Robust time-frequency model estimation in otolith images for fish age and growth analysis

We present a robust method for time-frequency model estimation. It involves a robust Leclerc’s estimator to ensure robustness w.r.t. noise and interferences present in timefrequency representations. This scheme is applied to fish age and growth analysis from otolith images. This application involves the estimation of the parameters of a priori fish growth models using this robust time-frequency analysis. We present a quantitative experimental validation over a large set of real images of Plaice otoliths. 1. PROBLEM STATEMENT Fish age and growth estimation is of key importance for marine living resources assessment and ecology applications. It mainly relies on the analysis of calcified structures, such as fish otoliths. Otolith images, as depicted by Fig.1 for a Plaice, are composed of successive concentric dark and light rings. Fish age is determined by counting these rings, whereas fish growth analysis consists in measuring the evolution of the distances between the successive rings. These tasks are routinely achieved by human readers, but they are extremely tedious for large sets of otoliths (typically, several thousands of otoliths a year) and depend on reader’s subjectivity. Different studies have already investigated computer vision techniques to develop automatic or semi-automatic tools for fish ageing issues from otolith images [3, 4]. Mainly, proposed approaches exploit either peak and valley detection on 1D radial signals taken from the nucleus to the edge of the otolith [4], or 2D techniques (such as deformable models [3]) exploiting ring continuity. In both cases, a knowledge of the fish otolith growth pattern would greatly ease ring detection, as highlighted by [4] using a priori growth models. In this paper, we propose a framework for the direct estimation of the otolith growth pattern from a two-dimensional time-frequency analysis [6] of 1D otolith image radials. More Precisely, given an image otolith such as in Fig.1.a, we extract a radial from the nucleus to the edge of the otolith. As 0 100 200 300 400 500 600 50 100 150 200 Length l G ra y le ve l s ig na l x a b Fig. 1. Example of a Plaice otolith: a) image of a Plaice otolith annual rings present on a plaice otolith displaying seasonal white and dark rings, b) gray level plot along an image radial taken from the nucleus to the edge of the Plaice otolith. displayed in Fig.1.b, the resulting gray level 1D signal involves oscillations corresponding to the successive growth rings. In fact, the growth pattern can be viewed as the frequency modulation of this real biological signal. Growth demodulation will then lead to a simple periodic signal, the period of which is given by the temporal period of ring appearance (e.g., one year in our case for the Plaice). Timefrequency analysis [6] is well-suited to process this category of non-stationary signal. Given a 1D time signal, it basically results in a two-dimensional time-frequency representation of signal content, which indicates signal frequencies at each time instant. Based on a priori growth modeling, we directly achieve the estimation of the parameters of the growth model from the two-dimensional time-frequency weight map within a robust framework. Robust estimation [7] is of key importance in our case due to to the low quality of the computed time-frequency representation, as highlighted by Fig.2. This paper is organized as follows. Section 2 presents the use of time-frequency analysis for growth demodulation. We present the framework for robust growth model estimation in the time-frequency representation in Section 3. Section 4 presents the experimental evaluation of our approach on a set of real Plaice otolith images, and concluding remarks are given in Section 5. 2. GROWTH MODULATION AND TIME FREQUENCY ANALYSIS 2.1. Growth modulation Given an otolith image, we extract a radial from the nucleus to the edge of the otolith. The resulting 1D signal represents the evolution of the gray level as a function of the distance along the considered radial, as illustrated by Fig.1. We denote this signal , where is the length computed from the nucleus taken within the interval with the radial length. As in [4], this radial gray level profile is extracted in a robust manner to reduce the noise level. In addition, to get rid of the long-term tendency due to lighting conditions, we apply a low-pass filter. Let us denote by the resulting signal. Since the biological ring signal underlying is known to be one-year periodic, is expressed as the result of the growth modulation : "! #%$& ')( * "! #%$+ ')( (1) where time instant is simply related to growth modulation by: , . Our goal is then to determine this growth modulation, from which we will directly deduce the growth pattern . 0/21) . 2.2. Time-frequency representations Due to the non-stationarity of the processed signal , Fourier analysis will only allow to evaluate its frequency content, but not to track these frequency components w.r.t. length . On the contrary, bilinear transforms used for time-frequency analysis [6] provide a well-suited tool to visualize both signal frequency components and their temporal localization from a two-dimensional time-frequency weight map. We will focus on the transforms of Cohen’s class. The reader should note that length variable plays a role similar to time in more standard signal applications, whereas the time notion here refers to the one-year periodic biological signal. Thus, the time-frequency analysis we will achieve should be viewed as a length-spatial frequency analysis. We will in particular use the Wigner-Ville transform, from which all bilinear transforms of Cohen’s group can be deduced. For given length and frequency