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The Science of Raster to Vector Conversion

Raster and Vector Data in Urban Climate Studies

The applications of raster and vector images transcend the usual CAD drawings (such as converting PDF files to CAD), GIS maps, photography, and graphic designs. Simply put, raster and vector uses are extensive. As Gal, Lindberg, and Unger sought to find out in their 2009 research paper titled Computing continuous sky view factors using 3D urban raster and vector databases: comparison and application to urban climate, the two types of images can be used in the calculation of sky view factors (SVF). 

Vector and raster images differ significantly when you look at them from a scaling perspective – the former doesn’t become distorted upon scaling regardless of the scale factor, whereas the latter type gets distorted (most noticeable with low-quality JPEG images) – and many other characteristic-based viewpoints. 

However, although this is the case for some, if not most, instances, the same cannot be said in certain cases. This implies that vector and raster images can be similar on various fronts. For instance, as Gal, Lindberg, and Unger found out, both the raster and vector data yielded similar results when they used them to calculate the SVF.

In the same breath, the researchers also observed that using raster images to obtain the SVF values was much faster than when they used vector images. Thus, even where there are similarities, underlying differences exist. This article summarizes the research by Gal and others, published on the 2009 issue of the Theoretical and Applied Climatology journal. The paper explored the use of raster and vector data in urban climate studies.

Basis of The Study

Before telling you how the researchers utilized raster and vector images, it’s important to give you an overview of why they conducted the study in the first place. Now, the rural and urban areas differ in several ways. Most of the differences arise from the infrastructural developments without which urban areas would not be referred to as such. One of the most fundamental issues that arise from such developments is changes in the climate.

Urban Heat Island

Urban areas have a microclimate whose key attribute is the formation of heat islands. The fact that these heat islands are found in urban or built environments makes the use of the term urban heat island apt. The microclimate arises from human-made activities, which have caused a shift in land-use practices. As a result, the materials and geometric form that existed prior to such practices don’t feature prominently anymore.

The result has been a modification of the water balance and surface energy, which have subsequently caused the nighttime temperatures to be higher than those in the areas surrounding the built environment. It is this difference in temperatures that creates the phenomenon referred to as an urban heat island (UHI), which is denoted by ΔT.

Notably, there are three distinguishable UHIs:

  •  Below the surface
  • On the surface
  • Urban canopy layer (UCL): extends from the surface to approximately the average rood level.
  •  Urban boundary layer

In the study, Gal, Lindberg, and Unger use the term UHI to mean the difference between the UCL and the temperature measured in a rural setup but at the same height. It is important to note that the differences in nighttime temperatures between rural and urban areas arise from the obstruction of longwave radiation, which helps cool the surface, by tall buildings present in the built environments. The buildings’ presence implies that only a small section of the surface can be seen from the sky.

Sky View Factor (SVF)

The obstruction of the sky from the surface gives rise to the sky view factor (SVF), which describes the urban geometry. By definition, the SVF is a dimensionless ratio of the radiation received (or emitted) by a point on the surface to the radiation emitted (or received) by a hemisphere whose center is the point being analyzed. When the SVF is 0, the obstacles around the point block the sky from view. Conversely, when the SVF is 1, there are no obstacles, and the sky is, therefore, open to view. 

Although many other factors contribute to the UHI, e.g., the ratio of the paved or built-up area and the heat that human activities release to the atmosphere etc., the study mainly focuses on surface geometry. Given that SVF is one of the most effective measures of urban surface geometry, it follows that that’s precisely what the researchers center their research on.

Study Area

The study was based in south-east Hungary in a city known as Szeged. The urban area covered a total of 30 square kilometers, but the precise area wherein the study focused on was 26.75 square kilometers. This area was subdivided into 107 cells whose dimensions were 500m by 500m, though the figure was further trimmed to 103 cells because 4 of the cells were in a location that was more of a rural area than an urban one.

Nonetheless, the researchers used these 4 cells to understand the temperature contrasts between urban and rural areas. Their average temperature was used in the calculation of ΔT, which, as stated earlier, denotes the urban heat island. In the study, ΔT was the difference between the average temperature of the 103 cells in the urban region and the average temperature of the 4 cells located in the rural area. Importantly, therefore, the exact urban study area was less than 26.75 square kilometers.

