02-landtrendr.Rmd

# LandTrendr

Each pixel in an image time series has a story to tell, LandTrendr aims to tell them succinctly. Let's look at an example; here we have a pixel intersecting Lon: -123.845, Lat: 45.889 (Fig 2.1) from a conifer-dominated,
industrial forest region of the Pacific Northwest, USA. At the
beginning of its record, it was a mature, second-growth conifer stand, and for 17 years, little changed.
Then, between the summers of 2000 and 2001 a service road was built through it, removing some of its vegetation. 
Over the next year it experienced a clearcut harvest, removing all of its remaining
vegetation. For the last 14 years it has been regenerating. Most
recently it was a closed canopy, maturing, conifer stand.

<img src='imgs/pixel_story.jpg'>

*Fig 2.1. Every pixel tells a story. Landsat provides a historical record of the character of landscapes. By
extracting a single pixel from a time series of Landsat imagery, it is possible to recount the state and change of 
the features composing the 1-hectare area of a pixel through time. In this example, we analyze the history of a conifer 
forest pixel from an industrial forest region of the Pacific Northwest (USA) that experiences a period of relative stability,
a dramatic, rapid loss of vegetation, and subsequent regeneration.*
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The description of this example pixel's history is of course abridged, and only conveys a moderate resolution perspective of state and change in forest character. The unabridged version of this pixel's story includes many other small changes in the forest stand it represents, but given 
the precision of the satellite sensor and methods in processing, the provided description is the type of pixel history interpretation we are 
confident are represented well in the image time series. LandTrendr is a brevity algorithm that listens to the annual, verbose, noisy detail of a pixel's story and writes an abridged version.

In practice, LandTrendr takes a single point-of-view from a pixel's spectral history, like a band or an index, and goes 
through a process to identify breakpoints separating periods of durable change or stability in spectral trajectory, and records the year that changes 
occurred. These breakpoints, defined by year and spectral index value, allow us to represent the spectral history of a 
pixel as a series of vertices bounding line segments (Fig 2.2).

<img src='imgs/segmentation.png'>


*Fig 2.2. LandTrendr pixel time series segmentation. Image data is reduced to a single band or spectral index and then 
divided into a series of straight line segments by breakpoint (vertex) identification.*
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There are two neat features that result from this segmented view of spectral history.

1. The ability to interpolate new values for years between vertices.
2. Simple geometry calculations on line segments provide information about distinct spectral epochs



## Fit-to-Vertex Image Data

The ability to interpolate new values for years between vertices is very useful. It ensures that each observation is aligned 
to a trajectory consistent with where the pixel has been and where it is going. We can think of this as hindsight-enhanced image 
time series data. It has two practical utilities. It can fill in data from missing observations in the time series (masked because 
of cloud or shadow) and it maintains consistency in predictive mapping through time; e.g. an annual forest classification is not 
likely to bounce between mature and old-growth conifer because of minor differences in spectral reflectance from atmosphere or 
shadow difference (Fig 2.3).

<img src='imgs/seg_index_ftv.png'>

*Fig 2.3. Hindsight-enhanced image time series data. Identification of time series breakpoints or vertices, allows the observations 
between vertices to be interpolated, removing extraneous information and placing each observation in the context of the trajectory 
it is part of. This is useful in filling missing observations because of cloud and shadow, and makes for more consistent annual 
map prediction.*
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Since breakpoints or vertices are defined by a year we also have the ability to impose breakpoints identified in one spectral band 
or index on any other. For instance, we can segment a pixel time series cast as Normalized Burn Ratio (NBR: [NIR-SWIR]/[NIR+SWIR]) 
to identify vertices, and then segment a short-wave infrared (SWIR) band based on the NBR-identified vertices (Fig 2.4).  

<img src='imgs/other_index_ftv.png'>

*Fig 2.4. Impose the segmentation structure of one spectral representation on another. Here we have identified four breakpoints or 
vertices for a pixel time series using NBR, and then used the year of those vertices to segment and interpolate the values of a 
SWIR band time series for the same pixel.*
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This is useful because we can make the whole data space for a pixel’s time series consistent relative to a single perspective (Fig 2.5) and
summarize starting, ending, and delta values for all spectral representations for the same temporal segments, 
which can be powerful predictors of land cover, agent of change, and state transitions.

<img src='imgs/all_index_ftv.png'>

*Fig 2.5. A stack of spectral representations can be standardized to the segmentation structure of a single spectral band or index. Here 
we are demonstrating the standardization of tasseled cap brightness, greenness, and wetness to the segmentation structure of NBR. 
This allows us to take advantage of multi-dimensional spectral space to describe the properties of spectral epochs and breakpoints 
to predict land cover, change process, and transitions from a consistent perspective (NBR).*
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## Epoch Information

The second neat feature of a segmented world view of spectral history is that simple geometry calculations can summarize attributes of 
spectral epochs (Fig 2.6). Temporal duration and spectral magnitude can be calculated for each segment based on the vertex time and 
spectral dimensions. These attributes allow us to easily query the data about when changes occur, how frequently they occur, on 
average how long do they last, what is the average magnitude of disturbance (or recovery) segments, etc. We can also query information about 
adjacent segments to focal segments. For instance, we can ask, what it the average rate of recovery following a disturbance segment, 
or what was the trajectory of a pixel time series prior to disturbance segments that we’ve attributed to fire.    

<img src='imgs/segment_attributes.png'>


*Fig 2.6. Diagram of segment attributes. From these attributes we can summarize and query change per pixel over the landscape.*
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