use of different MCE techniques: * Fuzzy sets, fuzzy logic & fuzzy modelling (also Vectoral Fuzzy Modeling) * AHP & Weighted factors in linear combination (WLC) * Probability estimates & distribution functions (Bayesian), weights of evidence modeling * Dempster-Shafer Theory (incorporate concepts of belief and plausibility)

Answer 42

Choice of method is made according to the type of problem, type of uncertainties involved, degree of understanding around the problem

Answer 43

* Revolutionary developement of **passive sensors** via the _combination_ of an **imaging system** with a **spectro-radiometer**, to a _collect continuous spectral signature or profile_ using bands of a **few** **nm width**. * This produces a **data cube** (dense volume): many rows, columns & 100s bands. * Demands processing via **analysis of the whole spectral signature** (or fingerprint) of a material rather than looking at differences in reflectance between bands. * Allows **_identification_ of materials** (not merely discrimination)

Answer 44

* The incoming EMR from land surface goes through the **sensor optics** and is split into _hundreds of very narrow spectral beams_ by a complicated **spectral dispersion device** (e.g. interference filter), * and finally the spectral beams are **detected by arrays of CCDs** corresponding to, say 224, spectral bands. * A hyper-spectral system can be either an **across track mechanical scanner** with a small number of detectors for each band, or an **along-track push-broom scanner** with a panel of hundreds of line arrays of CCDs. * Hyper-spectral sensors are mainly operating either in the **VNIR only** or in the **VNIR & SWIR spectral ranges**; there are very few _TIR hyperspectral sensors_ as yet but they are developing.

Answer 45

* One dimension used for **spectral separation** and the 2nd dimension used for **imaging in one spatial direction**. * _Second spatial dimension_ arises from **movement of scanning camera** over the scene (e.g. aircraft flight). * Result is _one 2D image for each spectral channel_, i.e. every pixel contains one full spectrum.

Answer 46

Collect data of very high spectral resolution, to rpovide a near contiguous spectral signature, and thus to identify minerals/substances

Answer 47

* The hyperspectral imagery data represent **radiance spectra**, of the land surface targets, which are dependent on **solar radiation**, **atmospheric scattering** and **absorption** and **target spectral reflectance**. * To analyse the hyperspectral data in terms of the target spectral properties (reflectance) the data must be _calibrated to be comparable with reflectance_. * There are several commonly used methods to achieve this.

Answer 48

* Flat Field Calibration * Internal Average Relative Reflectance (IARR) * Empirical Line Calibration The first two strategies rely on information from the image only; the last requires knowledge of the surface physical properties and atmospheric conditions at time of imaging.

Answer 49

* The ‘Flat Field Calibration’ technique is used to **normalise the images to an area of known ‘flat’ or uniform reflectance.** * The method requires that a **large, spectrally flat and uniform area can be located in the image data**. * The radiance spectrum for this area is assumed to be composed of primarily **atmospheric effects** (scattering & absorption) and the **solar spectrum** - and has a reletively flat spectral reflectance curve. * Preferably a bright area (with min. noise) - not always easy to find. * **The average radiance spectrum of the area is used as a reference spectrum**, which is then divided into the spectrum for each pixel of the image as defined below. * Result = _apparent reflectance_ data that can be compared with lab. spectra.

Answer 50

* The IARR calibration technique is used to **normalise images to a scene-average spectrum**. * The radience values in each spectrum are scaled so that their sum is constant over the entire image. * Remove gross topographic shading and overall brightness variations. * This is particularly effective in an area where **no ground measurements data available** and little is known about the scene. * It works particularly well for **arid and semi-arid areas with no dense vegetation**. * Result = _apparent reflectance_ data that can be compared with lab. spectra.

Answer 51

Method assumes the scene is heterogeneous enough that spatial variations in spectral relfectance characteristics cancel out, producing a mean spectrum similar to a flat field spectrum (generally, but not always true).

Answer 52

* Force image data to **match selected field reflectance spectra** - requires ground (field-spectral) measurements and/or knowledge. * Need 2+ ground targets for which reflectance is _measured in the field_ - targets of at least 1 light and 1 dark area. * Find linear regression for each band:band plot to find the transformation between **radience** and **reflectance**. * **Slope** quantifies combined effects of multiplicative radiance factors (gain), and interpret with the **radience axis** gives the additive component (offset). * **Gains and offsets (a and b) calculated in the regression** applied to the **radience spectra** to produce _apparent reflectance_ on a pixel-by-pixel basis. * _Does not account for all topographic effects_. * **ELC is best but not always possible**.