SVF Calculation Methods

GIS-based 3D models can be used to determine SVF, and this is where the raster and vector images are put into use. Using two different methods that are based on 3D models, the researchers calculated the SVFs. The vector method relied on forming a hemisphere – shown below – around each point on the surface but the raster method didn’t. 

Using Vector Images

Hemisphere at a point on the surface
Hemisphere at a point on the surface (source)

The researchers utilized a vector digital elevation model (DEM), which was a form of a 3D building database. They created the DEM using the Szeged municipality data and aerial photographs that helped them determine the heights of buildings.

Recall the SVF’s definition? Well, the hemisphere that was considered in the ratio’s denominator is usually drawn at different positions based on the resolution. In the study, the researchers found a 5 m resolution to be appropriate, given that it would enable them to “obtain continuous spatial distribution of the SVF.” Additionally, it would allow them to see the primary characteristics of the space.

As a result, a total of 1,030,000 points resulted, but the figure was further reduced to 897,188 points because buildings had overlapped some points, making deletion necessary. The SVF for each of the 897,188 points was calculated, using a computer, with the exercise lasting for more than 1 week (it didn’t exceed 2 weeks, though). Given that each of the 103 cells had a number of points, each cell’s averages were computed.

But how was the SVF for a single point calculated? The existence of angles β and α – which defined each slice (S) – point to trigonometry. In this regard, the view factor for each slice was calculated using the formula below:

VF=sin2360, where β was the angle of elevation while α is the angle of rotation.

It was observed that the smaller the angle of rotation was, the more accurate the SVF was. In order to obtain the SVF, though, all the VF values for all the slices in the hemisphere were added, and the resultant figure was subtracted from 1. These SVF values for all the points in a particular cell were then added and the average computed to obtain the cell’s SVF.

The image below shows the distribution of the points over a small portion of the study area. Being a vector image, the building’s outlines are clearly drawn, and the representation is more of a CAD drawing than a photographed image.

Vector image of spatially distributed points
Vector image of spatially distributed points source

Using Raster Images

The researchers obtained the raster images, used in this second method, from the local governmental vector database. They reckoned that the municipality’s raw data was both highly accurate and precise and would, therefore, produce a detailed raster image. As such, the raster images (DEM) obtained were converted from vector images.

Gal, Lindberg, and Unger observed that the raster model’s quality was dependent on the pixel size of the model and whether the vector-based information was detailed enough. The former is consistent with our recommendation that photographs should be of good quality. In raster photographs, quality depends on the number of pixels per inch (PPI) – resolution. The more the PPI, the higher the quality.

Upon converting the 3D vector database to a raster DEM, the result was the image below.  

Raster DEM
Raster DEM source.

This method relied on the shadow casting algorithm that was developed in 1999. The algorithm depends on two parameters: the azimuth and altitude of the sun to generate 1000 shadow maps. In each map, the azimuth and altitude are selected randomly. But how do the shadow maps come to be?

In the DEM, the x, y, and z components are defined using the azimuth and altitude. It’s common knowledge that in the presence of light (in this case, the sun), an object will have a shadow. Depending on the sun’s altitude, the shadow will vary in size. It is possible to obtain the shadow volume by moving the raster DEM, in processes mathematically referred to as translation and reduction, since doing so changes the x, y, and z components.

The process is much more elaborate than this, but it yields the raster image below. In this case, the original DEM is subtracted from the shadow volume obtained after several translations and reductions in order to “reduce the shadow volume to an actual map of shadows on the roofs and the ground.” In this regard, the image on the right (below) represents a map of the actual shadows on the ground or the roofs.

The SVF was calculated from the shadow-casting algorithm. Like the vector image method, the SVF values used were the averages of those obtained from 1000 different shadow images. The results were validated using the vector method. The SVF values from the raster image method were found to be similar to those obtained from the vector method.

A section of the shadow map
A section of the shadow map source.

From the discussion above, both vector and raster images can be used in urban climate studies to determine how the built environment contributes to the urban heat island phenomenon in urban areas. The approaches taken to come up with the sky view factors were different for raster and vector images, but the underlying fact is that both methods yielded similar results. Another important fact is that raster and vector data can be used in urban climate studies.

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