Image Expression Null Value Handling

• The entire expression is one single expression resulting in one single value.

• Everything is an expression and produces one single value. So, even an if then else is just one expression resulting in one single value. Therefore, you can sum the results of two separate if then elses like (if the else) + (if then else). Since even the test clause of an if then else is an expression, you can also replace that with another if then else. Example: if (if i1 > 0 then 1 else i2) then i2 else 1 + i3

• The if then else test assumes that 0 is false and any non-zero value is true.

• Every time the expression being evaluated results in null, the entire expression becomes null. So, i1 + null will always be null since something + null is always null.

• The only operators that can contain the destructive power of a null value are isnull( expression ) or expression1 ? expression2:
  1. isnull( expression ) evaluates the expression and results 1 if the expression evaluates to null, and 0 otherwise.
  2. expression1 ? expression2 evaluates the expression1 and, if the result is non-null, returns that value. Otherwise, it evaluates expression2 and returns the resulting value as its own result.

• Null can come from an image, but it can also be produced by some other events, such as dividing by zero, failing to find a key in a lookup table etc.

• If the if then else test evaluates to null, the entire if then else evaluates to null. Example:

• (if (i1/3 > 9) then i2 else 1 + i3) + 10:
  1. If i1 is null, i1/3 is also null, and i1/3 > 9 also becomes null. Therefore, the if then else test is null and the entire if then else is null.
  2. Now, null is being added to 10, and that also becomes null.

• ( (if (i1/3 > 9) then i2 else 1 + i3) + 10 ) ? 20 – Note that we are using the operator ? now:
  1. If i1 is null, i1/3 is also null, and i1/3 > 9 also becomes null. Therefore, the if then else test is null and the entire if then else is null.
  2. Then, null is being added to 10, and that also becomes null.
  3. Now, null is being caught by the expression null ? 20, since the if then else + 10 is null, and the result is 20.

The null evaluation mechanism allows us to write short expressions like i1 + 10 to add 10 to every valid cell of the i1 map, or i1 * i2 to multiply two maps. If one of the map cells is null, the result is null, so in the last example, we are basically just multiplying the corresponding cells where the two values are valid: everything else will be null.

If we want to treat all null values as values 1s, in the previous expression, we can write (i1 ? 1) * (i2 ? 1). We can also use the more complicated form using the if then else to achieve the same result:

(if isnull(i1) then 1 else i1) * (if isnull(i2) then 1 else i2),

or

if isnull(i1) and isnull(i2) then 1
else if not isnull(i1) and not isnull(i2) then i1*i2
else if not isnull(i1) and isnull(i2) then i1
else i2

If you need to retrieve the number corresponding to a image null value, you can use the null( iX ) expression. For instance, null(i1) returns the number corresponding to the null value of image i1. So if, so some reason, you need to retrieve the image value or its corresponding numeric null value, you can use i1 ? null(i1) or if isnull(i1) then null(i1) then i1. Note that null(i1) is very different from expression null, since null(i1) always returns a valid numeric value and null returns a special construct that, if not contained, invalidates the expression evaluation producing null as a result.