Answer 53

* Calibration and correction for apparent reflectance only. * Apparent reflectance spectrum presents the general spectral shape but: * Not actual reflectance values * Not corrected for albedo information

Answer 54

1. Each band DN represents average reflectance across very _narrow range of wavelengths_, few _nanometres_. 2. Analyse **individual spectral signatures**. 3. Interpretation is impossible without understanding spectral signatures of minerals & rocks. 4. First **calibrate** to apparent reflectance. 5. Identify **noise** component e.g. using MNF 6. Use n-dimensional plotting to identify pure pixels (PPI) - produce an **end-member spectral library**. 7. Use these image end-members (or lab. spectra) as references to **classify the image spectra** according to their similarity to the reference spectra 8. **Spectral classification** methods include: spectral matching, SAM, LSU, MTMF, SFM. 9. **Narrow bands (complete spectrum)** can be used to perform mineral species level discrimination and identification.

Answer 55

The Minimum Noise Fraction (MNF) transform

Answer 56

* Spectral Angle Mapper (SAM) * Linear spectral unmixing (LSU) * Matched Filtering (MF) & Mixture Tuned Match Filtering (MTMF) * Spectral Feature Fitting (SFF)

Answer 57

1. Each band DN represents average reflectance across _broad range of wavelengths_, _microns_. 2. **General image enhancement** (e.g. using BCET) and remove highly correlated information - spectral highs and lows remain. 3. Extract **broad spectral signatures** of target materials and identify **significant spectral absorptions**. 4. Devise **ratios** and '**band algebra**' to highlight or enhance particular spectral absorptions, e.g. iron-oxide ratio or clay ratio or NDVI. 5. Calculate **image statistics** to see contribution of each band to individual PCs etc. 6. Use other techniques like PCA, classification, HIS to **enhance spectrally significant portions of the data**. 7. Broad bands 'alias' spectral absorbtions and so can only **detect spectral differences between lithologies and _some_ mineral groups**.

Answer 58

* The 'Hyper' or '**over-sampled**' nature (more than enough bands) and **high degree of interband correlation** in HS data demands a **different approach** from 'hypo' or broad-band data. * High potential for **mixed pixels** but allows **sub-pixel spectral mapping** (although can never arrive at exact mixtures) * If data are not truly HS then the **Minimum Noise Fraction (MNF)** process will reveal this. * Some HS techniques (e.g. Spectral Angle Mapper, SAM) can sometimes be **used with non-HS data** (e.g. Aster, and potentially Worldview-3) to good effect - but with caution (spectral resolution will always limit the results). * HS processing focuses on **reducing data dimensionality** first, then allows us to **classify the data rich components** using image-derived or pure/library spectra. * **Species level identification and mapping** is possible and has been used to great effect over past 40 yrs. * Techniques and instruments now adapted to **core-scanning & outcrop mapping**. * HS sensors are already _onboard UAVs_ (VNIR only as yet) but soon will include SWIR and TIR.

Answer 59

Probability (likelyhood) of the occurence of an unwelcome event

Answer 60

The **expected degree of loss**, in terms of **probability** & **cost**, as **caused by an event**. Probability (hazard) modulated by the economic value of the losses per event

Answer 61

Risk = [(Hazard x Vunerability) x Exposure) or more simply: R = H x V

Answer 62

Refers to the physical aspects of vunerability; the sum of the elements at risk

Answer 63

Physical, social, economic or environmental conditions that increase the susceptibility of a community to the impact of hazards

Answer 64

* Slope stability hazard assessment is the principle objective * There are 3 sub-objectives * 6 input criteria and several possible outcomes or environmental states, representing differing levels of hazard (probability or likelyhood)

Answer 65

* High correlation generally exists among spectral bands of multi-spectral images. * As a result, original image bands displayed in RGB formulate a **slim cluster along the grey line** _occupying only a very small part of the space of the colour cube_ (left figure), * Contrast enhancement on individual image bands can elongate the cluster in the colour cube but it is _not effective to increase the volume of the cluster_ bc such stretch is equivalent to stretch intensity only (middle figure). * In order to increase the volume of data cluster in the colour cube, the data cluster should **expand in both directions** along and perpendicular to the grey line. * This is equivalent to **stretch both intensity and saturation components** (right figure). * IHSDS is interactive and flexible based on user observation of the saturation image and its histogram.

Answer 66

1. (BCET stretch - or linear stretch with appropriate clipping) 2. RGB-IHS transformation 3. Saturation component stretching 4. IHS-RGB transformation

Answer 67

* This technique **performs a direct saturation stretch without using RGS-IHS and IHS-RGB transformations.** * The DDS achieves the _same effect_ as the IHS decorrelation stretch. * As DDS involves only **simple arithmetic operations** and can be **controlled quantitatively**, it is much _faster_, _more flexible_ and _more effective_ than IHS DS technique. * As with IHSDS, the 3 bands for colour composition must be well stretched (e.g. BCET or linear stretch with appropriate clipping) before the DDS is applied.

