Position Invariant Spline Curve Based Image Retrieval Using Control Points

Abstract

In this paper Cubic Bezier curve-based image retrieval system is proposed. This system evaluates similarity of each image in its database to a query image in terms of shape characteristics. Then, returns those images within a desired range of similarity. The proposed system determines nonlinear relationship between image's features for more accurate similarity comparison between query image and existing database images. Among existing approaches to shape feature analysis, statistical approach to extract shape features is adopted here. It works in form of control points of spline curves from both given query image and images of available database. These control points are further used to find out the Fourier Descriptors. Control points and Fourier descriptors are used for image retrieval in proposed system. With the vast number of images available on-line, quality CBIR systems are critical. The performance and results obtained by proposed system are compared to other CBIR systems. Comparison reveals proposed system performance is state of the art. In many parameters it outperforms other CBIR systems.

Bezier Curve Based Medicinal Leaf Classification using Capsule Network

“…Then determining pointwise RMS error E occurred in approximation where E is the sum of distances between consecutive approximated and actual Bezier curve points. Hence modified two-stage learning algorithm presented below is used to find CPs [30]. Assuming N is the total number points of the Cubic Bezier curve along the shape boundary.…”

“…b) Presumption of 2nd and 3rd CPs Firstly, positions of second and third CPs, are approximated on the tangents to the given curve. CPs lie at vertical distance of H from the base line [29,30]. Here, H may take one of the 3h/4, h, 4h/3, and 1.6h values.…”

“…To recover the CPs, the intermediate CPs are translated along four directions, one at a time (x ± x, y), (x, y ± y). If the minimum E 1 is obtained at the position (x, y), the CPs are not further translated rather the step size  for the distance of translation  is brought down to half [30,32]. These iterations are carried until E 1 goes down some allowable (in this approach, 0.000001) value or the learning iteration goes more than the permitted value (in this approach, 90).…”

“…The above algorithm gives us CPs for a Bezier (see Figure 5). These CPs are further considered for feature generation like FD [30].…”

“…The Discrete Fourier Transform (DFT) is applied on the shape signature that generates coefficients identified as optimal feature vector that is FD of the shape. They are frequency domain representation of the shape [30]. Let r(t), t = 0, 1, …, M-1, be the given normalized shape signature to M points in the sampling stage, the DFT of r(t) is given by:…”