K. Raghunath Rao

Optimal ramp edge detection using expansion matching

In practical images, ideal step edges are actually transformed into ramp edges, due to the general low pass filtering nature of imaging systems. This paper discusses the application of the expansion matching (EXM) method for optimal ramp edge detection. EXM optimizes a novel matching criterion called discriminative signal-to-noise ratio (DSNR) and has been shown to robustly recognize templates under conditions of noise, severe occlusion, and superposition. We show that our ramp edge detector performs better than the ramp detector obtained from Cannys criteria in terms of DSNR and is relatively easier to derive for various noise levels and slopes.

Optimal template matching by nonorthogonal image expansion using restoration

In this paper we present a novel approach for template matching. The basic principle is expansion matching and it entails signal expansion into a set of nonorthogonal templatesimilar basis functions. The coefficients of this expansion signify the presence of the template in the corresponding locations in the image. We demonstrate that this matching technique is robust in conditions of noise, superposition, and severe occlusion. A new and more practical discriminative signal-to-noise ratio (DSNR) for matching is proposed that considers even the filters off-center response to the template as “noise”. We show that expansion yields the optimal linear operator that maximizes the DSNR and results in a sharp response to the matched template. Theoretical and experimental comparisons of expansion matching and the widely used correlation matching demonstrate the superiority of our approach. Correlation matching (also known as matched filtering) yields broad peaks and spurious responses, both of which hamper good detection. We also show that the special case of expansion with a dense set of self-similar basis functions is equivalent to signal restoration. Expansion matching can be implemented by restoration techniques and also by our recently developed lattice architecture.

Iconic recognition with affine-invariant spectral signatures

This paper presents a new approach for object recognition using affine-invariant recognition of image patches that correspond to object surfaces that are roughly planar. A novel set of affine-invariant spectral signatures (AISSs) are used to recognize each surface separately invariant to its 3D pose. These local spectral signatures are extracted by correlating the image with a novel configuration of Gaussian kernels. The spectral signature of each image patch is then matched against a set of iconic models using multidimensional indexing (MDI) in the frequency domain. Affine-invariance of the signatures is achieved by a new configuration of Gaussian kernels with modulation in two orthogonal axes. The proposed configuration of kernels is Cartesian with varying aspect ratios in two orthogonal directions. The kernels are organized in subsets where each subset has a distinct orientation. Each subset spans the entire frequency domain and provides invariance to slant, scale and limited translation. The complete set of orientations is utilized to achieve invariance to rotation and tilt. Hence, the proposed set of kernels achieve complete affine-invariance.

Robust shape description and recognition by gradient propagation

This paper presents a novel hierarchical shape description scheme based on propagating the gradient of the image. The propagated gradient field collides at centers of convex/concave shape components, which can be detected as points of high directional disparity. A novel vectorial disparity measure called cancelation energy is used to measure this collision of the gradient field, and local maxima of this measure yield feature tokens. These feature tokens form a compact description of shapes and their components and indicate their central location and size. In addition, a gradient signature is formed by the gradient field that collides at each center, which is itself a robust and size-independent description of the corresponding shape component. Experimental results demonstrate that the shape description is robust to distortion, noise and clutter. An important advantage of this scheme is that the feature tokens are obtained pre-attentively, without prior understanding of the image. The hierarchical description is also successfully used for similarity-invariant recognition of 2D shapes with a multi-dimensional indexing scheme based on the gradient signature.

Nonorthogonal image expansion related to optimal template matching in complex images

Abstract Expansion matching (EXM) is a novel method for template matching that optimizes a new similarity measure called discriminative signal-to-noise ratio (DSNR). Since EXM is designed to minimize off-center response, it yields results with very sharp matching peaks. EXM yields superior performance to the widely used correlation matching (also known as matched filtering), especially in conditions of noise, superposition, and severe occlusion. This paper presents an extended EXM formulation that matches multiple templates in the complex image domain. Complex template matching is useful in matching frequency domain templates and edge gradient images, and can be extended to multispectral images as well. Here, a single filter is designed to simultaneously match a set of given complex templates with optimal DSNR, while eliciting user-defined center responses for each template. It is shown that when the complex case is simplified to the case of matching a single real template, the result reduces exactly to the minimum squared error (MSE) restoration filter assuming the template as the blurring function. Here, we introduce a new generalized MSE restoration paradigm based on the analogy to multiple-template EXM. Furthermore, the output of the single-template EXM filter is also shown to be equivalent to a nonorthogonal expansion of the image with basis functions that are all shifted versions of the template. Experimental results prove that EXM is robust to minor rotation and scale distortions.

A generalized expansion matching based feature extractor

A novel and efficient generalized feature extraction method is presented based on the expansion matching (EXM) method and the Karhunen-Loueve (KL) transform. The EXM method is used to design optimal detectors for different features. The KL representation is used to define an optimal basis for representing these EXM feature detectors with minimum truncation error. Input images are then analyzed with the resulting KL basis set. The KL coefficients obtained from the analysis are used to efficiently reconstruct the response due to any combination of feature detectors. The method is applied to real images and successfully extracts a variety of arc and edge features as well as complex junction features formed by combining two or more arc or line features.

On the use of the Karhunen-Loeve transform and expansion matching for generalized feature detection

A novel generalized feature extraction method based on the expansion matching (EXM) method and the Karhunen-Loeve (KL) transform is presented. This yields an efficient method to locate a large variety of features with a single pass of parallel filtering operations. The EXM method is used to design optimal detectors for different features. The KL representation is used to define an optimal basis for representing these EXM feature detectors with minimum truncation error. Input images are then analyzed with the resulting KL bases. The KL coefficients obtained from the analysis are used to efficiently reconstruct the response due to any combination of feature detectors. The method is successfully applied to real images and extracts a variety of arc and edge features as well as more complex junction features formed by combining two or more arcs or line features.

Optimal DSNR detector for ramp edges

In practical images, ideal step edges are actually transformed into exponential ramp edges, due to the general low pass filtering nature of imaging systems. This paper discusses the application of a newly developed expansion matching method for optimal ramp edge detection. Expansion matching optimizes a novel matching criterion called discriminative signal to noise ratio (DSNR). The DSNR criterion represents the desirable qualities of a sharp matching response with good localization and minimal off-center response. These requirements are consistent with the three criteria of signal-to-noise ratio, localization, and multiple response suppression used by Canny (1986) and others for optimal edge detection. We compare the optimal ramp edge detector based on DSNR with the ramp edge detector derived from Cannys criteria. We show that our ramp edge detector performs better than the ramp detector obtained from Cannys criteria in terms of DSNR and is relatively easier to derive for various amounts of noise and slopes.