Principal curvature-based region detector

The principal curvature-based region detector, also called PCBR is a feature detector used in the fields of computer vision and image analysis. Specifically the PCBR detector is designed for object recognition applications. The principal curvature-based region detector, also called PCBR is a feature detector used in the fields of computer vision and image analysis. Specifically the PCBR detector is designed for object recognition applications. Local region detectors can typically be classified into two categories: intensity-based detectors and structure-based detectors. From the detection invariance point of view, feature detectors can be divided into fixed scale detectors such as normal Harris corner detector, scale invariant detectors such as SIFT and affine invariant detectors such as Hessian-affine. The PCBR detector is a structure-based affine-invariant detector. In many object recognition tasks, within-class changes in pose, lighting, color, and texture can cause considerable variation in local intensities. Consequently, local intensity no longer provides a stable detection cue. As such, intensity-based interest operators (e.g., SIFT, Harris-Affine)–and the object recognition systems based on them–often fail to identify discriminative features. An alternative to local intensity cues is to capture semi-local structural cues such as edges and curvilinear shapes. These structural cues tend to be more robust to intensity, color, and pose variations. As such, they provide the basis for a more stable interest operator, which in turn improves object recognition accuracy. PCBR detector was developed to exploit these more reliable image structural cues. As a structure-based detector, PCBR does not use edges, instead, it uses curvilinear structures, also called ridges. Curvilinear structures detection generates a single response for both lines and edges, producing a clearer structural sketch of an image than is usually provided by the gradient magnitude image. The Steger's algorithm is modified to get the curvilinear images. As only the first step of this algorithm is used which is to calculate the principal curvature images, the principal curvature is adopted as the name of this detector. To get the principal curvature, the Hessian matrix is calculated: H ( x ) = [ L x x ( x ) L x y ( x ) L x y ( x ) L y y ( x ) ] {displaystyle H(mathbf {x} )={egin{bmatrix}L_{xx}(mathbf {x} )&L_{xy}(mathbf {x} )\L_{xy}(mathbf {x} )&L_{yy}(mathbf {x} )\end{bmatrix}}} where L a a ( x ) {displaystyle L_{aa}(mathbf {x} )} is second partial derivative of the image evaluated at point x in the a {displaystyle a} direction and L a b ( x ) {displaystyle L_{ab}(mathbf {x} )} is the mixed partial second derivative of the image evaluated at point x in the a {displaystyle a} and b {displaystyle b} directions. The maximum and minimum eigenvalues of this matrix form two images which correspond to white lines on black background and black lines on white background. To make this detector scale invariance and improve the detection robustness, the process of David Lowe's SIFT detector is simulated to detect principal curvilinear structure in scale space. Local maximum images of principal curvature values are used to define regions.