Weed infestation in a cotton field. Source: Bogiani (Embrapa), 2017

Infestation of Ipomoea sp. in a sugarcane field. Source: Hirata (Campos e Negócios), 2016

How are we controlling weeds?

Source: Comas (Embrapa), 2016

Herbicide resistance. Source: https://www.upherb.com.br/

Weed scouting in a sugarcane field. Source: Christoffoleti, 2019 (https://www.grupocultivar.com.br/)

Okay! But what about Poland?

• 26 cases of weed resistance to herbicides
• 12 on winter wheat!

Source: Heap, 2021 (http://www.weedscience.org/)

And what should we do about it?

Source: Shawn, 2005 (Front. Ecol. Environ.)

And to automatically discriminate monocots and dicots:

Source: Da Silva, 2019 (J. Appl. Remote Sens.)

Field data

• 13 plots (20 x 20 m)
• Manual identification of weed species and density
• Flight height: 45 m (1024 x 1024 px, ~3cm/px)
• 80 spectral bands (500-900 nm)

(Pre)processing

• Reflectance conversion

\(R = \frac{V_{Raw} - V_D}{V_W - V_D}\)

• Segmentation of vegetation/background

\(OSAVI = (1+Y)\frac{R_{800} - R_{670}}{R_{800} + R_{670} + Y}\)

Otsu (Adaptive) thresholding

Detection of crop rows

Seeder coordinates or… Segmented image \(\rightarrow\) Image thinning \(\rightarrow\) (Morph. operation) \(\rightarrow\) Hough transform

Superpixels

Spectral + spatial info.

SLIC (Simple Linear Iterative Clustering)

SLIC

• K-means generalization (Achanta et al., 2012)
• K centroids (from the grid)
• Based on distances between regional (\(2S \times 2S\)) pixels and a centroid

\(D = \sqrt{d_c^2 + (d_s/S)^2 m^2}\)

where \(d_c\) is spectral-based and \(d_s\) is spatial-based (Euclidean, norm-2) distances; \(m\) is a compactness constant.

FD-SLIC

Fractional distance between the pixel \(x\) and the \(j\)-th surrounding pixel:

\(F_{j,x} = \frac{\sqrt{ \sum_{i, i \neq j}^n d_{i,x} }}{\sqrt{d_{j,x} + 1}}\)

where \(d\) is the Euclidean distance in the hyperspectral space.

A modified SLIC

\(d\) \(\rightarrow\) \(D^2\) (Mahalanobis distance)

\(D^2_{ii'} = ({\bf x}_i - {\bf x}_{i'})^T \Sigma^{-} ({\bf x}_i - {\bf x}_{i'})\)

where \(\Sigma\) is the covariance matrix of spectral bands.

Relative importance of spectral bands for discriminating superpixels

Mahalanobis generalized distance \(\rightarrow\) Singh (1981) criterion:

\(S_{.j} = \sum_{i=1}^{n-1} \sum_{i'>i}^{n} (x_{ij} - x_{i'j}) ({\bf x}_i - {\bf x}_{i'})^T {\Sigma}_{.j}^{-}\)

\(\frac{S_{.j}} {\sum_{j=1}^{p} S_{.j}} \in [0, 1]\)

under \(\sum_{j=1}^{p} S_{.j} = \sum_{i=1}^{n-1} \sum_{i'>i}^{n} D_{ii'}^2\)

Weed classification

• Spuperpixel labeling
• Spx. partitions: Training (70%) x Validation (30%)
• Machine Learning: SVM x Mixture discriminant analysis
• Apparent error rate
• Field validation
• (Deploy the model)

Computational tools