Learning SURF Cascade for Fast and Accurate Object DetectionSupplementary materials

Jianguo Li, Yimin ZhangIntel Labs China

1. Spatial Cell ConfigurationFigure 1 depicts spatial configuration of SURF patches.

Figure 1. Possible spatial cell configuration of local patches. Eachlocal patch has 4 same-size cells, but these cells may be in differentforms. From left to right, 2×2 cells, 4×1 cells, 1×4 cells.

2. L2HYS Feature NormalizationGiven a feature vector v = (v1, . . . , vd), the L2Hys nor-

malization works like below

(1) L2-normalization: ui = vi/√∥v∥22 + ϵ, where ϵ is

small positive value to avoid dividing by zero;

(2) Clipping ui with the following rule

ui =

θ if ui > θ−θ if ui < −θui otherwise,

where θ = 2/√d empirically 1.

(3) Re-normalization: v′i = ui/√∥u∥22 + ϵ, and v′ =

(v′1, . . . , v′d) is the L2Hys normalization result.

3. Results on UMass FDDBFigure 2 depicts ROC curve from both discrete score and

continuous score on FDDB benchmark by SURF cascade.1After normalization, assuming |ui| < θ, thus

∑u2i < dθ2. ui

can be viewed as samples for a Gaussian variable, the variance σ2 =(∑

u2i )/d = 1/d < θ2. As is known, about 95% samples from the

Gaussian distribution fall within the range [−2σ, 2σ]. Therefore, we de-fine θ = 2σ = 2/

√d.

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SURF_Front_AB [19]VJGPR [16]

Viola-Jones [21]Mikolajaczyk et al [25]

Subburaman [33]

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SURF_Front_AB [19]VJGPR [16]

Viola-Jones [21]Mikolajaczyk et al [25]

Subburaman [33]

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Figure 2. (a) Discrete score ROC curves and (b) Continuous scoreROC curves for different methods on UMass FDDB dataset.

4. Example Results of Face and Car DetectionFigure 3 depicts some face detection results on FDDB

and CMU+MIT datasets. Figure 4 depicts some car detec-tion results on TUGRAZ dataset.

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Figure 3. Example detection results on CMU+MIT (a) and UMass FDDB datasets (b,c,d).

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(d) (e) (f)

Figure 4. Some car detection results on TUGRAZ dataset.