Answer 68

* Both IHS and Brovey transform image fusion techniques can cause colour distortion if the spectral range of the intensity replacement (or modulation) image is different from the spectral range covered by the three bands used in a colour composite. * This problem is inevitable in colour composites that do not use consecutive spectral bands. * The problem may become serious for vegetation and crop fields if the images for fusion are taken in different growth seasons. * **Preserving the original spectral properties is very important for most remote sensing applications based on spectral signatures, such as lithology, soil and vegetation.** * The spectral distortion introduced by these fusion techniques is uncontrolled and not quantified bc the images for fusion are often taken by different sensor systems on different dates or in different seasons. * It t.f. cannot be regarded as spectral enhancement and should be eliminated by all means to avoid unreliable interpretation for applications. * The SFIM technique is a genuine **spectral preserve image fusion technique** applicable to co-registered multi-resolution images.

Answer 69

For the SFIM operations, the lower resolution image must be interpreted to the same pixel size as the higher resolution image by **bilinear or cubic interpolation** in the co-registration process.

Answer 70

* The advantage of the SFIM over the IHS and Brovey transform fusion technique is that it **improves spatial details** with the **fidelity to the image spectral properties and contrast**.

Answer 71

* The SFIM is **more sensitive to image co-registration accuracy** than the IHS and Brovey transform. * Inaccurate co-registration may result in **blurring edges** in the fused images. * This problem can be alleviated using a **smoothing filter with a kernel larger than the resolution ratio between the higher and lower resolution images**. * E.g., for TM and SPOT Pan fusion 5x5 and 7x7 filters will produce better results than a 3x3 filter. * We have developed **advanced pixel-wise image co-registration algorithm** that resolves the problem.

Answer 72

* For multi-spectral (or more generally, multi-layer) images, algebraic operations, such as four basic arithmetic operations (+, -, x, /), logarithmic, exponential, sin, tan etc., can be applied to the DNs of different bands for each pixel to produce a new image. * Such processing is called image algebraic operation. * Algebraic operations are performed pixel by pixel among DNs of spectral bands (or layers) for each pixel without involving neighbourhood pixels. * They can t.f. be considered as multi-image point operations.

Answer 73

*y = f (x₁, x₂, ..., x_n)* where *n* is the number of bands (or layers).

Answer 74

* Image subtraction produces a difference image from two input images Y = (1/*k*) (*w*_iX_i - *w*_jX_j) * The weights, wi and wj, are important to assure a balanced differencing is performed. * If the brightness of Xi is significantly higher than that of Xj, for instance, the difference image will be dominated by Xi and as a result, the true difference between the two images is not effectively revealed.

Answer 75

* Subtracting is one of the **simplest and most effective** techniques for _selective spectral enhancement_. * It is also useful for **change detection** and **removal of background illumination bias**.

Answer 76

* Subtraction operation reduces the image information and decreases SNR. * This is obvious bc image subtraction removes the common features while likely retaining the random noise in both images.

Answer 77

Y = **X_i / X_j** * For image division processing, certain protection is needed to avoid overflow in case than a number is divided by zero. * A commonly used trick is to shift up the value range of denominator image by 1 to avoid zero. * We can consider ratio as a coordinate transformation from a Cartesian coordinate system to a polar coordinate system, then Y = X_i / X_j = **tan (*a*)** * a* = arctan (X_i / X_j) * Ratio image Y is actually a tangent image of the angle *a*.

Answer 78

* Ratios are often designed to highlight the target features as high ratio DNs. * Direct stretch on ratio image Y may enhance the target features better, at the cost of losing the information represented by low ratio DNs * E.g. TM1/TM3 and TM3/TM1 contain the same information, but are different after linear scale. * Remember, when you design a ratio, make sure the target information is in high values in the ratio image.

Answer 79

* Ratio is an **effective technique to selectively enhance spectral features**. * Ratio images derived from different band pairs are often displayed in RGB system to generate ratio colour composites. * E.g. a colour composite of **TM5/TM7 (blue), TM4/TM3 (green) and TM3/TM1 (red)** may highlight clay mineral in blue, vegetation in green and iron oxide in red. * Many indices, such as **Normalized Difference Vegetation Index (NDVI)**, have been developed based on both differencing and ratio operations.

Answer 80

* For a given incident angle of solar radiation, the _radiation energy recived_ by a land surface depends on the _angle between the land surface and the incident radiation_. * T.f., solar illumination on land surface _varies_ with **terrain slope** and **aspect**, which results in **_topographic shadows_**. * The DNs in different spectral bands of a MS image are _proportional_ to the **solar radiation recieved** by land surface and its **spectral reflectance**. * Suppose a pixel representing a land surface _facing the sun_ receives _*n* times_ radiation energy of that received by another pixel of land surface _facing away from the sun_, then the DNs of the two pixels in spectral bands *i* and *j* are as below: