三阶矩能否表示Blob偏度？OpenCV中三阶矩的获取方法

Hey there! Let's tackle your questions about image moments and blob skewness one by one.

Absolutely correct—but with a small clarification: it's the 3rd-order central moments (not raw moments) that directly map to skewness.

Skewness measures how asymmetric a blob's shape is around its centroid. Raw moments (like m03) depend on the blob's absolute position in the image, so they don't capture the inherent asymmetry. But central moments (like mu03) are calculated relative to the blob's centroid, making them perfect for quantifying left/right or up/down "lean" of the shape. When you normalize this central moment to remove scale effects (resulting in nu03), you get a scale-invariant skewness measure.

You're already on the right path using the moments() function! When you compute moments for a contour (or image), the returned Moments struct includes several third-order moment variants. Let's break down the ones you mentioned:

Moments m = moments(contour, false);

• The false flag means we use the actual pixel values of the contour (not treating it as a binary mask) to compute moments.

All three members you asked about are third-order moments, just different types:

• m.m03: 3rd-order raw moment (depends on the blob's absolute position)
• m.mu03: 3rd-order central moment (calculated relative to the blob's centroid)
• m.nu03: Normalized 3rd-order central moment (scale-invariant, since it's adjusted by the blob's area)

Let's formalize each moment type using I(x,y) to represent the pixel intensity at coordinates (x,y):

Raw Moments (m_pq) #

Raw moments use absolute coordinates. For 3rd-order moments, p + q = 3:

m_{pq} = Σ(x,y) [x^p * y^q * I(x,y)]

For m03 specifically:

m_{03} = Σ(x,y) [y³ * I(x,y)]

Central Moments (mu_pq) #

Central moments shift the coordinate system to the blob's centroid (x̄, ȳ), where x̄ = m_{10}/m_{00} and ȳ = m_{01}/m_{00} (m00 is the blob's area/zero-th moment):

μ_{pq} = Σ(x,y) [(x - x̄)^p * (y - ȳ)^q * I(x,y)]

For mu03 (y-direction 3rd-order central moment):

μ_{03} = Σ(x,y) [(y - ȳ)³ * I(x,y)]

Normalized Central Moments (nu_pq) #

These are central moments normalized by the area to eliminate scale bias:

ν_{pq} = μ_{pq} / (m_{00}^((p+q+2)/2))

For nu03:

ν_{03} = μ_{03} / (m_{00}^(2.5))

Bonus: Calculating Exact Skewness #

If you want the standard statistical skewness value, divide the central moment by the cube of the standard deviation. For the y-direction:

skew_y = μ_{03} / (σ_y³)

Where σ_y = sqrt(μ_{02}) (the standard deviation of the blob's shape in the y-direction). Alternatively, nu03 already acts as a scale-invariant skewness proxy.

内容的提问来源于stack exchange，提问作者sazr