
APHELION™ VERSION 3.X
Aphelion Developer Measurement List
Regions
 AREA
 The calibrated area of the region.
 BOUNDING_RECT_FILL
 PIXEL_COUNT / (HEIGHT *WIDTH). This measure is 1.0 for a perfect rectangle and approaches zero for very sparse structures.
 BR_TO_PERIMETER
 PERIMETER / (2 * HEIGHT + 2 * WIDTH). This measure is 1.0 for a convex region, larger for regions with boundaries which double back on themselves.
 CENTROID.[X,Y]
 The center of mass of the region, the average location of the pixels. Pixels are considered to have area 1.0, covering the entire int32 of the coordinate system. Thus, the centroid of a single pixel will appear at the center of the pixel.
 COMPACTNESS
 16*PIXEL_COUNT / (PERIMETER ** 2). This measure is 1.0 for a perfect square, smaller for shapes with irregular boundaries. This is discussed in the literature as maximal for a circle, but that is the case only for continuous geometry, and our representation is discrete.
 ELONGATION
 The difference between the lengths of the major and minor axes of the best ellipse fit, divided by the sum of the lengths. This measure is zero for a circle and approaches 1.0 for an ellipse which is long and narrow.
 HEIGHT
 The height of the region. Calibrated.
 INTENSITY
 The minimum, maximum, mean, and standard deviation of the pixel values within the region.
 LOG_HEIGHT_TO_WIDTH
 logl0(HEIGHT/WIDTH). This gives a symmetric measure of aspect ratio.
 MAJOR_AXIS
 The direction of the longest projection.
 MBR_ANGLE
 The angle of the major, or longer, axis of the minimum bounding rectangle.
 MBR_CENTER.[X,Y]
 The coordinates of the center of the minimum bounding rectangle.
 MBR_DIAMETERS
 An array of Feret diameters.
 MBR_FILL
 The ratio of PIXEL_COUNT to the area of the minimum bounding rectangle.
 MBR_HEIGHT
 The height of the minimum bounding rectangle.
 MBR_POLYGON
 A 4side polygon representing the oriented minimum bounding rectangle. This is useful for visualizing the MBR.
 MBR_WIDTH
 The width of the minimum bounding rectangle.
 NUMBER_OF_BLOBS
 The number of 4way connected groups of pixels in the region. If, for example, we represented the white squares of a chess board in a region, this measure would be 32.
 NUMBER_OF_HOLES
 The number of 4way connected groups of off pixels completely surrounded by on pixels in the region. A donut shape would have a value of 1. The white squares of a chess board would have a value of 18.
 PERIMETER
 The number of occurrences of a pixel in the region that is 4way adjacent to pixel not in the region. Each boundary is counted once, so a single pixel region has a perimeter of four. Calibrated.
 PIXEL_COUNT
 The number of pixels in the region.
 REGION_EXTENTS.LL.[X,Y]
 The lowest coordinates of the region.
 REGION_EXENTS.UR.[X,Y]
 The highest coordinates of the region.
 WIDTH
 The calibrated width of the region.


Color Attributes
 RED
 The minimum, maximum, mean, and standard deviation of the values of the red band within the region.
 GREEN
 The minimum, maximum, mean, and standard deviation of the values of the green band within the region
 BLUE
 The minimum, maximum, mean, and standard deviation of the values of the blue band within the region
 EXRED
 (2 * Red)  Green Blue. A good indication of whether the region appears red.
 EXGREEN
 (2* Green)  Red  Blue. A good indication of whether the region appears green.
 EXBLUE
 (2* Blue) Red Green. A good indication of whether the region appears blue.
 HUE
 The minimum, maximum, mean, and standard deviation of the hue values at each pixel within the region.
 SATURATION
 The minimum, maximum, mean, and standard deviation of the values of the saturation at each pixel within the region.


Points and Edgels
 ANGLE
 The angles, in radians, of the pixellength edgel.
 EDGEL.X
 The X coordinate of the center of the edgel.
 EDGEL.Y
 The Y coordinate of the center of the edgel.
 MAGNITUDE
 The strength of the edgel.


Lines
 DISPERSION
 
 liNE.P1.X
 The X coordinate of the first endpoint of the line.
 liNE.P1.Y
 The Y coordinate of the first endpoint of the line.
 liNE.P2.X
 The X coordinate of the second endpoint of the line.
 liNE.P2.Y
 The Y coordinate of the second endpoint of the line.
 liNE_ANGLE
 The angle, in radians, of the line.
 liNE_CONTRAST
 The average change in intensity across the line.
 liNE_INTENSITY
 The average intensity of the pixels under the line.
 liNE_MIDPOINT.[X,Y]
 The coordinates of the midpoint in the line segment.
 liNE_MAX_T
 The maximum T value in polar coordinates.
 liNE_MIN_T
 The minimum T value in polar coordinates.
 liNE_RHO
 The perpendicular distance of the line from the origin.
 liNE_THETA
 The angle of the line in polar coordinates.
 liNE_LENGTH
 The length of the line in pixels.
 PIXEL_COUNT
 The number of pixels in the support region.
 REGION
 The “support region”: the pixel under the line.


Rectangles
 PIXEL_COUNT
 The number of pixels in the underlying region.
 RECTANGLE.LL.X
 The lowest X value of the rectangle.
 RECTANGLE.LL.Y
 The lowest Y value of the rectangle.
 RECTANCLE.UR.X
 The highest X value of the rectangle.
 RECTANGLE.UR.Y
 The highest Y value of the rectangle.


Chains
 CHAIN.EXTENTS.LL.X
 The lowest X value of the points in the chain.
 CHAIN.EXTENTS.LL.Y
 The lowest Y value of the point in the chain.
 CHAIN.EXTENTS.UR.X
 The highest X value of the points in the chain.
 CHAIN.EXTENTS.UR.Y
 The highest Y value of the points in the chain.
 CHAIN.FLAGS
 2 if the chain is open, 0 otherwise.
 CHAIN.NUMPOINTS
 The number of points in the chain.
 MEMBER_EDGELS
 The lowest edgel objects that make up the chain.


Polygons
 AREA
 Calibrated area of the polygon.
 POLYGON.EXTENTS.L.LX
 The lowest X value of the polygon.
 POLYGON.EXTENTS.LL.Y
 The lowest Y value of the polygon.
 POLYOON.EXTENTS.UR.X
 The highest X value of the polygon.
 POLYGON.EXTENTS.UR.Y
 The highest Y value of the polygon.
 POLYGON.NUMPOINTS
 The number of points in the polygon.



