Create steps_shadow_qaul_algo.txt

steps_shadow_qaul_algo.txt

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+Algorithm: Shadow Classification for Vehicle
+Input:
+
+A mask image of the vehicle (binary values of 0 and 255).
+Four keypoints corresponding to the bottom-most points of the vehicle's tires: front-left, front-right, rear-left, rear-right. These are crucial for shadow generation.
+Steps:
+Step 1: Input and Preprocessing
+Take the vehicle mask (M) as input, which is a binary matrix where each pixel has a value of 0 (background) or 255 (vehicle).
+The four keypoints (K_fl, K_fr, K_rl, K_rr) are provided as pixel coordinates:
+𝐾
+𝑓
+𝑙
+=
+(
+𝑥
+𝑓
+𝑙
+,
+𝑦
+𝑓
+𝑙
+)
+K 
+fl
+​
+ =(x 
+fl
+​
+ ,y 
+fl
+​
+ )
+𝐾
+𝑟
+𝑙
+=
+(
+𝑥
+𝑟
+𝑙
+,
+𝑦
+𝑟
+𝑙
+)
+K 
+rl
+​
+ =(x 
+rl
+​
+ ,y 
+rl
+​
+ )
+Step 2: Calculate the Angle Between Keypoints
+Use the front-left and rear-left keypoints to calculate the angle the vehicle makes with the x-axis:
+
+𝜃
+=
+tan
+⁡
+−
+1
+(
+𝑦
+𝑓
+𝑙
+−
+𝑦
+𝑟
+𝑙
+𝑥
+𝑓
+𝑙
+−
+𝑥
+𝑟
+𝑙
+)
+θ=tan 
+−1
+ ( 
+x 
+fl
+​
+ −x 
+rl
+​
+ 
+y 
+fl
+​
+ −y 
+rl
+​
+ 
+​
+ )
+This gives the angle 
+𝜃
+θ in radians, which indicates how much the vehicle is inclined relative to the x-axis.
+Step 3: Rotate the Mask
+Rotate the mask M clockwise by angle 
+𝜃
+θ to align the vehicle along the x-axis. The rotation can be done using a rotation matrix or a simple image rotation function (e.g., using OpenCV's warpAffine).
+
+Mathematically, each pixel's new coordinates after rotation:
+
+(
+𝑥
+′
+𝑦
+′
+)
+=
+(
+cos
+⁡
+(
+𝜃
+)
+sin
+⁡
+(
+𝜃
+)
+−
+sin
+⁡
+(
+𝜃
+)
+cos
+⁡
+(
+𝜃
+)
+)
+(
+𝑥
+𝑦
+)
+( 
+x 
+′
+ 
+y 
+′
+ 
+​
+ )=( 
+cos(θ)
+−sin(θ)
+​
+  
+sin(θ)
+cos(θ)
+​
+ )( 
+x
+y
+​
+ )
+Step 4: Recalculate Rear-left Keypoint
+After the mask rotation, recalculate the new position of the rear-left keypoint. Apply the same rotation transformation to get the new coordinates:
+
+𝐾
+𝑟
+𝑙
+′
+=
+(
+𝑥
+𝑟
+𝑙
+′
+,
+𝑦
+𝑟
+𝑙
+′
+)
+K 
+rl
+′
+​
+ =(x 
+rl
+′
+​
+ ,y 
+rl
+′
+​
+ )
+Where:
+
+𝑥
+𝑟
+𝑙
+′
+=
+𝑥
+𝑟
+𝑙
+cos
+⁡
+(
+𝜃
+)
+−
+𝑦
+𝑟
+𝑙
+sin
+⁡
+(
+𝜃
+)
+x 
+rl
+′
+​
+ =x 
+rl
+​
+ cos(θ)−y 
+rl
+​
+ sin(θ)
+𝑦
+𝑟
+𝑙
+′
+=
+𝑥
+𝑟
+𝑙
+sin
+⁡
+(
+𝜃
+)
++
+𝑦
+𝑟
+𝑙
+cos
+⁡
+(
+𝜃
+)
+y 
+rl
+′
+​
+ =x 
+rl
+​
+ sin(θ)+y 
+rl
+​
+ cos(θ)
+Step 5: Crop the Mask
+Center the cropped region around the new rear-left keypoint 
+𝐾
+𝑟
+𝑙
+′
+K 
+rl
+′
+​
+  and crop a square of size 
+(
+𝑤
+𝑖
+𝑑
+𝑡
+ℎ
+=
+ℎ
+𝑒
+𝑖
+𝑔
+ℎ
+𝑡
+=
+100
+ pixels
+)
+(width=height=100 pixels).
+
+Crop dimensions:
+
+𝑥
+𝑚
+𝑖
+𝑛
+=
+𝑥
+𝑟
+𝑙
+′
+−
+50
+,
+𝑥
+𝑚
+𝑎
+𝑥
+=
+𝑥
+𝑟
+𝑙
+′
++
+50
+x 
+min
+​
+ =x 
+rl
+′
+​
+ −50,x 
+max
+​
+ =x 
+rl
+′
+​
+ +50
+𝑦
+𝑚
+𝑖
+𝑛
+=
+𝑦
+𝑟
+𝑙
+′
+−
+50
+,
+𝑦
+𝑚
+𝑎
+𝑥
+=
+𝑦
+𝑟
+𝑙
+′
++
+50
+y 
+min
+​
+ =y 
+rl
+′
+​
+ −50,y 
+max
+​
+ =y 
+rl
+′
+​
+ +50
+Step 6: Find Bottom-most Point
+In the cropped mask, identify the bottom-most point 
+𝐵
+=
+(
+𝑥
+𝑏
+,
+𝑦
+𝑏
+)
+B=(x 
+b
+​
+ ,y 
+b
+​
+ ), where the pixel value is 255.
+
+𝑦
+𝑏
+=
+max
+⁡
+{
+𝑦
+∣
+𝑀
+(
+𝑥
+,
+𝑦
+)
+=
+255
+}
+y 
+b
+​
+ =max{y∣M(x,y)=255}
+Step 7: Calculate Distance
+Compute the Euclidean distance 
+𝐷
+D between the new rear-left keypoint 
+𝐾
+𝑟
+𝑙
+′
+K 
+rl
+′
+​
+  and the bottom-most point 
+𝐵
+B:
+
+𝐷
+=
+(
+𝑥
+𝑟
+𝑙
+′
+−
+𝑥
+𝑏
+)
+2
++
+(
+𝑦
+𝑟
+𝑙
+′
+−
+𝑦
+𝑏
+)
+2
+D= 
+(x 
+rl
+′
+​
+ −x 
+b
+​
+ ) 
+2
+ +(y 
+rl
+′
+​
+ −y 
+b
+​
+ ) 
+2
+ 
+​
+ 
+Step 8: Shadow Classification
+If 
+𝐷
+>
+50
+D>50 pixels, classify the shadow as bad (unrealistic or incorrect). Otherwise, classify the shadow as good.
+Mathematical Justification:
+Rotation is used to align the vehicle to the x-axis, ensuring that the keypoints are more easily analyzed.
+The distance threshold of 50 pixels helps determine if the shadow is too far from the vehicle’s edge (indicating that it might be unrealistic).
+This refined version adds mathematical clarity to each step and ensures the algorithm is robust in detecting unrealistic shadows.