MOPEX Online Manual

Box Outlier Detection

The fourth outlier detection method is designed to use both the temporal and spatial information like the dual outlier, but it uses the statistical analysis of the kind used by the temporal outlier. It is implemented by module Box Outlier.

Important: Using this module does not mean that MOPEX will automatically use the results for outlier detection. In order to use the results from this module, you must include the USE_BOX_OUTLIER_FOR_RMASK trigger in the namelist and set the RMask_Fatal_BitPattern to use bit 3. Note that this is not the same as setting it to a value of 3. See Appendix 2: Fatal Bit Patterns for more information.

For each mosaic pixel position, Box Outlier creates two stacks of pixel values. The first stack is the same as the one created for the regular outlier detection method. It includes pixels from each interpolated image corresponding to the mosaic pixel position. This pixel in each interpolated image will be referred to as the main pixel. In each interpolated image a box of the user defined size is created centered on the main pixel. Input parameters Box X and Box Y define the size of the box. The second stack -- the box stack -- includes pixels from the above box in each interpolated image. The values of M and σ are computer in the box stack:

M = biased_meadian(I_k)

σ = MAD(I_k) = biased_median(|I_k biased_median(I_i)|)/0.6745

The biased_median is defined as follows. If there are N pixels in the stack, then the biased median is equal to the N/2-Bias element of the stack:

biased_median(I_k) = I[N/2-Bias]

The input parameter Box Median Bias controls the value of Bias.

The product of this step is an outlier map. The pixel value O_k in an outlier map is the deviation of the pixel k in the input images from the mean M in the stack in terms of the number of standard deviations:

O_k = (I_k - M) / σ

If all the pixels in the main stack are outside of the M +/- σ range, the programs falls back on the temporal outlier method 1 using the main stack and the uncertainty images, if the latter are available.

Inclusion of the neighboring pixels allows for outlier detection, even in the case of coverage of two, where the simple temporal detection is completely powerless. Clearly, a single pixel radhit on a relatively constant background can be easily identified as outlier, even with the smallest box size of 3. However, even radhit in the shape of wide and long streaks can be successfully detected by this method owing to the Box Median Bias. Suppose, the box size is 3, so the stack consists of 18 pixels, and the size of the radhit is at least 3x3 pixels. Out of the 18 pixels 9 background pixels have values relatively close to each other. The 9 radhit pixels will in general have greater scatter, then the 9 background pixels. Because of the bias, the median will be equal to the highest value of the background pixels. The difference between the highest and the lowest values of the background pixels are expected to be smaller, than the difference between the highest value of the background pixel and the lowest value of the radhit pixels. Consequently, the biased median deviation will be equal to the difference between the highest and lowest values of the background pixels.

Figure 1: The 18 pixel values shown here are from two images and the box size of 3. The 9 lower pixel values are the background and the 9 higher pixel values are from a radhit.

Figure 2: The pixels inside the red rectangle are included in the box stack. The red rectangle is centered around the solid red pixel, which is the mosaic pixel for which the estimation is performed. The solid red pixel is part of the main stack. In the figure BOX_X = 5 and BOX_Y = 3.

Figure 3: Interpolated images (red) are stacked up and shown here in the side view. The underlying FIF grid is shown in black. The solid red pixels comprise the main stack and the solid red and pink pixels comprise the box stack. In this figure BOX_X = 3 and BOX_Y is not shown.