Individual Measurements

For an introduction: Image Analysis

Most of these algorithms have a field to set one or several input measurements.

Filtering objects in an image

The object filtering algorithms remove or preserve shapes from a binary or label image according to measurement criteria.

The following algorithms filter an image with a criterion defined in a formula:

• LabelFiltering
• LabelFilteringAnalysis
• FilterAnalysis

For example, to define a filter preserving particles having a diameter lower than 50, in the coordinate system defined by the image calibration, in C#:

      labelFilter.inputFilter = NativeMeasurements.EqDiameter.name + "< 50"
      

Custom Formula syntax

A custom formula syntax is checked by several ImageDev algorithms:

• ImageFormula
• Individual analysis with custom measurements
• Object filtering algorithms

Custom measurement formula and custom filter formula follow the same basic rules and can use the same set of predefined functions. Custom measurement formula must be a numerical value, whereas custom filter formula must be a logical value to be accepted.
Formula can be composed of constants, operators, functions, and variables (native measurements and custom measurements).

Remarks:

• The following (unless specified) constants, operators, functions, and variables are case-insensitive and can be used both with custom measurements and custom filters.
• The following (unless specified) operators and functions are insensitive to spaces. Constants and variables must not be directly attached to alpha numerical symbols.

The following syntax can be used to define a formula:

Basic operators

• (): brackets allow you to group elements and to modify operator precedence
  example: (2 + 3)*4
• +: unary arithmetic operator [plus]
  example: + a
• -: unary arithmetic operator [minus]
  example: - b
• +: binary arithmetic operator [plus]
  example: a + b
• -: binary arithmetic operator [minus]
  example: a - b
• *: binary arithmetic operator [multiply]
  example: a * b
• /: binary arithmetic operator [divide]
  example: a / b
  remark: a division by 0 returns the value 0 in order to avoid exceptions.
• **: binary arithmetic operator [power]
  example: a ** b
• !: unary logical operator [not]
  example: !(a> b)
• && or And: binary logical operator [and]
  example: (a > b) && (a < c)
  example: (a > c) And (a < c)
  remark: And operator must not be directly attached to alpha numerical symbols.
• || or Or: binary logical operator [or]
  example: (a > b) || (a < c)
  example: (a > b) Or (a < c)
  remark: Or operator must not be directly attached to alpha numerical symbols.
• ==: comparison operator (logical and arithmetic) [equal]
  example: a==b
  example: true==true
• !=: comparison operator (logical and arithmetic) [different]
  example: a != b
  example: true != false
• <: arithmetic comparison operator [strictly inferior]
  example: a < b
• <=: arithmetic comparison operator [less]
  example: a<= b
• >: arithmetic comparison operator [strictly superior]
  example: a > b
• >=: arithmetic comparison operator [superior]
  example: a >= b

Constant values

• Pi: $\pi$, the pi constant
  example: 3 * Pi
• E: the Euler's constant
  example: 2 * E
• True: the true boolean value
  example: (3< Pi)==True
• False: the false boolean value
  example: (3> Pi)==False
• NbFeret: distribution size for Feret measurements
  example: 3*NbFeret
• gx, gy and gz: image X, Y, and Z dimensions
  example: 3*gx
  remark: not available for custom filters
• cx, cy and cz: pixel real size according to calibration
  example: 3*cx
  remark: not available for custom filters

Functions

• Abs: absolute value of a numerical value
  example: Abs(a)
• Sqrt: square root value of a numerical value
  example: Sqrt(a)
  remark: a must be positive or null
• Exp: exponential value of a numerical value
  example: Exp(a)
• Log: natural logarithm value of a numerical value
  example: Log(a)
  remark: a must be strictly positive
• Cos: cosine value of a numerical value
  example: Cos(a)
• Sin: sine value of a numerical value
  example: Sin(a)
• Tan: tangent value of a numerical value
  example: Tan(a)
• ACos: arccosine value of a numerical value
  example: ACos(a)
  remark: a must be within the range [-1, 1]
• ASin: sine arcvalue of a numerical value
  example: ASin(a)
  remark: a must be within the range [-1, 1]
• ATan: arctangent value of a numerical value
  example: ATan(a)
• ATan2: arctangent value of a 2d point
  example: ATan2(y, x)
• CosH: hyperbolic cosine value of a numerical value
  example: CosH(a)
• SinH: hyperbolic sine value of a numerical value
  example: SinH(a)
• TanH: hyperbolic tangent value of a numerical value
  example: TanH(a)
• Min: retrieve minimum value of a variable sized set of numerical values
  example: Min(a, b, c, d)
• Max: retrieve maximum value of a variable sized set of numerical values
  example: Max(a, b, c, d, e)
• Avg: retrieve mean value of a variable sized set of numerical values
  example: Avg(a, b, c)
• Median: retrieve median value of a variable sized set of numerical values
  example: Median(a, b, c, d)
• Sum: compute the sum of a variable sized set of numerical values
  example: Sum(a, b, c)
• Product: compute the product of a variable sized set of numerical values
  example: Product(a, b, c, d, e)
• If: conditional evaluation of an expression
  example: If(predicat, value_true, value_false)
  remark: Each member of a conditional expression is systematically evaluated even if it is not supposed to be reached by the condition. Thus, an instruction can raise an error even if the condition is supposed to prevent invalid evaluations.
  example: If(I1< =0, 0, log(I1)) will raise an error if a voxel value is lower or equal to 0 since the log expression will be evaluated before the if statement.