Signal-to-noise behavior for matches to gradient direction models of corners in images

Abstract

Gradient direction models for corners of prescribed acuteness, leg length, and leg thickness are constructed by generating fields of unit vectors emanating from leg pixels that point normal to the edges. A novel FFT-based algorithm that quickly matches models of corners at all possible positions and orientations in the image to fields of gradient directions for image pixels is described. The signal strength of a corner is discussed in terms of the number of pixels along the edges of a corner in an image, while noise is characterized by the coherence of gradient directions along those edges. The detection-false alarm rate behavior of our corner detector is evaluated empirically by manually constructing maps of corner locations in typical overhead images, and then generating different ROC curves for matches to models of corners with different leg lengths and thicknesses. We then demonstrate how corners found with our detector can be used to quickly and automatically find families of polygons of arbitrary position, size and orientation in overhead images.

Detecting polygons of variable dimension in overhead images with particle filters

“…Corners are detected at locations of strong match between pixel gradient directions and gradient directions normal to edges in models of corners and sides [6].…”

“…For each corner acuteness α in polygon model *, we search the 3D array {s(c, r, θ | α)} of corner similarities for clusters of at least m 8-connected points [c,r,θ] (say m>10) that satisfy (7) [c,r,θ ] : s(c,r,θ | α ) ≥ s min As discussed in [6], there are N θ quantized corner orientations θ. s min is either user specified or the minimum similarity over all detected corners. Only points [c,r,θ | α] that satisfy (7) are assigned cluster labels.…”

“…A similarity measure s(c, r, θ | α) ∈ [0,1] sensitive to corners of acuteness α and orientation θ at vertex pixel location [c,r] was proposed in [6]. For each corner acuteness α in polygon model *, we search the 3D array {s(c, r, θ | α)} of corner similarities for clusters of at least m 8-connected points [c,r,θ] (say m>10) that satisfy (7) [c,r,θ ] : s(c,r,θ | α ) ≥ s min As discussed in [6], there are N θ quantized corner orientations θ. s min is either user specified or the minimum similarity over all detected corners.…”

“…Weighted ensemble averages of particle tracks (the "blended" tracks in [7]) cannot be used to estimate true polygon boundaries when the distributions of particles are multi-modal -and there is no assurance that each mode will be well-sampled. Our contribution is to address these issues by using the corner similarity measure in [6] (which also contributes to particle importance weights) to form particle clusters during particle filtering. This clustering method naturally determines the correct number of clusters and does not depend on initial conditions or parameters.…”