Line-by-Line Response of Copilot While Reasoning
• • • • • • • • • •
Assessing request specifics Piecing together accuracy Analyzing image colors Analyzing pixel distances
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Coding and executing Identifying the error Coding and executing Mapping out positions Trying another way Coding and executing Adjusting detection Coding and executing
Figure 1. Original Image of Data
Coding and executing Refining thresholds Coding and executing
Weighing options
Refining the approach Applying color-based segmentation
Map out results
Pulling together visual tools
Taking a closer look
Copilot Response: Got it. I’ll treat the yellow square as the aim point (target) and the pink squares as hits. Using your photo, I measured the centers of the squares, converted pixels to inches by calibrating to a known ½-inch square, and computed signed left-right (LR), up-down (UD), and radial miss distance (RMD) for each hit. I also calculated CEP (Circular Error Probable). The Results Scale used. ~58.88 px/in (average of detected square side lengths; assumes the camera plane is close to parallel to the floor and mild perspective distortion). Sign convention. LR > 0 = right of target, LR < 0 = left; UD > 0 = above target, UD < 0 = below. Method (brief) 1. Locate squares. Detect bright color outliers vs. the gray carpet, then filter to squarelike connected components. 2. Identify target. Among the detected components, the one with the highest (G−B) and the highest (R) is the yellow square; the rest are pink (hits). 3. Calibrate. Convert pixel distances to inches using the average side length of the squares (0.5 in) . 4. Compute metrics. For each hit, compute LR, UD, and RMD relative to the target; compute MPI and CEP (median radial). Scatter plot (inches; origin at target center)
Source. Author
Figure 2. What Copilot Saw: Scatter of Hit Offsets (Inches)
• Axes: +x is right, +y is up.
• Gold square: target center.
• Pink dots: hits (numbered).
Miss Distances per Hit (Inches)
1 2 3 4 5 6 7
+1.28 +2.87 −2.26 −2.44 −2.28 +3.07 +2.52
+6.45 +5.34 +5.18 +3.80 +3.54 +2.87 −0.46
6.58 6.06 5.65 4.52 4.21 4.20 2.56
Source. Author
Figure 3. How Copilot Analyzed Data Scatter Plot of Hits Relative to Target Center
Scatter Plot of Hits Relative to Target Center • Dashed orange circle. CEP about the target (median radial distance to the aim point). • Dotted navy circle. CEP about the MPI (median radial distance to the mean point of impact ). • Navy dot. MPI (mean of hit locations). CEP and Bias • CEP about the target (aim point): 4.52 in (Median of distances from each hit to the target.) • Mean Point of Impact (MPI) relative to target: (0.39 in right, 3.82 in up) (Average LR/UD of all hits; this is the systematic bias.) • CEP about the MPI: 2.84 in (Median of distances from each hit to the MPI—reflects the precision independent of bias.) These two CEPs answer different questions: • CEP\@Target (4.52”) = “What radius around the aim point contains 50% of shots?” (includes bias + dispersion) • CEP\@MPI (2.84”) = “What radius around the average impact point contains 50% of shots?” (dispersion only)
Source. Author
34 DEFENSE ACQUISITION MAGAZINE | SEPTEMBER –OCTOBER 2026
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