Fig. 1. flowchart of ADGMC

Fig. 2. target near the highlighted edge

Fig. 3. Gradient detection structure of each associated direction (a) is the upper associate left, (b) is the upper associate right, (c) is the right associate lower, (d) is the lower associate left

Fig. 4. Infrared small target near the highlighted edge (a) Local enlargement，(b) Pixel schematic

Fig. 5. structure of left associate upper direction，with size of 7*7

Fig. 6. Comparison before and after nonlinear mapping (a) original infrared image，(b) ADG，(c) 3D grayscale view of ADG，(d)ADGmappedx,y，(e) 3D grayscale view of ADGmappedx,y

Fig. 7. structure of mean contrast filter

Fig. 8. test image

Fig. 9. Comparison of assoicated directional gradient and single directional gradient (a) left gradient，(b) upper gradient，(c) down gradient，(d) right direction，(e) single-direction gradient product，(f) mesh of (e)，(g) left-upper gradient，(h) upper-right gradient，(i) down-left gradient，(j) right-down gradient，(k) associated directional gradient product，(l) mesh of (k)

Fig. 10. IR image with isolated noise added

Fig. 11. MC calculation process diagram (a) left mean contrast; (b) upper mean contrast; (c) down mean contrast; (d) right mean contrast; (e) final MC

Fig. 12. Diagram of ADGMC calculation process (a) grayscale diagram of MC; (b) mesh of MC; (c) grayscale diagram of ADG; (d) mesh of ADG; (e) grayscale diagram of ADGMC; (f) mesh of ADGMC

Fig. 13. top to bottom: Data1-Data4 (a) original image，(b)ADG，(c)ADGmapped，(d) MC，(e) ADGMC，(f) Result(The top right corner is a zoomed-in view near the small target)

Fig. 14. Part of Data5 processing process (a) original image，(b)ADG，(c)ADGmapped，(d) MC，(e) ADGMC，(f) Result(The top right corner is a zoomed-in view near the small target)

Fig. 15. Data1 to Data5 corresponding ROC curves (a) Data 1，(b) Data 2，(c) Data 3，(d) Data 4